Table of Contents

Drawing from the optimal transport theory adapted to the Lorentzian setting, we propose and study the extension of the Sorkin–Woolgar causal relation $K^{+}$ onto the space of Borel probability measures on a given spacetime. We show that it retains its fundamental properties of transitivity and closedness. Furthermore, we list and prove several characterizations of this relation, including the “measure-theoretic” analogue of the characterization of $K^{+}$ in terms of time functions. Full article

We study the variation of fundamental constants in cosmology while dealing with thermodynamic aspects of gravity. We focus on the variation of the speed of light, c, and Newton’s gravitational constant, G, with respect to cosmic time. We find the constraints on the possible variation of these constants by comparing varying constants of cosmological models with the latest observational data. Full article

We review the concept of ‘noncommutative spacetime’ approached from an operational stand-point and explain how to endow it with suitable geometrical structures. The latter involves i.a. the causal structure, which we illustrate with a simple—‘almost-commutative’—example. Furthermore, we trace the footprints of noncommutive geometry in the foundations of quantum field theory. Full article

An extensive review of past work on relativistic gravimetry, gradiometry and chronometric geodesy is given. Then, general theoretical tools are presented and applied for the case of a stationary parameterized post-Newtonian metric. The special case of a stationary clock on the surface of the Earth is studied. Full article

Recent developments in gravitation theory indicate that the classic general relativity is an effective macroscopic theory which will be eventually replaced with a more fundamental theory based on thermodynamics of yet unknown microscopic degrees of freedom. Here we consider thermodynamics of an effective spacetime which may be formed under the influence of an external magnetic field in a cobalt ferrofluid. It appears that the extraordinary photons propagating inside the ferrofluid perceive thermal gradients in the ferrofluid as an effective gravitational field, which obeys the Newton law. Moreover, the effective de Sitter spacetime behaviour near the metric signature transition may mimic various cosmological inflation scenarios, which may be visualized directly using an optical microscope. Thus, some features of the hypothetic microscopic theory of gravity are illustrated in the ferrofluid-based analogue models of inflation. Full article

In this review we present the most general form of the Janis–Newman algorithm. This extension allows generating configurations which contain all bosonic fields with spin less than or equal to two (real and complex scalar fields, gauge fields, metric field) and with five of the six parameters of the Plebański–Demiański metric (mass, electric charge, magnetic charge, NUT charge and angular momentum). Several examples are included to illustrate the algorithm. We also discuss the extension of the algorithm to other dimensions. Full article

The ΛCDM paradigm, characterised by a constant equation of state $w=-1$ for dark energy, is the model that better fits observations. However, the same observations strongly support the possibility of a dark energy content where the corresponding equation of state is close to but slightly smaller than $-1$ . In this regard, we focus on three different models where the dark energy content is described by a perfect fluid with an equation of state $w\lesssim -1$ which can evolve or not. The three proposals show very similar behaviour at present, while the asymptotic evolution of each model drives the Universe to different abrupt events known as (i) Big Rip; (ii) Little Rip (LR); and (iii) Little Sibling of the Big Rip. With the aim of comparing these models and finding possible imprints in their predicted matter distribution, we compute the matter power spectrum and the growth rate $f{\sigma }_8$ . We conclude that the model which induces a LR seems to be favoured by observations. Full article

The latest cosmological observations by the Planck collaboration (and combined with others) are compatible with a phantom-like behaviour ( $w<-1$ ) for the dark energy equation of state that drives the current acceleration of the Universe. With this mindset, we look into models where dark energy is described by a 3-form field minimally coupled to gravity. When compared to a scalar field, these models have the advantage of more naturally accommodating a cosmological-constant and phantom-like behaviours. We show how the latter happens for a fairly general class of positive-valued potentials, and through a dynamical system approach, we find that in such cases the 3-form field leads the Universe into a Little Sibling of the Big Rip singular event into the future. In this work, we explore the possibility of avoiding such singularity via an interaction in the dark sector between cold dark matter and the 3-form field. For the kind of interactions considered, we deduce a condition for replacing the LSBR by a late time de Sitter phase. For specific examples of interactions that meet this condition, we look for distinctive imprints in the statefinder hierarchy $\{{S_3}^{\left(1\right)};{S_4}^{\left(1\right)}\}$ , $\{{S_3}^{\left(1\right)};{S_5}^{\left(1\right)}\}$ , and in the growth rate of matter, $ϵ\left(z\right)$ , through the composite null diagnostic (CND). Full article

The Petrov classification of stress-energy tensors provides a model-independent definition of a vacuum by the algebraic structure of its stress-energy tensor and implies the existence of vacua whose symmetry is reduced as compared with the maximally symmetric de Sitter vacuum associated with the Einstein cosmological term. This allows to describe a vacuum in general setting by dynamical vacuum dark fluid, presented by a variable cosmological term with the reduced symmetry which makes vacuum fluid essentially anisotropic and allows it to be evolving and clustering. The relevant solutions to the Einstein equations describe regular cosmological models with time-evolving and spatially inhomogeneous vacuum dark energy, and compact vacuum objects generically related to a dark energy: regular black holes, their remnants and self-gravitating vacuum solitons with de Sitter vacuum interiors—which can be responsible for observational effects typically related to a dark matter. The mass of objects with de Sitter interior is generically related to vacuum dark energy and to breaking of space-time symmetry. In the cosmological context spacetime symmetry provides a mechanism for relaxing cosmological constant to a needed non-zero value. Full article

The Standard Model of Cosmology (SMC) has evolved in the decades since the 1965 Penzias and Wilson observations of the Cosmic Microwave Background (CMB). Over this 50-year period, the SMC has become increasingly strange due to a number of questionable assumptions. This paper examines some of these assumptions and compares them to our Baryon Phase-Transition cosmological model. Full article

Recent analyses of cosmic microwave background surveys have revealed hints that there may be a non-trivial running of the running of the spectral index. If future experiments were to confirm these hints, it would prove a powerful discriminator of inflationary models, ruling out simple single field models. We discuss how isocurvature perturbations in multi-field models can be invoked to generate large runnings in a non-standard hierarchy, and find that a minimal model capable of practically realising this would be a two-field model with a non-canonical kinetic structure. We also consider alternative scenarios such as variable speed-of-light models and canonical quantum gravity effects and their implications for runnings of the spectral index. Full article

Some important problems of general relativity, such as the quantisation of gravity or classical singularity problems, crucially depend on geometry on very small scales. The so-called synthetic differential geometry—a categorical counterpart of the standard differential geometry—provides a tool to penetrate infinitesimally small portions of space-time. We use this tool to show that on any “infinitesimal neighbourhood” the components of the curvature tensor are themselves infinitesimal, and construct a simplified model in which the curvature singularity disappears, owing to this effect. However, one pays a price for this result. Using topoi as a generalisation of spaces requires a weakening of arithmetic (the existence of infinitesimals) and of logic (to the intuitionistic logic). Is this too high a price to pay for acquiring a new method of solving unsolved problems in physics? Without trying, we shall never know the answer. Full article

In this paper, we have worked on the possibility of setting up an Bell’s inequality violating experiment in the context of primordial cosmology following the fundamental principles of quantum mechanics. To set up this proposal, we have introduced a model-independent theoretical framework using which we have studied the creation of new massive particles for the scalar fluctuations in the presence of an additional time-dependent mass parameter. Next we explicitly computed the one-point and two-point correlation functions from this setup. Then, we comment on the measurement techniques of isospin breaking interactions of newly introduced massive particles and its further prospects. After that, we give an example of the string theory-originated axion monodromy model in this context. Finally, we provide a bound on the heavy particle mass parameter for any arbitrary spin field. Full article

We review results about the development and asymptotic nature of singularities in “brane–bulk” systems. These arise for warped metrics obeying the five-dimensional Einstein equations with fluid-like sources, and including a brane four-metric that is either Minkowski, de Sitter, or Anti-de Sitter. We characterize all singular Minkowski brane solutions, and look for regular solutions with nonzero curvature. We briefly comment on matching solutions, energy conditions, and finite Planck mass criteria for admissibility, and we briefly discuss the connection of these results to ambient theory. Full article

We consider the thermodynamic and stability problem of Kerr black holes arising from the nonextensive/nonadditive nature of the Bekenstein–Hawking entropy formula. Nonadditive thermodynamics is often criticized by asserting that the zeroth law cannot be compatible with nonadditive composition rules, so in this work we follow the so-called formal logarithm method to derive an additive entropy function for Kerr black holes also satisfying the zeroth law’s requirement. Starting from the most general, equilibrium compatible, nonadditive entropy composition rule of Abe, we consider the simplest non-parametric approach that is generated by the explicit nonadditive form of the Bekenstein–Hawking formula. This analysis extends our previous results on the Schwarzschild case, and shows that the zeroth law-compatible temperature function in the model is independent of the mass–energy parameter of the black hole. By applying the Poincaré turning point method, we also study the thermodynamic stability problem in the system. Full article

We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple-scale method. The spectrum of the several orders of approximation show maxima of the energy distribution dependent on the azimuthal-angle and the winding numbers of the subsequent orders of the scalar field. This breakup of the quantized flux quanta does not lead to instability of the asymptotic wavelike solution due to the suppression of the n-dependency in the energy momentum tensor components by the warp factor. This effect is triggered by the contribution of the five dimensional Weyl tensor on the brane. This contribution can be understood as dark energy and can trigger the self-acceleration of the universe without the need of a cosmological constant. There is a striking relation between the symmetry breaking of the Higgs field described by the winding number and the SO(2) breaking of the axially symmetric configuration into a discrete subgroup of rotations of about 180 ${}^{\circ }$ . The discrete sequence of non-axially symmetric deviations, cancelled by the emission of gravitational waves in order to restore the SO(2) symmetry, triggers the pressure $T_{zz}$ for discrete values of the azimuthal-angle. There could be a possible relation between the recently discovered angle-preferences of polarization axes of quasars on large scales and our theoretical predicted angle-dependency and this could be evidence for the existence of cosmic strings. Careful comparison of this spectrum of extremal values of the first and second order φ-dependency and the distribution of the alignment of the quasar polarizations is necessary. This can be accomplished when more observational data become available. It turns out that, for late time, the vacuum 5D spacetime is conformally invariant if the warp factor fulfils the equation of a vibrating “drum”, describing standing normal modes of the brane. Full article

In a recent paper (Mod. Phys. Lett. A 2015, 30, 1550104), the black-hole/qubit correspondence (BHQC) was exploited to define “black hole quantum circuits” allowing for a change of the supersymmetry-preserving features of electromagnetic charge configurations supporting the black hole solution. This resulted in switching from one U-duality orbit to another, or equivalently, from an element of the corresponding Freudenthal triple system with a definite rank to another one. On the supergravity side of BHQC, such quantum gates are related to particular symplectic transformations acting on the black hole charges; namely, such transformations cannot belong to the U-duality group, otherwise switching among orbits would be impossible. In this paper, we consider a particular class of such symplectic transformations, namely the ones belonging to the so-called Peccei–Quinn symplectic group, introduced some time ago within the study of very special Kähler geometries of the vector multiplets’ scalar manifolds in N = 2 supergravity in D =4 spacetime dimensions. Full article

John Nash has proposed a new theory of gravity. We define a Nash-tensor equal to the curvature tensor appearing in the Nash field equations for empty space, and calculate its components for two cases: 1. A static, spherically symmetric space; and 2. The expanding, homogeneous and isotropic space of the Friedmann-Lemaitre-Robertson-Walker (FLRW) universe models. We find the general, exact solution of Nash’s field equations for empty space in the static case. The line element turns out to represent the Schwarzschild-de Sitter spacetime. Also we find the simplest non-trivial solution of the field equations in the cosmological case, which gives the scale factor corresponding to the de Sitter spacetime. Hence empty space in the Nash theory corresponds to a space with Lorentz Invariant Vacuum Energy (LIVE) in the Einstein theory. This suggests that dark energy may be superfluous according to the Nash theory. We also consider a radiation filled universe model in an effort to find out how energy and matter may be incorporated into the Nash theory. A tentative interpretation of the Nash theory as a unified theory of gravity and electromagnetism leads to a very simple form of the field equations in the presence of matter. It should be noted, however, that the Nash theory is still unfinished. A satisfying way of including energy momentum into the theory has yet to be found. Full article

Results from the Relativistic Heavy Ion Colloder (RHIC) and the Large Hadron Collider (LHC) experiments show that in relativistic heavy ion collisions, a new state of matter, a strongly interacting perfect fluid, is created. Accelerating, exact and explicit solutions of relativistic hydrodynamics allow for a simple and natural description of this medium. A finite rapidity distribution arises from these solutions, leading to an advanced estimate of the initial energy density of high energy collisions. These solutions can be utilized to describe various aspects of proton–proton collisions, as originally suggested by Landau. We show that an advanced estimate based on hydrodynamics yields an initial energy density in $\sqrt{s}=7$ and 8 TeV proton–proton (p–p) collisions at the LHC on the same order as the critical energy density from lattice Quantum Chromodynamics (QCD). The advanced estimate yields a corresponding initial temperature that is around the critical temperature from QCD and the Hagedorn temperature. The multiplicity dependence of the estimated initial energy density suggests that in high multiplicity p–p collisions at the LHC, there is large enough initial energy density to create a non-hadronic perfect fluid. Full article

We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic framework of approaches to quantum gravity. We employ moduli of convexity and smoothness which are eventually extremized by Hilbert spaces. We point out the potential physical significance that functional analytical dualities play in this framework. Following the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a generalized functional integral approach. The metric of space-time is induced by the inner product of such Hilbert spaces. Full article

In this review, we present an up-to-date phenomenological summary of research developments in the physics of the Quark–Gluon Plasma (QGP). A short historical perspective and theoretical motivation for this rapidly developing field of contemporary particle physics is provided. In addition, we introduce and discuss the role of the quantum chromodynamics (QCD) ground state, non-perturbative and lattice QCD results on the QGP properties, as well as the transport models used to make a connection between theory and experiment. The experimental part presents the selected results on bulk observables, hard and penetrating probes obtained in the ultra-relativistic heavy-ion experiments carried out at the Brookhaven National Laboratory Relativistic Heavy Ion Collider (BNL RHIC) and CERN Super Proton Synchrotron (SPS) and Large Hadron Collider (LHC) accelerators. We also give a brief overview of new developments related to the ongoing searches of the QCD critical point and to the collectivity in small (p + p and p + A) systems. Full article

The observed constraints on the variability of the proton to electron mass ratio μ and the fine structure constant α are used to establish constraints on the variability of the Quantum Chromodynamic Scale and a combination of the Higgs Vacuum Expectation Value and the Yukawa couplings. Further model dependent assumptions provide constraints on the Higgs VEV and the Yukawa couplings separately. A primary conclusion is that limits on the variability of dimensionless fundamental constants such as μ and α provide important constraints on the parameter space of new physics and cosmologies. Full article

In this paper, we use a three flavor non-local Nambu–Jona-Lasinio (NJL) model, an improved effective model of Quantum Chromodynamics (QCD) at low energies, to investigate the existence of deconfined quarks in the cores of neutron stars. Particular emphasis is put on the possible existence of quark matter in the cores of rotating neutron stars (pulsars). In contrast to non-rotating neutron stars, whose particle compositions do not change with time (are frozen in), the type and structure of the matter in the cores of rotating neutron stars depends on the spin frequencies of these stars, which opens up a possible new window on the nature of matter deep in the cores of neutron stars. Our study shows that, depending on mass and rotational frequency, up to around 8% of the mass of a massive neutron star may be in the mixed quark-hadron phase, if the phase transition is treated as a Gibbs transition. We also find that the gravitational mass at which quark deconfinement occurs in rotating neutron stars varies quadratically with spin frequency, which can be fitted by a simple formula. Full article

Electromagnetic rays travel on curved paths under the influence of gravity. When a dispersive optical medium is included, these trajectories are frequency-dependent. In this work we consider the behaviour of rays when a spherically symmetric, luminous compact object described by the Schwarzschild metric is surrounded by an optically thin shell of plasma supported by radiation pressure. Such levitating atmospheres occupy a position of stable radial equilibrium, where radiative flux and gravitational effects are balanced. Using general relativity and an inhomogeneous plasma we find the existence of a stable circular orbit within the atmospheric shell for low-frequency rays. We explore families of bound orbits that exist between the shell and the compact object, and identify sets of novel periodic orbits. Finally, we examine conditions necessary for the trapping and escape of low-frequency radiation. Full article

We study quantum correlation of a massive scalar field in a maximally entangled state in de Sitter space. We prepare two observers, one in a global chart and the other in an open chart of de Sitter space. We find that the state becomes less entangled as the curvature of the open chart gets larger. In particular, for the cases of a massless and a conformally coupled scalar field, the quantum entanglement vanishes in the limit of infinite curvature. However, we find that the quantum discord never disappears, even in the limit that entanglement disappears. Full article

We review matter bounce scenarios where the matter content is dark matter and dark energy. These cosmologies predict a nearly scale-invariant power spectrum with a slightly red tilt for scalar perturbations and a small tensor-to-scalar ratio. Importantly, these models predict a positive running of the scalar index, contrary to the predictions of the simplest inflationary and ekpyrotic models, and hence, could potentially be falsified by future observations. We also review how bouncing cosmological space-times can arise in theories where either the Einstein equations are modified or where matter fields that violate the null energy condition are included. Full article