The sounds of the Little and Big Bangs

Studies of heavy ion collisions have discovered that tiny fireballs of new phase of matter -- quark gluon plasma (QGP) -- undergoes explosion, called the Little Bang. In spite of its small size, it is not only well described by hydrodynamics, but even small perturbations on top of the explosion turned to be well described by hydrodynamical sound modes. The cosmological Big Bang also went through phase transitions, the QCD and electroweak ones, which are expected to produce sounds as well. We discuss their subsequent evolution and hypothetical inverse acoustic cascade, amplifying the amplitude. Ultimately, collision of two sound waves leads to formation of gravity waves, with the smallest wavelength. We briefly discuss how those can be detected.


. INTRODUCTION
A. An outline This paper is a short review describing some recent developments in two very different fields, united by some common physics but being at very different stages of their develoment.
One of them is Heavy Ion Collisions, creating the Little Bangs mentioned in the title.In an explosion, lasting in a small volume for very short time, they recreate the hottest matter created in the laboratory -known as Quark-Gluon Plasma (QGP)-which was not present in Universe since the early stages of its cosmological evolution, the Big Bang.QGP turned out to be rather unusual fluid, and we will briefly discuss why we believe it is the case.But the common topic which holds two parts of this paper together are the sounds, mentioned in the title.As always, those are small amplitude perturbations of hydrodynamical nature.Not unusual by themselves, they still surprised us, since nobody expected them to be experimentally detected in a system as small as the Little Bangs.The latest developments has shown that in fact they are to certain extent present even is smaller systems, such as central proton-nuclei collisions and even in proton-proton collisions, in events with unusually high multiplcity.
In cosmological settings sound perturbations have been rather well studied, using perturbations of the Cosmic Microwave Background (CMB), and, to some extent, correlation functions of Galaxies.However, those correspond to relatively late stage of the Universe, at which the temperature is low enough for matter to get de-ionized, with the temperature T < 1 eV .We will touch these phenomena only peripherally, because of certain similarities to sounds in the Little Bang.The main question we will be discussing in the second part of the paper is the title of section II: Are cosmological phase transitions observable?Transitions are in plural because we mean here both the electroweak transition, at T c ∼ 100 T eV and the QCD phase transitions at T c ∼ 160 M eV .We hope the answer is affirmative, but one still has to figure out how it can be done.
A specific scenario we will discuss is a possibility of inverse acoustic cascade, which can carry sounds, from the UV end of the spectra, with momenta p ∼ πT ∼ 1 GeV , (for QCD) and ∼ 1 T eV for electroweak transition, to the IR end of the spectra provided by the cosmological horizon at the corresponding times.If such cascade is there, it works like an powerful acoustic amplifier.At the end of the process, two sound waves can be converted into a gravity wave, which survive all the later eras and can be potentially detectable today.

I. THE LITTLE BANG
A. The quest for Quark-Gluon Plasma Aiming at non-experts, we start with motivations and brief history of the field.What was the reasons to study high energy Heavy Ion Collisions?What has been found, and why it is rather different from what is observed in high energy pp collisions?
There are three different (but of course interrelated) aspects of it.One is the theoretical path, coming from 1970's after the discovery of QCD, first in its perturbative form, and then in a non-perturbative theory.Development of QCD at finite temperature and/or density lead to realization that QGP is a completely new phases of matter.Now work in this direction includes not only certain number of theorists, specializing in QFTs and statistical physics, but also a community performing large scale computer simulations of lattice gauge theories, and rather sophisticated models based on them.This activity also has grown up and includes collaborations of dozens of people.As we will discuss below, QGP is a very peculiar plasma, with rather unusual kinetic properties.We will discuss one proposed explanation of that, based on the fact that this plasma includes both electric and magnetic charges, The second (and now perhaps the dominant) aspect of the quest for QGP is the experimental one.Let me here just mention that experimental activity is now dominated by five large collaborations: STAR and PHENIX (now under complete rebuilding of the detector) at Relativistic heavy ion collider (RHIC) at Brookhaven National Laboratory, and ALICE,CMS and ATLAS at Large Hadron Collider (LHC) at CERN.The last two have been basically built by high energy physics community and designed for other purposes, but both also work just fine for heavy ion collisions as well, recording thousands of secondaries per event.Each of the collaborations have hundreds of members, so the "Quark Matter" and other conferences on the subject has become huge in size, and obviously dominated by experimental talks.It is completely justifiable, as the list of discoveries -often puzzling or at least unexpected -continues.
We will only focus on data indicating collective flows of QGP, including its perturbations in connection with the sound waves.Of course, there are many different aspects of heavy ion collisions which we will not touch upon in this short text.In particular, we will not discuss dynamics of jet quenching, of heavy flavor quarks/hadrons, large event-by-event fluctuations perhaps indicative to QCD critical point, etc.For a more complete recent review, aimed at experts, see [1].
The third direction to be discussed below is related with certain connections which the QGP physics have with cosmology.Today's cosmology is not just an intellectually challenging field, but it is now among the most rapidly developing parts of physics.And yet, since QGP/electroweak plasma in the early Universe happened at rather early stage, it remains challenging to find any observable trace of its presence.It is even more so for the electroweak plasma, undergoing a phase transition into a "Higgsed" phase we now live in.So, very few people think about, and even those do, turn to it intermittently.
Covering brief history of the QGP physics, let me follow a time-honored tradition of the historians and divide it into three periods called (i) pre-RHIC, (ii) the RHIC era, and (iii) RHIC+LHC era.
The first period was the longest one, it started at mid-1970's and lasted for a quarter of a century, till the year 2000.While there were important experiments addressing heavy ion collisions in fixed target mode, at CERN SPS and Brookhaven AGS accelerators, it is fair to say that in this period the experimental program and the whole community only started to be built.Most talks at the conferences of that era were theory-driven.
Since the start of the RHIC era in 2000, it has become soon apparent that the data on particle spectra show evidences to strong collective flows.Those, especially the quadrupole or elliptic flow, confirm nicely predictions of hydrodynamics.Most successful were hydro codes supplemented by hadronic cascades at freezeout [2][3][4], as they correctly take care of the final (near-freezeout) stage of the collisions.All relevant dependences -as a function of p ⊥ , centrality, particle mass, rapidity and collision energy -were checked and found to be in good agreement.Since the famous 2004 RBRC workshop in Brookhaven, with theory and experiment summaries collected in a special volume, Nucl.Phys.A750 , the statements that QGP "is a near-perfect liquid" which does flow hydrodynamically has been repeated many times since.
The theorists at this point had recognized that QGP in these conditions should be in the special, strongly coupled regime, now called sQGP for short , and hundreds of theoretical papers have been written, developing gauge field dynamics at strong coupling.It was a a very fortunate coincidence, that at the same time (from mid-1990's) string theory community invented a wonderful theoretical tool, the AdS/CFT duality, connecting strongly coupled gauge theories to 5-dimensional weakly coupled variants of supergravity.We will not be able to discuss this direction, as it needs a lot of theoretical background.Let me just mention that it shed an entirely new light on the process of QGP equilibration, which is dual to a process of (5-dimensional) black hole formation.The entropy produced in a Little Bang is nothing else but the information classically lost to outside observers, as some part of a system happen to be inside the "trapped surfaces".
We will also not go into discussion of other strongly coupled systems which has been also addressed by theorists and their similarity to sQGP noticed.Those include a strongly coupled classical QED plasmas at one end , and quantum ultracold atomic gases in their "unitary" regime at the other.These studies focus on unusual kinetic properties, essentially unusually small mean free paths, which such systems display.
The last (and so far the shortest) era started in the year 2010, when the largest instrument of high energy/nuclear physics, LHC at CERN, had joined the quest for QGP.These experiments confirmed what has been learned at RHIC and, due to their highly sophisticated detectors and experience collaboration teams, has added invaluable additions to what we know about its properties.Perhaps the most surprising discovery made at LHC was that QGP and its explosion does not happen only in heavy ion collisions.Central pA and even high multiplicity pp had shown (in my opinion, beyond any reasonable doubt)

B. Thermodynamics and screening masses of QGP
Omitting the "prehistoric" period before QCD was discovered in 1973, we start at the time when QCD was first applied for description of hot/dense matter.At high T the typical momenta of quarks and gluons have scale T , and, due to asymptotic freedom, the coupling is expected to be small so it was promptly suggested be Collins and Perry [5] and others, that the high temperature (and or density) matter should be close to an ideal gas of quarks and gluons.There remained however the following important question: since the asymptotic freedom means that in QCD (unlike in QED and other simpler theories) the charge is anti-screened by virtual one-loop corrections.Will there be screening or anti-screening by thermal quarks and gluons.The calculation of the polarization tensor [6] have shown that unlike the virtual gluon loops which anti-screen the charge, the real in-matter gluons behave more reasonable and screen the charge: therefore this new phase I called Quark-gluon Plasma, QGP for short.This happens at the so called electric scale given by the electric screening (Debye) mass The second statement, found from the same polarization tensor [6], tells us that in the perturbation theory static magnetic fields are not screened.First re-summation of the so called ring diagrams produced a finite plasmon term [6,7], but higher order diagrams are still infrared divergent.In general, infrared divergences and other non-perturbative phenomena survive in the magnetic sector, even at very high T .
Jumping over decades of work, let us discuss the values of the electric and magnetic screening masses extracted from various approaches of today.Those are listed in Table 1, including predictions from various strong coupling approaches: the first line corresponds to a (large N c ) holographic model, the next two to lattice (the last with small physical quark masses), and the last to the dimensionally reduced 3D effective theory for N f = 3 light quarks.Looking at this Table, one finds that the electric mass is not much smaller than the temperature: instead M E /T > 1.This means the coupling is not small and pQCD is not applicable.Second important observation: while the magnetic mass is still smaller than the electric one, it is smaller only by a factor of 2 or so.This means magnetic charges play a significant role, comparable to that of its electrically charged quasiparticles, quarks and gluons.Below we will discuss the role of magnetically charged quasiparticles, the monopoles, which are believed to play an important role in QGP dynamics.Let us end this section with brief summary of the QCD thermodynamics on the lattice, a numerical way to calculate the thermodynamical observables from the first principles.the QCD Lagrangian, using numerical simulations of he gauge and quark fields discretized on a 4-dimensional lattice in Euclidean time.For a recent review see e.g.[12], from which we took Fig. 1.The quantities plotted are the pressure p, the energy density and the entropy density s.
Strong but smooth rise of all quantities plotted indicate smooth but radical phase transition, from the curves marked HRG (hadron resonance gas).The first thing to note is that quantities plotted are all normalized to corresponding powers of the temperature given by its dimension: so at high T the QGP becomes approximately scale-invariant, corresponding to T -independent constants at the r.h.s. of the plot.The second thing to note is that these constants seem to be lower than the dashed line at high temperatures, corresponding to a non-interacting quark-gluon gas.Interesting that the value for infinitely strongly interacting supersymmetric plasma is predicted to be 3/4 of this non-interacting value, which is not far from the values observed.
Temperature range scanned in heavy ion experiments has been selected to include the QCD phase transition.The matter produced at RHIC/LHC has the initial temperature T ≈ 2T c , and the final one, at the kinetic freezeouts of the largest systems, is low as T ≈ 0.5T c .While this happened more or less due to accidental factors -like the size of the tunnels used for RHIC and LHC construction, and the magnetic field in superconducting magnets available -it could not be better suited for studies of the near-T c phenomena.

C. sQGP as the most perfect fluid
One may think, in retrospect, that development of the working model of the Little Bang was a rather straightforward task: all one needed to do was to plug the QGP equation of state into the equations of relativistic hydrodynamics, and solve it with the appropriate initial conditions.This was indeed so, modulo some complications.Some of them were at the freezeout stage, solved via switching to hadronic cascades at the hadronic phase T < T c .Some of them were at the initial stage, such as to define the exact "almond-shaped" fireball, created at the overlap of two colliding nuclei, separated by the impact parameter b.
The main difficulty on the way was psychological: it was completely unclear if the macroscopic approach has any chance to work.Most theorist were very skeptical.Also, among firmly known facts known prior to RHIC experiments, was that for the "minimally biased" (typical) pp collisions it did not worked.Indeed, no collective effects -signals of H.-T. Ding, F. Karsch and S. Mukherjee s allows to reconstruct the energy density as well as the entropy density s/T 3 = P )/T 4 .he determination of thermodynamic quantities in QCD is a parameter free ulation.All input parameters needed in the calculation, e.g. the quark masses = m d , m s ) and the relation between the lattice cut-o↵, a, and the bare gauge ling, = 6/g 2 , are determined through calculations at zero temperature.Like-, there is only a single independent thermodynamic observable that is calculated lattice QCD calculation, for instance the trace anomaly, ⇥ µµ (T ).All other bulk modynamic observables are obtained from ⇥ µµ (T ) through standard thermoamic relations.In Fig. 10 (left) we show recent results for the trace anomaly 2+1)-flavor QCD 113,114 obtained with two di↵erent discretization schemes by di↵erent groups.The results are extrapolated to the continuum limit and are ined with a strange quark mass tuned to its physical value and light quark ses that di↵er slightly (m s /m l = 27 113 and 20 114 ).The right hand panel in this re shows results for the pressure, energy density and entropy density obtained the trace anomaly by using Eqs.39 and 40.lso shown in Fig. 10   the flows -were observed.And the change from one proton to nuclei is not numerically large, since even the heaviest nuclei are not that large.
The particular observable most watched was the so called "elliptic flow" (see Appendix A for definition) induced by geometry of the system: at nonzero impact parameter it is an almond-shaped in the transverse plane.Parton cascade models predicted that partons traveling along the longer side of the almond will create more secondaries, so they predicted small and negative v 2 .Hydrodynamics, on the other hand, predicted higher pressure gradient along the shorter side of the almond, and thus larger and positive v 2 .The very first data from RHIC decided the argument: predictions of hydro+cascade models were confirmed, as a function of transverse momentum, centrality, particle type etc.The present day hydro+cascade models do it on event-by-event basis, starting from certain ensemble of initial state configurations.They do excellent job in describing the RHIC/LHC data, see e.g.s [13] for review.

D. Sounds in the Little Bang
After the average pattern of the fireball explosion has been firmly established, by 2004 or so, the next goal was to study fluctuations, or deviations from it on event-by-event basis.
According to hydrodynamics, any small perturbation of a flow can be described in terms of elementary excited modes of the media.Those are longitudinal sound waves and transverse "diffusive" mode, also associated with vorticity.So far we only have evidences for the former ones, the subject of this section.
Before we proceed, let me add the following comment.An existence of sound in various media is a well known fact (e.g.we use sound in air for communication), and their finding in a QGP fireball may not look at first glance very exciting.Note however, that we speak of fireballs of a size of atomic nuclei, only 10 f m or so across, containing say ∼ 10 3 particles.Taking a cubic root, one realizes that it is just 10 × 10 × 10 particles.Most theorists could not believe, prior to RHIC experiments, that such small system can show any collective hydro effects at all.To observe sounds inside this tiny fireball is really a triumph, brought both by luck (a very unusual fluid, sQGP) as well as huge statistical power of LHC detectors.It would not be possible for any gas or drop of water, for such a small system.
Let me now explain the physics of it using analogy with waves on the sea.Suppose somewhere near Japan there is an Earthquake, producing tsunami wave across Pacific.Suppose we can only observe its consequences from very large distances, say from the coast of America.It can still be done by a correlation of small signals, like it is done for now famous detection of gravity waves.Say, there are two detectors, in Canada and somewhere in Chile.By correlating their signals, shifted by the appropriate amount of time needed for the wave to come there, one may be able to extract the correlation of sea waves and tell it from a random noise.
This proposition may look as an unlikely scenario: but, as we will see shortly, RHIC/LHC experiments do observe correlated of emission of secondaries, separated by an angle of about 120 degrees (nearly opposite sides of the fireball).What one needs for that is large number of events, to get rid statistically of the random noise .Not going into detail, consider few relevant numbers.Typically, there are about 10 9 events, each with the multiplicity ∼ 10 3 .So the number of pairs of secondaries is about ∼ 10 2 * 3+9 , a huge number.In fact, correlations of not just two, but also 4 and 6 secondaries have been measured.It is enough to detect even rather weak perturbations of the fireball.
Theoretical evaluation of these correlations proceed in two stages.At first, it was done by a Green function method, with a delta-function like source and linearized equation (riding on top of the average explosion, of course).One group was myself and my student Pilar Staig, another lead by Ollitrault and the Brasilian group (Kodama, Grassi et al).It's high point was at Annecy Quark Matter conference of 2011, in which these theory prediction for the shape of the correlation function and the relevant data were shown, basically one after another.Their good agreement was rather shocking, even for experienced physicists.Then the Brasilian group pioneered the so called event − by − event hydro, performed for an ensemble of certain "realistic" initial conditions.This approach now became a mainstream industry, with several group developing it further, and finding, with satisfaction, that it works spectacularly.Several angular moments of the flow perturbation as a function of transverse momentum, particle type and centrality v n (p t , m, N p) are reproduced.
The calculations typically start from initial state, which includes geometrical shape important for elliptic flow (harmonics n = 2) and random perturbations created by particular locations of the nucleons and their relative impact parameters in the collision.The role of geometry reduces toward the central collisions.
The dependence on the harmonics amplitude on their number (n) are basically independent on n.What that tells us is that statistically independent "elementary perturbations" have small angular size δφ 2π, so we basically deal with a "white noise", an angular Fourier transform of the delta function.Their magnitude depends on the number of statistically independent "cells" in the transverse plane, and this tells us what the centrality dependence of the effects should be.Models of the initial state give us not only the r.m.s.amplitudes, but also their distribution and even correlations.Remarkably, the experimentally observed distributions over flow harmonics v n directly reflect those distributions P ( n ).That means hydrodynamics does not generate any noise by itself.
There is a qualitative difference between the main (called radial) flow and other angular harmonics.While the former is driven by the sign-definite outward pressure gradient, and thus monotonously grows with time, the higher angular harmonics are basically sounds, and thus they behave as some damped oscillators.Therefore the signal observed should, on general grounds, be the product of the two factors: (i) the amplitude reduction due to losses, or viscous damping , and (ii) the phase factor depending on the oscillation phases φ f reezeout , at the so called system freezeout.time.
Let us start with the "acoustic systematics" which includes the viscous damping factor only.It provides good qualitative account of the data and hydro calculations into a simple expression, reproducing dependence on the viscosity value η, the size of the system R and the harmonic number n in question.Let us motivate it as follows.The micro scale is the particle mean free path, and the macro scale is the system size.Their ratio can be defined with the viscosity-to-entropy-density dimensionless ratio The main effect of viscosity on sounds is the damping of their amplitudes.The expression for that [14] is Since the scaling of the freeze out time is linear in R or t f ∼ R, and the wave vector k corresponds to the fireball circumference which is m times the wavelength the expression (5) yields Thus the viscous damping is exponential of the product of two factors, η/s and 1/T R, each of them small, times the harmonics number squared.Extensive comparison of this expression with the AA data, from central to peripheral, has been done in Ref. [15]: all its conclusions are indeed observed.So, the acoustic damping provides the correct systematics of the harmonic strength.This increases our confidence that -in spite of somewhat different geometrythe perturbations observed are actually just a form of a sound waves.
For central PbPb LHC collisions with both small factors ∼ (1/10), their product is O(10 −2 ).So one can immediately see from this expression why harmonics up to m = O(10) can be observed.The highest harmonics really observed is actually m = 6.Proceeding to smaller systems, by keeping a similar initial temperature T i ∼ 400 M eV ∼ 1/(0.5 f m) but a smaller size R, results in a macro-to-micro parameter that is no longer small, 1/T R ∼ 1, respectively.For a usual liquid/gas, with η/s 1, there would not be any small parameter left and one would have to conclude that hydrodynamics be inapplicable.However, since the quark-gluon plasma is an exceptionally good fluid with a very small η/s, one can still observe harmonics up to m = 3, even for the small systems.Now, if one would like to do actual hydrodynamical calculation, rather than a simple damping evaluation by a "pocket formula" just discussed, the problem appears very complicated.Indeed, the events have multiple shapes, describe by multidimensional probability function P ( 2 , 3 ...).Except that it is not.All those shapes are however just a statistical superposition of relatively simply phenomenon, a somewhat distorted analog of an expanding circle from a stone thrown into the pond.
Since columns of nucleons sitting at different locations of the transverse plane cannot possibly know about each other fluctuations at the collision moment, they must be statistically independent.A "hydrogen atom" of the problem is just one bump, of the size of a nucleon, on top of a smooth average fireball, and all one has to do to reproduce the correlation function is to calculate the Green function of the linearized hydrodynamical equation.A particular model of the initial state expressing locality and statistical independence of "bumps" has been formulated in [16]: the correlator of fluctuations is given by the simple local expression In order to calculate perturbation at later time one needs to calculate the Green function G(x, y), from the original location x to the observation point y.It has been done by (my student) P.Staig and myself [17] analytically, since for Gubser flow one can show that in co-moving coordinates all four of them can be separated.Not going into details of this excersize, let me just note that that analytic calculation included viscosity.The predicted correlation function of two secondaries in central collision, as a function of relative azimuthal angle, is shown in Fig. 2(a).The central feature is that there is one central peak, at δφ = 0, and two more peaks, at δφ = ±2 radian.Their origin is simple and can be easily understood as soon as it is recognized that the main perturbation at freezeout is located at the intercept of the "sound circle" and the fireball edge.Projected onto the transverse plane both are circles, of comparable size, so the intercepts are just two points.The peak at δφ = 0 appears when both observed secondaries come from the same point: the radial flow thus carry them in the same direction.The peaks at δφ = ±2 rad corresponding to one particle coming from one intercept, and the other at the other.The particular angle -about 1/3 of the circleappears because the sound horizon radius R h = c s τ f reezeout happens to be numerically close to the fireball radius.As expected its area is about twice that of the other peaks.
This calculation has been presented at the first day of Annecy Quark Matter bef ore the experimental data.The ATLAS correlation function (for "super-central bin", with the fraction of the total cross section 0-1%) presented a bit later is shown in Fig. 2(b).The agreement of the shape is not perfect -because a model is with conformal QGP and a bit different shape -but all elements of its shape are there.

E. Relation to the sounds of Big Bang
Unlike sounds to be discussed at the end of this paper, here we consider sounds propagating in Universe at much later time, when the primordial plasma gets neutralized into atoms.The corresponding temperature was of the order of an electron-Volt, 12 orders lower than in electroweak and 9 orders lower than in QCD phase transitions.It is at this stage of Big Bang at which photons which we now see as cosmic microwave background radiation were emitted.These sounds lead to famous deviations of the background radiation temperature, of magnitude 10 −5 , from the mean T of the Universe.The data by Planck collaboration on their angular harmonics power spectrum (distributed over the sky θ, φ angles) of these perturbations are shown in Fig. 3.
They show a dissipation toward higher harmonics, modulated by a number of the so called "acoustic peaks".Their explanation is as follows: since all harmonics start at the same time by Big Bang -hydro velocities at time zero are assumed zero for all harmonics -and get frozen at the same time as well, they have exactly the same propagation time.Their oscillation phases are however all different because different harmonics have different oscillation frequencies.Those with larger n rotate more rapidly -the frequency is ∼ n.Binary correlator is proportional to cos 2 (φ n f reezout ) and harmonics with the optimal phases close to π/2 or 3π/2 etc show maxima, maxima in between.quency combination are shown in Fig. 11, and compared to spectra derived from the 70 GHz and 353 GHz Planck maps.We use the likelihood to estimate six ⇤CDM cosmological parameters, together with a set of 14 nuisance parameters (11 foreground parameters, two relative calibration para-meters, and one beam error parameter 7 , described in Sect.3. Tables 5 and 6 summarize these parameters and the associated priors 8 .Apart from the beam eigenmode amplitude and calibration factors, we adopt uniform priors.To map out the corresponding posterior distributions we use the methods described in Planck Collaboration XVI (2013), and the resulting marginal distributions are shown in Fig. 12.Note that on the parameters A tSZ , A kSZ and A CIB 143 we are using larger prior ranges as compared to Planck Collaboration XVI (2013).
Figure 12 shows the strong constraining power of the Planck data, but also highlights some of the deficiencies of a 'Planck -alone' analysis.The thermal SZ amplitude provides a good example; the distribution is broad, and the 'best fit' value is ex-FIG.3. Power spectrum of cosmic microwave background radiation measured by Planck collaboration [20].
At this point the curious reader would probably ask, if the power spectrum of harmonics do show similar oscillations for the Little Bang as well?In fact in our hydro calculation we do see them in hydro calculations described above: with the peak around m = 3 and the next at m = 9, with the minimum predicted to be around m = 7, see Fig. 4(a).More recent sophisticated event-by-event hydro calculation by Rose et al [18] does not reproduce oscillations around the smooth sound damping trend, see Fig. 4(b).One may think that averaging over many bumps in multiple configurations may indeed average out the freeze out phase factor.Yet the ultra-central data one can still see clear deviation from the damping curve ∼ exp(−n 2 * const).In particular, the third harmonics is more robust than the second v 3 > v 2 , while v 6 is lower than the curve.The point at m = 9 is a one-sigma effect, not a statistically significant observation.
Let me conclude this discussion with a statement, that unlike in the Big Bang, for the Little one we only have certain hints for an oscillatory deviations from the "acoustic systematics".At this time one cannot claim that such oscillation do exist, and even if so, that they agree or not with the theory.

F. The smallest drops of QGP have sounds as well
In the chapters above we have described successes of hydrodynamics for description of the flow harmonics, resulting from sound waves generated by the initial state perturbations.We also emphasised the debate about the initial out-of-equilibrium stage of the collisions, and a significant gap which still exists between approaches based on weak and strong couplings, in respect to equilibration time and matter viscosity.Needless to say, the key to all those issues m , based on a Green function from a point source [17] for four values of viscosety 4πη/s =0,1,1.68,2(top to bottom at the right).The closed circles are the Atlas data for the ultra-central bin.(b) vn{2} plotted vs n 2 .Blue closed circles are calculation of via viscous even-by-event hydrodynamics [18], "IP Glasma+Music", with η/s = 0.14.The straight line, shown to guide the eye, demonstrate that "acoustic systematics" does in fact describe the results of this heavy calculation quite accurately.The CMS data for the 0-1% centrality bin, shown by the red squares, in fact display larger deviations, perhaps an oscillatory ones.
should be found in experimentations with systems smaller than central AA collisions.They should eventually should the limits of hydrodynamics and reveal what exactly happen in this hotly disputed "the first 1 fm/c" of the collisions.
Let us start this discussion with another look at the flow harmonics.What spatial scale corresponds to the highest n of the v n observed, and does that shed light on the equilibration issue?Here one should split discussion of sounds moving so to say in φ direction, along the fireball surf ace, and those along the radius.
A successful description of the n-th harmonics along the fireball surf ace implies that hydro still works at a scale 2πR/n: taken the nuclear radius R ∼ 6 f m and the largest harmonic studied in hydro n = 6 one concludes that this scale is still few fm.So, it is still large enough, and it is impossible to tell the difference between the initial states of the Glauber model (operating with nucleons) from those generated by parton or glasma-based models (operating on quark-gluon level) .And indeed, as we argued in detail above, we don't see harmonics with larger n simply because of current statistical limitations of the data sample.Higher harmonics suffer stronger viscous damping, during the long time to freezeout.In short, non-observation of v n , n > 6 does not reveal the limits of hydrodynamics.
Obviously, one can observe smaller and smaller systems, e.g.CuCu and lighter nuclei, and see what happens to flow harmonics.Note that in such case the time to freeze out is shorter, and n larger, so one may hope to understand the sound damping phenomena more systematically.Monitoring of the collective phenomena in them would be extremely valuable for answering those questions.However, it is not how the actual development went.Unexpectedly harmonic flows were found in very small systems -pp and pA collisions, with certain high multiplicity trigger.
Before we go into details, let us try to see how large those systems really are.At freezeout the size can be directly measured, using femtoscopy method.(Brief history: so called Hanbury-Brown-Twiss (HBT) radii.This interferometry method came from radio astronomy.The influence of Bose symmetrization of the wave function of the observed mesons in particle physics was first emphasized by Goldhaber et al [22] and applied to proton-antiproton annihilation.Its use for the determination of the size/duration of the particle production processes had been proposed by Kopylov and Podgoretsky [23] and myself [24].With the advent of heavy ion collisions this "femtoscopy" technique had grew into a large industry.Early applications for RHIC heavy ion collisions were in certain tension with the hydrodynamical models, although this issue was later resolved [25].) The corresponding data are shown in Fig. 5, which combines the traditional 2-pion and more novel 3-pion correlation functions of identical pions.An overall growth of the freezeout size with multiplicity, roughly as < N ch > 1/3 , is expected already from the simplest picture, in which the freezeout density is some universal constant.For AA collisions this simple idea roughly works: 3 orders of magnitude of the growth in multiplicity correspond to one order of magnitude growth of the size.
Yet the pp, pA data apparently fall on a different line, with significantly smaller radii, even if compared to the peripheral AA collisions at the same multiplicity.Why do those systems get frozen at higher density, than those produced in AA?To understand why can it be the case one should recall the freezeout condition: "the collision rate becomes comparable to the expansion rate" J.F. Grosse-Oetringhaus / Nuclear Physics A 931 (2014) 22-31 . 6. Left panel: Proton to φ ratio as a function of p T for different Pb-Pb centrality classes [47].Right panel: Femtopic radii extracted from two-and three-pion cumulants together with the associated λ parameters [50].
ape is driven by radial flow.Combining this finding with that for the v 2 suggests that the mass nd not the number of constituent quarks) drives v 2 and spectra in central Pb-Pb collisions for < 4 GeV/c.It is interesting to note that also in p-Pb collisions the shape of the p T spectra of and p become more similar for high-multiplicity events [3]. .

Identified-particle spectra
The ALICE Collaboration has presented yields and spectra for 12 particle species (π , K ± , K * , , p, φ, Λ, Ξ , Ω, d, 3 He, 3 Λ H) in up to 3 collision systems (and, for pp collisions, 3 different nter of mass energies).In particular the measurement of the p T and centrality dependence of e d and the nuclei ( 3 He, 3  Λ H) spectra should be pointed out [25].It is interesting to note that the elds of d, 3 He and 3  Λ H are correctly calculated in equilibrium thermal models.Furthermore, the elds of multi-strange baryons have been measured as a function of event multiplicity showing mooth evolution from pp over p-Pb to Pb-Pb collisions for the yield ratios to π or p [2].The ge amount of data allows a stringent comparison to thermal models which describe particle oduction on a statistical basis [49].

. Source sizes
For the first time, femtoscopic radii were extracted with three-pion cumulants [16,50].This proach reduces non-femtoscopic effects contributing to the extracted radii significantly.Fig. 6 FIG. 5. (From [21]) Alice data on the femtoscopy radii (upper part) and "coherence parameter" (lower part) as a function of multiplicity, for pp, pP b, P bP b collisions.
Higher density means larger l.h.s., and thus we need a larger r.h.s.. So, we see that new "very small Bangs" are in fact more "explosive", with larger expansion rate.We will not go into relevant data and theory, but just state that indeed this conclusion is supported by stronger radial flow in pp, pA high-multiplcity systems, supporting directly what we just learned from the HBT radii.
But how those systems become "more explosive" in the first place?Where is the room for that, people usually ask, given that even the f inal sizes of these objects are small?Well, the only space left is at the beginning: those systems must be born very small indeed, and start accelerating stronger, to generate strong collective flows observed.How it may happen is a puzzle which is now hotly debated in the field.

G. Why is the QGP such an unusual fluid?
Multiple experiments, with heavy ions and "smaller systems" just described above, allowed us to extract the values of kinetic coefficients, such as shear viscosity η.In a kinetic theory it is proportional to mean free path, which is inversely proportional to density of constituents and their transport cross section.The ratio of the entropy density to it is basically the ratio of interparticle separation to the mean free path.It should be small in weak coupling (small cross section), but is in fact much larger than one, see Fig. 6.The density of "electric" (quark and gluon) quasiparticles rapidly decrease as T → T c since they are eliminated by the phenomenon of electric confinement.One might then expect the s/η ratio to decrease as well, but in fact (see Fig. 6) s/η has instead a peak there.This peak correlates with similar peaks claimed for two more kinetic parameters, the heavy quark diffusion constant and the jet quenching parameter q.As we have already mentioned in the introduction, Xu, C. Greiner and Stöcker [8] have suggested an alternative explanation for small QGP viscosity, namely the next-order radiative processes, gg $ ggg.Using perturbative matrix elements and ↵ s = 0.3..0.6, they found ⌘/s several times smaller than for the gg $ gg process, close to what we get from the gm scattering.Obviously, both mechanisms, albeit having such di↵erent origin, would thus be su cient to explain the well-known hydrodynamic results for radial and elliptic flow at RHIC.
It will require much more work to see how both results will change, when further refinements are performed.We have discussed those for monopoles above: let us now mention a few questions for gg $ ggg : (i) Xu et al used near-massless perturbative gluons: while in RHIC-LHC range the lattice quasiparticle masses are instead much larger than T , about 3T or so.This would suppress emission of extra gluons.(ii) in RHIC-LHC range one should include the suppression by the Polyakov VEV hLi for any gluon e↵ects (see Fig. 1 (iii) Inclusion of higher order corrections in badly divergent perturbative series needs further studies.As shown years ago in [46], similarly treated processes gg !ng with larger n = 4, ... lead to even larger rates!The development of convergent series for ⌘/s itself still remains to be an open challanging problem.
Acknowledgements We thank Jinfeng Liao and Alfred Goldhaber for multiple useful discussions, as well as Ernst-Michael Ilgenfritz and Massimo D'Elia, who provided us with unpublished lattice results.The work is partially supported by the US-DOE grants DE-FG02-88ER40388 and DE-FG03-97ER4014.

51
FIG. 6. Left plot: The entropy density to shear viscosity ratio s/η versus the temperature T (GeV ).The upper range of the plot, s/η = 4π corresponds to the value in infinitely strongly coupled N =4 plasma [26].The curve without points on the left corresponds to hadronic/pion rescattering according to chiral perturbation theory [27].The single (red) triangle corresponds to a molecular dynamics study of classical strongly coupled colored plasma [28], the single (black) square corresponds to numerical evaluation on the lattice [29].The single point with the error bar corresponds to the phenomenological value extracted from the data, see text.The series of points connected by a line on the right side correspond to gluon-monopole scattering [30].Right plot: The inverse ratio η/s as a function of the temperature normalized to its critical value T /Tc.The solid line marked gm corresponds to the gluon-monopole scattering [30], same as in the upper plot, the dashed line shows the perturbative gluon-gluon scattering: this line is shown for comparison.
As T decreases, toward the end of the QGP phase at T c , the effective coupling grows, and one need to use some non-perturbative methods rather than Feynman diagrams.Opinions differ on how one should describe matter in this domain.Different schools of thought can be classified as (i) perturbative, (ii) semiclassical; (iii) dual magnetic; and (iv) dual holographic ones.
What can be called "the semiclassical direction" focuses on evaluation of the path integral over the fields using generalization of the saddle point method.The extrema of its integrand are identified and their contributions evaluated.It is so far most developed in quantum mechanical models, for which 2 and even 3-loop corrections have been calculated.In the case of gauge theories extrema are "instantons", complementing perturbative series by terms ∼ exp(−const/g 2 ) times the so called "instanton series" in g 2 .This result in the so called trans-series, which are not only more accurate than perturbative ones, but they are suppose to be free from ambiguities and unphysical imaginary parts, which perturbative and instanton series have separately.
For the finite-temperature applications, plugging logarithmic running of the coupling into such exponential terms one finds some power dependences of the type So, these effects are not important at high T but explode -as inverse powers of T -near T c .In 1980-1990's it has been shown how instanton-induced interaction between light quarks break the chiral symmetries, the U A (1) explicitly and SU (N f ) spontaneously.The latter is understood via collectivization of fermionic zero modes, for a review see [31].Account for non-zero average Polyakov line, or non-zero vacuum expectation value of the zeroth component of the gauge potential < A 0 > require re-defined solitons, in which this gauge field component does not vanish at large distances.Account for this changed instantons into a set of N c instanton constituents, the so called Lee-Li-Kraan-van Baal (LLKvB) instanton-dyons, or instanton-monopoles [32,33].It has been recently shown that those, if dense enough, can naturally generate both confinement and chiral symmetry breaking, see [34,35], for recent review see [36].These works are however too recent to have impact on heavy ion physics, and we will not discuss them here.
(iii) A "dual magnetic" school consists of two distinct approaches.A "puristic" point of view assumes that at the momentum scale of interest the electric coupling is large, α s 1, and therefore there is no hope to progress with the usual "electric" formulation of the gauge theory, and therefore one should proceed with building its "magnetic" formulation, with weak "magnetic coupling" α m = 1/α s 1. Working example of effective magnetic theory of such kind were demonstrated for supersymmetric theories, see e.g.[37].For applications of the dual magnetic model to QCD flux tubes see [38].
A more pragmatic point of view -known as "magnetic scenario" -starts with acknowledgement that both electric and magnetic couplings are close to one, α m ∼ α e ∼ 1.So, neither perturbative/semiclassical nor dual formulation will work quantitatively.Effective masses, couplings and other properties of all coexisting quasiparticles -quarks, gluons and magnetic monopoles -can only be deduced phenomenologically, from the analysis of lattice simulations.We will discuss this scenario below in this section.
(iv) Finally, very popular during the last decade are "holographic dualities", connecting strongly coupled gauge theories to a string theory in the curved space with extra dimensions.As shown by [39], in the limit of the large number of colors, N c → ∞, it is a duality to much simpler -and weakly coupled -theory, a modification of classical gravity.Such duality relates problems we wish to study "holographically" to some problems in general relativity.In particular, the thermally equilibrated QGP at strong coupling is related to certain black hole solutions in 5 dimensions, in which the plasma temperature is identified with the Hawking temperature, and the QGP entropy with the Bekenstein entropy.
Completing this round of comments, we now return to (iii), the approach focused on magnetically charged quasiparticles, and provide more details on its history, basic ideas and results.
Already J.J.Thompson, the discoverer of the electron, noticed that something unusual should happen already for static electric and magnetic charges existing together.While both the electric field E (pointing from the center of the electric charge e) and the magnetic field B (pointing from the center of the magnetic charge g) are static (time independent), the Pointing vector S = [ E × B] indicates that the energy of the electromagnetic field rotates around the line connecting the charges.
A.Poincare went further, allowing one of the charges to move in the field of another.The Lorentz force is proportional to the product of two charges, electric e and magnetic g.The total angular momentum of the system has a Thompson term, also with such product Its conservation leads to unusual consequences: unlike for the usual potential forces, in this case the particle motion is not restricted to the scattering plane, normal to J, but to a different surface, the Poincare cone.
The quantum-mechanical version of this problem, involving a pair of electrically and magnetically charged particles, provides further surprises.The angular momentum of the field mentioned above must take values proportional to with integer or semi-integer coefficient: this leads to famous Dirac quantization condition [40] (where we keep , unlike most other formulae) with an integer n in the r.h.s.Dirac himself derived it differently, arguing that the unavoidable singularities of the gauge potential of the form of the Dirac strings should be pure gauge artifacts and thus invisible.He emphatically noted that this relation was the first suggested reason in theoretical literature for the electric charge quantization.If there be just one monopole in Universe, all electric charges must obey this relation, or electrodynamics gets inconsistent with quantum theory!Many outstanding theorists -Dirac and Tamm among them -wrote papers about a quantum-mechanical version of the quantum-mechanical problem of a monopole in a field of a charge, yet this problem was fully solved only decades later [41,42].It is unfortunate that this beautiful and instructive problem is not -to our knowledge -part of any textbooks on quantum mechanics.The key element was substitution the usual angular harmonics Y l,m (θ, φ) by other functions, which for large l, m replicates the Poincare cone (rather than the scattering plane).
The resurfaced interest to monopoles in 1970s was of course inspired by the discovery of 't Hooft-Polyakov monopole solution [43,44] for Georgi-Glashow model, with an adjoint scalar field complementing the non-Abelian gauge field.Can such monopoles be quasiparticles in QGP?A confinement mechanism conjectured in [45,46] suggested that spinzero monopoles may undergo a Bose-Einstein condensation, provided their density is large enough and the temperature sufficiently low.These ideas, known as the "dual superconductor" model, were strongly supported by lattice studies, in which one can detect monopoles and do see how those make a "magnetic current coil" stabilizing the electric flux tubes.
The monopole story continued at the level of quantum field theories (QFTs), with another fascinating turn.Dirac considered the electric and magnetic charges e, g to be some parameters, defined at large distances from the charges.But in QFTs the charges run as a function of the momentum scale, as prescribed by the renormalization group (RG) flows.So, we came to important realization: in order to keep the Dirac condition valid at all scales, e(Q) and g(Q) must be running in the opposite directions, keeping their product fixed!In QCD-like theories, with the so called asymptotic freedom, the electric coupling is small in UV (large momenta Q and temperature T ) and increases toward the IR (small Q and T ).
How the electric and magnetic RG flows work has been first demonstrated by a great example, the N =2 supersymmetric theory, for which the solution was found by Seiberg and Witten in [37].In this theory the monopoles do exist as particles, with well-defined masses.When the vacuum expectation value (VEV) of the Higgs field is large, there is weak (perturbative) regime for electric particles, gluinoes and gluons.In this limit monopoles are heavy and strongly interacting.However, for certain special values of VEV, they do indeed become light and weakly interacting, while the electric ones -gluons and gluinos -are very heavy and strongly interacting.The corresponding low energy magnetic theory is nothing else but the (supersymmetric version of) QED, and its beta function, as expected, has the opposite sign to that of the electric theory.
Even greater examples are provided by the 4-dimensional conformal theories, such as N =4 super-Yang-Mills.Those theories are electric-magnetic selfdual.This means that monopoles, dressed by all fermions bound to them, form the same supermultiplet as the original fields of the "electric theory".Therefore, the beta function of this theory should be equal to itself with the minus sign!The only solution to that requirement is that the beta function must be identically zero, the is no running of the coupling at all, the theory is conformal.
Completing this brief pedagogical update, let us return to [47] paper, considering properties of a classical plasma, including both electrically and magnetically charged particles.Let us proceed in steps of complexity of the problem, starting from 3 particles: a pair of ±q static electric charges, plus a monopole which can move in their "dipole field".Numerical integration of the equation of motion had showed that the monopole's motion takes place on a curious surface, interpolating two Poincare cones with ends at the two charges: so-to-say, two charges play ping-pong with a monopole, without even moving!Another way to explain it is by noting that an electric dipole is "dual" to a "magnetic bottle", with magnetic coils, invented to keep electrically charged particles inside.
The next example was a cell with 8 alternating static positive and negative charges -modeling a grain of salt.A monopole, which is initially placed inside the cell, has formidable obstacles to get out of it: hundreds of scattering with the corner charges happen before it takes place.The Lorentz force acting on magnetic charge forces it to rotate around the electric field.Closer to the charge the field grows and thus rotation radius decreases, and eventually two particles collide.
Finally, multiple (hundreds) of electric and magnetic particles were considered in [47], moving according to classical equation of motions.It was found that their paths essentially replicate the previous example, with each particle being in a "cage", made by its dual neighbors.These findings provide some explanation of why electric-magnetic plasma has unusually small mean free path and, as a result, an unusually perfect collective behavior.
At the quantum-mechanical level the many-body studies of such plasma are still to be done.So one has to rely on kinetic theory and binary cross sections.Those for gluon-monopole scattering were calculated in [30].It was found that gluon-monopole scattering dominates over the gluon-gluon one, as far as transport cross sections are concerned.and produce values of the viscosity quite comparable with that is observed in sQGP experimentally, as was already shown in Fig. 6 .What is also worth noting, it does predict a maximum of this ratio at T = T c , reflecting the behavior of the density of monopoles.
Returning to QCD-like theories which do not have powerful extended supersymmetries which would prevent any phase transitions and guarantee smooth transition from UV to IR, one finds transition to confining and chirally broken phases.Those have certain quantum condensates which divert the RG flow to hadronic phase at T < T c .Therefore the duality argument must hold at least in the plasma phase, at T > T c .We can follow the duality argument and the Dirac condition only half way, till e 2 /4π c ∼ g 2 /4π c ∼ 1.This is a plasma of coexisting electric quasiparticles and magnetic monopoles.
One can summarize the picture of the so called "magnetic scenario" by a schematic plot shown in Fig. 7, from [47].At the top -the high T domain -and at the right -the high density domain -one finds weakly coupled or "electrically dominated" regimes, or wQGP.On the contrary, near the origin of the plot, in vacuum, the electric fields are, subdominant and confined into the flux tubes.The vacuum is filled by the magnetically charged condensate, known as "dual superconductor".The region in between (relevant for matter produced at RHIC/LHC) is close to the "equilibrium line", marked by e = g on the plot.(People for whom couplings are too abstract, can for example define it by an equality of the electric and magnetic screening masses.)In this region both electric and magnetic coupling are equal and thus α electric = α magnetic = 1: so neither the electric nor magnetic formulations of the theory are simple.Do we have any evidence for a presence or importance for heavy ion physics of "magnetic" objects?Here are some arguments for that based on lattice studies and phenomenology, more or less in historical order: (i) In the RHIC/LHC region T c < T < 2T c the VEV of the Polyakov line < P > is substantially different from 1.It was argued by [48] that < P > must be incorporated into density of thermal quarks and gluons, and thus suppress their contributions.They called such matter "semi-QGP" emphasizing that say only about half of QGP degrees of freedom should actually contribute to thermodynamics at such T .And yet, the lattice data insist that the thermal energy density normalized as /T 4 remains constant nearly all the way to T c .main issues discussed are how the transport properties (in particular the shear viscosity) of the plasma depend on them.More specifically, the issue is whether admixture of weaker-coupled MQPs increases or decreases it.The (blue) shaded region shows "magnetically dominated" region g < e, which includes the e-confined hadronic phase as well as "postconfined" part of the QGP domain.Light region includes "electrically dominated" part of QGP and also color superconductivity (CS) region, which has e-charged diquark condensates and therefore obviously m-confined.The dashed line called "e=g line" is the line of electric-magnetic equilibrium.The solid lines indicate true phase transitions, while the dash-dotted line is a deconfinement cross-over line.

A. Strongly coupled Quark-Gluon plasma in heavy ion collisions
A realization [3,4] that QGP at RHIC is not a weakly coupled gas but rather a strongly coupled liquid has led to a paradigm shift in the field.It was extensively debated at the "discovery" BNL workshop in 2004 [5] (at which the abbreviation sQGP was established) and multiple other meetings since.
Collective flows, related with explosive behavior of hot matter, were observed at RHIC and studied in detail: the conclusion is that they are reproduced by the ideal hydrodynamics remarkably well.Indeed, although these flows affect different secondaries differently, yet their spectra are in quantitative agreement with the data for all of them, from π to Ω − .At non-zero impact parameter the original excited system is deformed in the transverse plane, creating the so called elliptic flow described by where φ is the azimuthal angle and the o for the collision energy, transverse momentu mass, rapidity, centrality and system size.Hy ics explains all of those dependence, for about particles 3 .
Naturally, theorists want to understand th this behavior by looking at other fields of ph have prior experiences with liquid-like plasm them is related with the so called AdS/CFT dence between strongly coupled N =4 supe Yang-Mills theory (a relative of QCD) to wea string theory in Anti-de-Sitter space (AdS) SUGRA regime.We will not discuss it in th a recent brief summary of the results and re e.g.[6].
Zahed and one of us [4] argued that margi states create resonances which can strong transport cross section.Similar phenomeno pen for ultracold trapped atoms, due to Fe resonances at which the binary scattering len which was indeed shown to lead to a near-pe van Hees, Greco and Rapp [7] studied qc reso found enhancement of charm stopping.
Combining lattice data on quasiparticle ma terparticle potentials, one finds a lot of quar bound states [8,9] which contribute to ther cal quantities and help explain the "pressure an apparent contradiction between heavy qu near T c and rather large pressure.The m tor discussed in this paper provides another c that of MQPs (monopoles and dyons), which resolve the pressure puzzle.
A very interesting issue is related with coun bound states of all quasiparticles.Here the ce is that of curves of marginal stability (CMS) not thermodynamic singularities but lines i significant change of physics where a switc language to another (like E ⇀ ↽M ) is appropr mandatory.Let us mention one example related with qu ing "metamorphosis" discussed in literature, text of N =2 SUSY theories.The CMS in related with the following reaction gluon ↔ monopole + dyon in which the r.h.s.system is magnetically (obviously with zero total magnetic charge).itself is defined by the equality of thresholds M (gluon) = M (dyon) + M (monopole 3 The remaining ∼ 1% resigning at larger tra menta pt > 2GeV are influenced by hard proces 4 And prevention of the double counting. 2 FIG. 7. A schematic phase diagram on a ("compactified") plane of temperature and baryonic chemical potential, T − µ, from [47].The (blue) shaded region shows "magnetically dominated" region g < e, which includes the deconfined hadronic phase as well as a small part of the QGP domain.Unshaded region includes the "electrically dominated" part of QGP and the color superconducting (CS) region, which has e-charged diquark condensates and is therefore "magnetically confined".The dashed line called "e=g line" is the line of electric-magnetic equilibrium.The solid lines indicate true phase transitions, while the dash-dotted line is a deconfinement cross-over line.
(ii) "Magnetic scenario" [47] proposes to explain this puzzle by ascribing "another half" of such contributions to the magnetic monopoles, which are not subject to < P > suppression because they do not have the electric charge.A number of lattice studies found magnetic monopoles and had shown that they behave as physical quasiparticles in the medium.Their motion definitely shows Bose-Einstein condensation at T < T c [49].Their spatial correlation functions are very much plasma-like.Even more striking is the observation [50] revealing magnetic coupling which grows with T , being indeed an inverse of the asymptotic freedom curve.
The magnetic scenario also has difficulties.Unlike instanton-dyons we mentioned, lattice monopoles so far defined are gauge dependent.The original 'tHooft-Polyakov solution require an adjoint scalar field, absent in QCD Lagrangian, but perhaps an effective scalar can be generated dynamically.In the Euclidean time finite-temperature setting this is not a problem, as A 0 naturally takes this role, but it cannot be used in real-time applications required for kinetic calculations.
(iii) Plasmas with electric and magnetic charges show unusual transport properties: Lorenz force enhances collision rate and reduce viscosity [47].Quantum gluon-monopole scattering leads to large transport cross section [30], providing small viscosity in the range close to that observed at RHIC/LHC.
(iv) The high density of (non-condensed) monopoles near T c leads to compression of the electric flux tubes, perhaps explaining curious lattice observations of very high tension in the potential energy (not free energy) of the heavy-quark potentials near T c [47].
(v) Last but not least, the peaking density of monopoles near T c seem to be directly relevant to jet quenching.Completing this introduction to monopole applications, it is impossible not to mention the remaining unresolved issues.Theories with adjoint scalar fields -such as e.g.celebrated N =2 Seiberg-Witten theory -naturally have particle-like monopole solutions.Yet in QCD-like theories without scalars the exact structure of the lattice monopole are not yet well understood.

II. ARE COSMOLOGICAL PHASE TRANSITIONS OBSERVABLE?
Since this review is aimed at non-specialists, some introductory information about the cosmological phase transitions is included in Appendix B.
Admittedly, the question in the title of this section is too general: there are many ways in which electroweak and QCD transitions may affect present day Universe.For example, electroweak transitions must be crucially important for the baryon asymmetry of the Universe.We of course will discuss only one possible answer to it, related with gravitational waves.no visible tendency of movement of the maximum.We attribute this to the fact that the total time of the simulation is simply not enough time for the sound cascade -and self-similar solution -to develop.
Note that the typical magnitude of v 2 in this simulation is 10 4 (in relativistic units, with the speed of light c = 1).Results of these simulations provide, in principle, the initial sound power spectrum, from which the inverse acoustic cascade may start evolving.Since we expect it to start as weak turbulence in a self-similar form (40), we only need to know the conserved N .The energy of the sound waves, to the second order, is the unperturbed density of matter times the fluid velocity squared (✏ + p) 0 V 2 .So one can relate this spectrum to the sound wave occupation numbers via Approximately flat l.h.s.observed means that the e↵ective initial value of the index is close to 4 (of course, only in a limited range of scales and time).Then it is supposed to become the weak turbulence, and the slope for V. GENERATION

A. The spectral de cor
General expressions for well known, and we will n ceeding directly to the ma the two-point correlator o Note that while the Big B so 3-momentum can well b is time-dependent.We wi sistatic, with well defined with a cuto↵ at the lowest Using hydrodynamical e T µ⌫ = (✏ + and expanding it in powe sound amplitude -one ca sound wave.Associating t matter rest frame, one intr by and one expands the stres The correlator is to be c bations h µ⌫ h µ 0 ⌫ 0 and we responding to two polariz momentum k ↵ .Such com the term with velocities, a Z d 4 x d 4 y e ik ↵ (x ↵ y ↵ ) h where we dropped the ove scripts "(1)" for the first o The next step is to split for which we use the "sou where we changed indices FIG. 8. From [51].Power spectrum of the velocity squared versus the (log of) the wave number k.The grey upper curves are for sounds, from down up as time progresses,for tTc = 600, 800, 1000, 1200, 1400.The black curves in the bottom are for rotational excitations.

A. Sounds from the phase transitions
We think that our Universe has been "boiling" at its early stages (at least) three times: (i) at the initial equilibration, when entropy was produced, at (ii) electroweak and (iii) QCD phase transitions.On general grounds, these should have produced certain out-of-equilibrium effects, resulting in inhomogeneuities and thus sound.(As an example well familiar to anyone, recall that a cattle start "singing" as tea is ready.The critical phenomenon is production of vapor bubbles, which then collapse and pass their energy to sounds.)Theoretical studies of this process, both for electroweak and QCD transitions, are carried out for at least three decades.An example of such calculation for electroweak transition is shown in Fig, 8 assuming the transition is of the first order.One lesson from it is that the sounds (upper grey curves) dominate the rotations (lower black curves).Another impressive result is that the simulation was able to cover two orders of magnitude of the wavelengths.And yet, there are many more decades of k to the left of this plot which needs to be explored, before we reach the IR cutoff of the process, the scale at which we hope to observe gravity waves.
Experiments with heavy ion collisions, which do create passing through T c and do observe sounds (as we discussed already above).And yet, those sounds so far observed originate from inhomogeneous initial conditions, not the near-T c critical region.How it can be done has been proposed -e.g. in my paper with Staig [52] -but not so far carried out.
Yet sound production is not the main issue here, the fate of subsequent acoustic cascade is.The main proposal of our paper [53] is that it can go into a regime known as inverse acoustic cascade.If it does, the sounds created at the thermal scale can get hugely amplified toward the IR scale.In simpler terms, it is possible that a huge storm may develop, with a cutoff only at the scale of Universe horizon.At the time of QCD transition, this scale is 18 orders of magnitude different from the thermal scale.
Earth atmosphere is basically 2-dimensional, its hight is three orders of magnitude smaller than Earth's diameter, and that is why the inverse cascades create large storms.The amplification rate can be truly huge.The Universe is 3-dimensional, and in this case it can appear only in very special circumstances.It remains a great challenge to figure out whether it is the case, maybe for one of the transitions.
The challenge is to understand when and how the can be developed.The answer, first of all, crucially depend on the sign of small corrections to sound dispersion, which we write as The sign of the correction constant A is not known, both for QGP and electroweak plasma.If A > 0 the phonon decays 1 → 2 are possible.The turbulent cascade based on such 3-wave interactions was shown to develop in the direct -that is large k or UV -direction, which is not the one we are interested in.Another alternative, when the dispersive correction coefficient A < 0 is negative, turns out to be much more interesting.In this case the cascade switches to higher order processes, of 2 ↔ 2 scattering and/or 1 ↔ 3 processes.
The analysis of corresponding acoustic cascade is much more involved but it does show existence of the inverse cascade, with a particle flow directed to IR, with the weak turbulence index of the density momentum distribution n k ∼ k −s , s weak = 10/3 (16) Furthermore, as discussed in [53], large value of the density at small k leads to violation of weak turbulence applicability condition and the regime is known as "strong turbulence" in which case the evaluated index is even larger, s strong = 4 − 6.This is an interesting and complex problem, since the sound-sound scattering processes are not simple.It can and should be numerically simulated, like it was done for scalar fields and gluonic cascades, but it was not studied yet.
B. From the sounds to the gravitational waves Before we come into more technical discussion, let us briefly note why do we need to focus on such (still rather exotic) observable.Gravitational waves, as a cosmology tool, looked as a science fiction for about a century, but not anymore, due to recent LIGO observations.
From the onset of the QGP physics in heavy ion collisions a specially important role has been attributed to the "penetrating probes", which for heavy ion collisions mean photons/dileptons [54].So it is quite logical to think also about the only "penetrating probe" of the Big Bang, the gravity waves (GW).
30 years ago Witten [55] had discussed the cosmological QCD phase transition, assuming it to be of the first order: he pointed out bubble production and coalescence, producing inhomogenuities in energy distribution and mentioned production of the gravity waves.Among papers followed it were estimates of how much gravity waves will be produced.
Jumping many years to recent time, the fascinating observation was made by Hindmarsh et al [51].These authors calculated gravity wave production, by numerically evaluating a correlator of two stress tensors < T µν (x)T µν (y) > during the electroweak transition.They followed phase transitions till its end, and obtained the sound spectra already shown above.During the time of the simulation, the Higgs value does settle to its eternal value and no changes are seen in electroweak sector any more.And yet, the calculated rate of gravity wave production has shown no sign of disappearing, all the way to the end of the simulation!It turned out that the dominant source of the GW in those simulations are hydrodynamical sound waves.Furthermore, the GW generation rate remains constant even long after the phase transition itself is over.So, we argued [53] , there must be some acoustic cascade involved, since only large wavelength small-k sounds can survive viscous losses for a long time.
In that work [53] we discussed the sound-based GW production further.We argue that generation of the cosmological GW can be divided into four distinct stages, each with its own physics and scales.We will list them starting from the UV end of the spectrum k ∼ T and ending at the IR end of the spectrum k ∼ 1/t lif e cutoff by the Universe lifetime at the era : (i) the production of the sounds (ii) the inverse cascade" of the acoustic turbulence, moving the sound from UV to IR (iii) the final transition from sounds to GW.
The stage (i) remains highly nontrivial, associated with the dynamical details of the QCD and electroweak (EW) phase transition.The stage (ii), on the other hand, is in fact amenable to perturbative studies of the acoustic cascade, which is governed by Boltzmann equation.It has been already rather well studied in literature on turbulence, in which power attractor solutions has been identified.Application of this theory allows to see how small-amplitude sounds can be amplified, as one goes to smaller k.
The stage (iii) can be treated via a simple approximation allowing to calculate the correlator of two stress tensors.In hydrodynamic approximation stress tensor contains T µν ≈ ( + p)u µ u ν where the first bracket contains the energy density and pressure of the medium, and u µ is 4-velocity of its motion.If one u µ is produced by one sound wave, and the second by another, one finds that the standard loop diagram for the correlator splits into a square of the amplitude describing new elementary process:

sound + sound → graviton
There is no place here for technical discussions, and we only comment on the kinematics of the process.The speed of sound c s ≈ 1/ √ 3 is only about half speed of light, so to get enough energy for a graviton two sounds need to cancel half of their momenta: in a symmetric case the angle between them should be about 100 o or so.
Finally, let us briefly touch the question whether and how the gravitational waves can be detected experimentally.In appendix B we estimate the corresponding period expected from electroweak and QCD transitions.They are much much longer than those observed by LIGO (micro-seconds).
GW from the electroweak era are expected to have periods of hours: those will be searched for by future GW observatories in space, such as eLISA.
The GW from the QCD transition are expected to have periods of about a year.It turns out that for that time window there exists a very nice method as well: possible observational tools for them are the correlations of the millisecond pulsar signal coming from different direction.The basic idea is that when GW is falling on Earth and, say, stretches distances in a certain direction, then in the orthogonal direction one expects distances to be reduced.The binary correlation function for the pulsar time delay is an expected function of the angle θ between them on the sky.There are existing collaborations -North American Nanohertz Observatory for Gravitational Radiation, European Pulsar Timing Array (EPTA), and Parkes Pulsar Timing Array -which actively pursue both the search for new millisecond pulsars and collecting the timing data for some known pulsars.It is believed that about 200 known millisecond pulsars constitute only about 1 percent of the total number of them in our Galaxy.The current bound on the GW fraction of the energy density of the Universe is approximately Ω GW (f ∼ 10 −8 Hz)h 2 100 < 10 −9 . ( Rapid progress in the field, including better pulsar timing and formation of a global collaborations of observers, is expected to improve the sensitivity of the method , perhaps making it possible to detect GW radiation, either from merging supermassive black holes (everyone is expecting to find now) and perhaps even some stochastic background coming from the QCD Big Bang phase transition we discuss.

III. SUMMARY
This paper covers two fields, which are at very different stage of their development.Heavy ion community is now dominated by large-scale experiments at two colliders, RHIC and LHC.We did observed the production of new form of matter, sQGP, followed by rapid explosion, the Little Bang.Many details of it are rather well studied.Not only the average behavior is recorded and explained, but also its event-by-event fluctuations.Small point-like perturbations lead to the "sound circles", observed in great details for a number of harmonics.The unusual kinetic properties of sQGP are quantified, and explained by a number of approaches.We discussed one of them, blaming short mean free path on peculiar magnetically charged quasiparticles, the monopoles, copiously present in QGP near its critical temperature.
In connection to the central issues of this paper, the observability of cosmic phase transitions at Big Bang, basically two things remain to be done.One, in heavy ion collisions, is to detect sounds originating from the QCD phase transition era (rather than from the initial state perturbation, as it has been described above).The other is to figure out details of the sound dispersion curve, since we would like to know whether sound waves can or cannot decay.
In the case of electroweak plasma at its critical temperature there are obviously no laboratory experiments.But in this case the coupling is weak, and thus sall questions can perhaps be studied theoretically.
The cosmology community related to QCD and electroweak phase transitions is just making its first steps.At this stage, one needs to develop even qualitative understanding of the relevant acoustic turbulence regime.Depending on the particular scenario realized, the expected magnitude of gravity waves varies by many orders of magnitude.Perhaps some of scenarios are already excluded by the pulsar correlation data.As for the electroweak transition, the decisive experiment are space gravity wave detectors like eLISA.Their sensitivity is so far tuned to black hole merger events, not so far to a random background of gravity wave we discuss.A lot of work is ahead.
Left) Comparison of the trace anomaly (✏ 3P )/T 4 , pressure and entropy density lated with the HISQ (colored) 114 and stout (grey) 113 discretization schemes for staggered ions.(Right) Continuum extrapolated results for pressure, energy density and entropy denobtained with the HISQ action. 114Solid lines on the low temperature side correspond to ts obtained from hadron resonance gas (HRG) model calculations.The dashed line at high eratures shows the result for a non-interacting quark-gluon gas.

FIG. 1 .
FIG. 1. Continuum extrapolated results for pressure, energy density and entropy.Solid lines on the low temperature side correspond to results obtained from hadron resonance gas (HRG) model calculations.The (yellow) band marked Tc indicate the phase transition region for deconfinement and chiral symmetry restoration.

Figure 2 :
Figure 2: The steps involved in the extraction of the v n for 2-3 GeV fixed-p T correlation: a) the twodimensional correlation function (shown for |∆η| < 4.75 to reduce the fluctuations near the edge), b) the one-dimensional ∆φ correlation function for 2 < |∆η| < 5 (re-binned into 100 bins), overlaid with contributions from individual Fourier components as well as the sum, c) Fourier coefficient v n,n vs n, and d) v n vs n.The bottom two panels show the full dependence of v n,n and v n on ∆η.The v 1 is not shown since it breaks the factorization from v n,n to v n of Eq. 13.The shaded bands in c)-f) indicate the systematic uncertainties.The range 2 < p a T , p b T < 3 GeV is chosen, since collective flow is expected to be large in this range while the pair statistics are still high.

Figure 11 .
Figure 11.Planck power spectra and data selection.The coloured tick marks indicate the `-range of the four cross-spectra included in CamSpec (and computed with the same mask, see Table4).Although not used, the 70 GHz and 143 x 353 GHz spectra demonstrate the consistency of the data.The dashed line indicates the best-fit Planck spectrum.

FIG. 4 .
FIG. 4. (a) The lines are hydro calculations of the correlation function harmonics, v 2m , based on a Green function from a point source[17] for four values of viscosety 4πη/s =0,1,1.68,2(top to bottom at the right).The closed circles are the Atlas data for the ultra-central bin.(b) vn{2} plotted vs n 2 .Blue closed circles are calculation of via viscous even-by-event hydrodynamics[18], "IP Glasma+Music", with η/s = 0.14.The straight line, shown to guide the eye, demonstrate that "acoustic systematics" does in fact describe the results of this heavy calculation quite accurately.The CMS data for the 0-1% centrality bin, shown by the red squares, in fact display larger deviations, perhaps an oscillatory ones.

FIG. 1 .
FIG. 1. (color online)A schematic phase diagram on a ("compactified") plane of temperature and baryonic chemical potential T − µ.The (blue) shaded region shows "magnetically dominated" region g < e, which includes the e-confined hadronic phase as well as "postconfined" part of the QGP domain.Light region includes "electrically dominated" part of QGP and also color superconductivity (CS) region, which has e-charged diquark condensates and therefore obviously m-confined.The dashed line called "e=g line" is the line of electric-magnetic equilibrium.The solid lines indicate true phase transitions, while the dash-dotted line is a deconfinement cross-over line.

1 FIG. 2 :
FIG.2:(From[1]) Power spectrum of the velocity squared versus the (log of) the wave number k.The grey upper curves are for sounds, from down up as time progresses, t = 600, 800, 1000, 1200, 1400 T 1 c .The black curves in the bottom are for rotational excitations.

TABLE I .
The electric and magnetic screening masses, normalized to the temperature.The last column is the square of their ratio.

Table 4 .
Overview of of cross-spectra, multipole ranges and masks used in the Planck high-`likelihood.Reduced 2 s with respect to the best-fit minimal ⇤CDM model are given in the fourth column, and the corresponding probability-to-exceed in the fifth column.