Universe

35 pages, 646 KiB

Open AccessArticle

The Spectrum of Gravitational Waves, Their Overproduction in Quintessential Inflation and Its Influence in the Reheating Temperature

by Jaume Haro Cases and Llibert Aresté Saló

Universe 2020, 6(6), 87; https://doi.org/10.3390/universe6060087 - 23 Jun 2020

Cited by 5 | Viewed by 2702

Abstract

One of the most important issues in an inflationary theory as standard or quintessential inflation is the mechanism to reheat the universe after the end of the inflationary period in order to match with the Hot Big Bang universe. In quintessential inflation two [...] Read more.

One of the most important issues in an inflationary theory as standard or quintessential inflation is the mechanism to reheat the universe after the end of the inflationary period in order to match with the Hot Big Bang universe. In quintessential inflation two mechanisms are frequently used, namely the reheating via gravitational particle production which is, as we will see, very efficient when the phase transition from the end of inflation to a kinetic regime (all the energy of the inflaton field is kinetic) is very abrupt, and the so-called instant preheating which is used for a very smooth phase transition because in that case the gravitational particle production is very inefficient. In the present work, a detailed study of these mechanisms is done, obtaining bounds for the reheating temperature and the range of the parameters involved in each reheating mechanism in order that the Gravitational Waves (GWs) produced at the beginning of kination do not disturb the Big Bang Nucleosynthesis (BBN) success. Full article

(This article belongs to the Section Cosmology)

► Show Figures

Figure 1

19 pages, 783 KiB

Open AccessArticle

Identifying the Λ_b(6146)⁰ and Λ_b(6152)⁰ as D-Wave Bottom Baryons

by Qiang Mao, Hua-Xing Chen and Hui-Min Yang

Universe 2020, 6(6), 86; https://doi.org/10.3390/universe6060086 - 23 Jun 2020

Cited by 8 | Viewed by 2540

Abstract

We study the

Λ_{b} {(6146)}^{0}

and

Λ_{b} {(6152)}^{0}

recently observed by LHCb using the method of Quantum Chromodynamics (QCD) sum rules within the framework of heavy quark effective theory. Our results suggest that they can [...] Read more.

We study the

Λ_{b} {(6146)}^{0}

and

Λ_{b} {(6152)}^{0}

recently observed by LHCb using the method of Quantum Chromodynamics (QCD) sum rules within the framework of heavy quark effective theory. Our results suggest that they can be interpreted as D-wave bottom baryons of

J^{P} = 3 / 2^{+}

and

5 / 2^{+}

respectively, both of which contain two

λ

-mode excitations. We also investigate other possible assignments containing

ρ

-mode excitations. We extract all the parameters that are necessary to study their decay properties when using the method of light-cone sum rules. We predict masses of their strangeness partners to be

m_{Ξ_{b} (3 / 2^{+})} = {6.26}_{- 0.14}^{+ 0.11}

GeV and

m_{Ξ_{b} (5 / 2^{+})} = {6.26}_{- 0.14}^{+ 0.11}

GeV with the mass splitting

Δ M = m_{Ξ_{b} (5 / 2^{+})} - m_{Ξ_{b} (3 / 2^{+})} = {4.5}_{- 1.5}^{+ 1.9}

MeV, and propose to search for them in future CMS, EIC, and LHCb experiments. Full article

(This article belongs to the Section High Energy Nuclear and Particle Physics)

► Show Figures

Figure 1

24 pages, 857 KiB

Open AccessArticle

Is There Still Something Left That Gravity Probe B Can Measure?

by Lorenzo Iorio

Universe 2020, 6(6), 85; https://doi.org/10.3390/universe6060085 - 20 Jun 2020

Cited by 2 | Viewed by 2149

Abstract

We perform a full analytical and numerical treatment, to the first post-Newtonian (1pN) order, of the general relativistic long-term spin precession of an orbiting gyroscope due to the mass quadrupole moment

J_{2}

of its primary without any restriction on either the gyro’s [...] Read more.

We perform a full analytical and numerical treatment, to the first post-Newtonian (1pN) order, of the general relativistic long-term spin precession of an orbiting gyroscope due to the mass quadrupole moment

J_{2}

of its primary without any restriction on either the gyro’s orbital configuration and the orientation in space of the symmetry axis

\hat{k}

of the central body. We apply our results to the past spaceborne Gravity Probe B (GP-B) mission by finding a secular rate of its spin’s declination

δ

which may be as large as ≲30–40

milliarcseconds per year (mas {yr}^{- 1})

, depending on the initial orbital phase

f_{0}

. Both our analytical calculation and our simultaneous integration of the equations for the parallel transport of the spin 4-vector S and of the geodesic equations of motion of the gyroscope confirm such a finding. For GP-B, the reported mean error in measuring the spin’s declination rate amounts to

σ_{\dot{δ}}^{GP - B} = 18.3 mas {yr}^{- 1}

. We also calculate the general analytical expressions of the gravitomagnetic spin precession induced by the primary’s angular momentum

J

. In view of their generality, our results can be extended also to other astronomical and astrophysical scenarios of interest like, e.g., stars orbiting galactic supermassive black holes, exoplanets close to their parent stars, tight binaries hosting compact stellar corpses. Full article

(This article belongs to the Special Issue Universe: 5th Anniversary)

► Show Figures

Figure 1

10 pages, 253 KiB

Open AccessArticle

Hyperfine Splitting of Excited States of New Heavy Hadrons and Low-Energy Interaction of Hadronic Dark Matter with Photons, Nucleons, and Leptons

by Vladimir Kuksa and Vitaly Beylin

Universe 2020, 6(6), 84; https://doi.org/10.3390/universe6060084 - 19 Jun 2020

Cited by 6 | Viewed by 1890

Abstract

We consider the structure of excited states and low-energy interaction of hadronic dark matter with photons, leptons, and nucleons. Description of the lowest excited levels is fulfilled in an analogy with the standard heavy-light mesons. Using the effective vertex of new heavy hadrons [...] Read more.

We consider the structure of excited states and low-energy interaction of hadronic dark matter with photons, leptons, and nucleons. Description of the lowest excited levels is fulfilled in an analogy with the standard heavy-light mesons. Using the effective vertex of new heavy hadrons interaction with W-boson, we calculate cross-section of the lepton scattering on the dark matter particle. Analysis of strong low-energy interaction of new hadrons was carried out within the effective meson-exchange model based on dynamical realization of SU(3)-symmetry. A cross-section of nucleon scattering on the hadronic dark matter was also calculated using this model. The most essential phenomenological consequences of the low-energy dark matter interaction with leptons and nucleons are discussed. Full article

(This article belongs to the Special Issue Focus on Dark Matter)

12 pages, 589 KiB

Open AccessArticle

General Relativistic Mean-Field Dynamo Model for Proto-Neutron Stars

by Kevin Franceschetti and Luca Del Zanna

Universe 2020, 6(6), 83; https://doi.org/10.3390/universe6060083 - 17 Jun 2020

Cited by 12 | Viewed by 2578

Abstract

Neutron stars, and magnetars in particular, are known to host the strongest magnetic fields in the Universe. The origin of these strong fields is a matter of controversy. In this preliminary work, via numerical simulations, we study, for the first time in non-ideal [...] Read more.

Neutron stars, and magnetars in particular, are known to host the strongest magnetic fields in the Universe. The origin of these strong fields is a matter of controversy. In this preliminary work, via numerical simulations, we study, for the first time in non-ideal general relativistic magnetohydrodynamic (GRMHD) regime, the growth of the magnetic field due to the action of the mean-field dynamo due to sub-scale, unresolved turbulence. The dynamo process, combined with the differential rotation of the (proto-)star, is able to produce an exponential growth of any initial magnetic seed field up to the values required to explain the observations. By varying the dynamo coefficient we obtain different growth rates. We find a quasi-linear dependence of the growth rates on the intensity of the dynamo. Furthermore, the time interval in which exponential growth occurs and the growth rates also seems to depend on the initial configuration of the magnetic field. Full article

(This article belongs to the Special Issue Universe: 5th Anniversary)

► Show Figures

Figure 1

13 pages, 291 KiB

Open AccessArticle

Comments on P. Jordan’s Cosmological Model

by Eve-Aline Dubois and André Füzfa

Universe 2020, 6(6), 82; https://doi.org/10.3390/universe6060082 - 17 Jun 2020

Cited by 1 | Viewed by 2163

Abstract

We analyse the original cosmology of P. Jordan through his 1939 key paper entitled “Bemerkungen zur Kosmologie” or “Comments on cosmology”. In this almost forgotten work, the author introduced a model of dynamical cosmology with spontaneous creation of matter, based on the [...] Read more.

We analyse the original cosmology of P. Jordan through his 1939 key paper entitled “Bemerkungen zur Kosmologie” or “Comments on cosmology”. In this almost forgotten work, the author introduced a model of dynamical cosmology with spontaneous creation of matter, based on the Large Numbers study, initiated by Eddington and further developed by Dirac. Jordan’s will to explore heuristically all possible cosmological models in order to be prepared in case of surprising future astronomical data is very compelling in this article. Since we think it is wise to learn from our predecessors and from the unsuccessful theories that were later left behind, the present article also offers an overview of Jordan’s work during the 1930s through the analysis of a series of some of his other original pieces. An English translation of Jordan’s key paper can be found in the appendix. Full article

(This article belongs to the Section Cosmology)

22 pages, 3003 KiB

Open AccessEditor’s ChoiceArticle

Was GW170817 a Canonical Neutron Star Merger? Bayesian Analysis with a Third Family of Compact Stars

by David Blaschke, Alexander Ayriyan, David Edwin Alvarez-Castillo and Hovik Grigorian

Universe 2020, 6(6), 81; https://doi.org/10.3390/universe6060081 - 10 Jun 2020

Cited by 72 | Viewed by 4330

Abstract

We investigate the possibility that GW170817 was not the merger of two conventional neutron stars (NS), but involved at least one if not two hybrid stars with a quark matter core that might even belong to a third family of compact stars. To [...] Read more.

We investigate the possibility that GW170817 was not the merger of two conventional neutron stars (NS), but involved at least one if not two hybrid stars with a quark matter core that might even belong to a third family of compact stars. To this end, we develop a Bayesian analysis method for selecting the most probable equation of state (EoS) under a set of constraints from compact star physics, which now also include the tidal deformability from GW170817 and the first result for the mass and radius determination for PSR J0030+0451 by the NICER Collaboration. We apply this method for the first time to a two-parameter family of hybrid EoS based on the DD2 model with nucleonic excluded volume for hadronic matter and the color superconducting generalized nlNJL model for quark matter. The model has a variable onset density for deconfinement and can mimic the effects of pasta phases with the possibility of producing a third family of hybrid stars in the mass-radius diagram. The main findings of this study are that: (1) the presence of multiple configurations for a given mass (twins or even triples) corresponds to a set of disconnected lines in the

Λ_{1}

–

Λ_{2}

diagram of tidal deformabilities for binary mergers, so that merger events from the same mass range may result in a probability landscape with different peak positions; (2) the Bayesian analysis with the above observational constraints favors an early onset of the deconfinement transition, at masses of

M_{onset} \leq 0.8 M_{⊙}

with an M–R relationship that in the range of observed neutron star masses is almost indistinguishable from that of a soft hadronic Akmal, Pandharipande, and Ravenhall (APR) EoS; (3) a few, yet fictitious measurements of the NICER experiment two times more accurate than the present value and a different mass and radius that would change the posterior likelihood so that hybrid EoS with a phase transition onset in the range

M_{onset}

= 1.1–1.6

M_{⊙}

would be favored. Full article

(This article belongs to the Special Issue Compact Stars in the QCD Phase Diagram and in the Multi-Messenger Era of Astronomy)

► Show Figures

Graphical abstract

24 pages, 7273 KiB

Open AccessReview

Observation of Atmospheric Neutrinos

by Yusuke Koshio

Universe 2020, 6(6), 80; https://doi.org/10.3390/universe6060080 - 5 Jun 2020

Cited by 2 | Viewed by 3737

Abstract

In 1998, the Super-Kamiokande discovered neutrino oscillation using atmospheric neutrino anomalies. It was the first direct evidence of neutrino mass and the first phenomenon to be discovered beyond the standard model of particle physics. Recently, more precise measurements of neutrino oscillation parameters using [...] Read more.

In 1998, the Super-Kamiokande discovered neutrino oscillation using atmospheric neutrino anomalies. It was the first direct evidence of neutrino mass and the first phenomenon to be discovered beyond the standard model of particle physics. Recently, more precise measurements of neutrino oscillation parameters using atmospheric neutrinos have been achieved by several detectors, such as Super-Kamiokande, IceCube, and ANTARES. In addition, precise predictions and measurements of atmospheric neutrino flux have been performed. This paper presents the history, current status, and future prospects of the atmospheric neutrino observation. Full article

(This article belongs to the Special Issue Neutrino Oscillations)

► Show Figures

Figure 1

70 pages, 5422 KiB

Open AccessArticle

Cosmological Spectrum of Two-Point Correlation Function from Vacuum Fluctuation of Stringy Axion Field in De Sitter Space: A Study of the Role of Quantum Entanglement

by Sayantan Choudhury and Sudhakar Panda

Universe 2020, 6(6), 79; https://doi.org/10.3390/universe6060079 - 5 Jun 2020

Cited by 15 | Viewed by 3142

Abstract

In this work, we study the impact of quantum entanglement on the two-point correlation function and the associated primordial power spectrum of mean square vacuum fluctuation in a bipartite quantum field theoretic system. The field theory that we consider is the effective theory [...] Read more.

In this work, we study the impact of quantum entanglement on the two-point correlation function and the associated primordial power spectrum of mean square vacuum fluctuation in a bipartite quantum field theoretic system. The field theory that we consider is the effective theory of axion field arising from Type IIB string theory compacted to four dimensions. We compute the expression for the power spectrum of vacuum fluctuation in three different approaches, namely (1) field operator expansion (FOE) technique with the quantum entangled state, (2) reduced density matrix (RDM) formalism with mixed quantum state and (3) the method of non-entangled state (NES). For a massless axion field, in all three formalisms, we reproduce, at the leading order, the exact scale invariant power spectrum which is well known in the literature. We observe that due to quantum entanglement, the sub-leading terms for these thee formalisms are different. Thus, such correction terms break the degeneracy among the analysis of the FOE, RDM and NES formalisms in the super-horizon limit. On the other hand, for massive axion field we get a slight deviation from scale invariance and exactly quantify the spectral tilt of the power spectrum in small scales. Apart from that, for massless and massive axion field, we find distinguishable features of the power spectrum for the FOE, RDM, and NES on the large scales, which is the result of quantum entanglement. We also find that such large-scale effects are comparable to or greater than the curvature radius of the de Sitter space. Most importantly, in near future if experiments probe for early universe phenomena, one can detect such small quantum effects. In such a scenario, it is possible to test the implications of quantum entanglement in primordial cosmology. Full article

(This article belongs to the Special Issue Cosmic String Theory and Observations)

► Show Figures

Figure 1

13 pages, 448 KiB

Open AccessArticle

Unified Description of Dark Energy and Dark Matter within the Generalized Hybrid Metric-Palatini Theory of Gravity

by Paulo M. Sá

Universe 2020, 6(6), 78; https://doi.org/10.3390/universe6060078 - 5 Jun 2020

Cited by 21 | Viewed by 2599

Abstract

The generalized hybrid metric-Palatini theory of gravity admits a scalar-tensor representation in terms of two interacting scalar fields. We show that, upon an appropriate choice of the interaction potential, one of the scalar fields behaves like dark energy, inducing a late-time accelerated expansion [...] Read more.

The generalized hybrid metric-Palatini theory of gravity admits a scalar-tensor representation in terms of two interacting scalar fields. We show that, upon an appropriate choice of the interaction potential, one of the scalar fields behaves like dark energy, inducing a late-time accelerated expansion of the universe, while the other scalar field behaves like pressureless dark matter that, together with ordinary baryonic matter, dominates the intermediate phases of cosmic evolution. This unified description of dark energy and dark matter gives rise to viable cosmological solutions, which reproduce the main features of the evolution of the universe. Full article

(This article belongs to the Section Cosmology)

► Show Figures

Figure 1

70 pages, 2792 KiB

Open AccessArticle

Black Hole as a Quantum Field Configuration

by Hikaru Kawai and Yuki Yokokura

Universe 2020, 6(6), 77; https://doi.org/10.3390/universe6060077 - 4 Jun 2020

Cited by 23 | Viewed by 12054

Abstract

We describe 4D evaporating black holes as quantum field configurations by solving the semi-classical Einstein equation

G_{μ ν} = 8 π G ⟨ ψ | T_{μ ν} | ψ ⟩

and quantum matter fields in a self-consistent manner. As the matter [...] Read more.

We describe 4D evaporating black holes as quantum field configurations by solving the semi-classical Einstein equation

G_{μ ν} = 8 π G ⟨ ψ | T_{μ ν} | ψ ⟩

and quantum matter fields in a self-consistent manner. As the matter fields, we consider N massless free scalar fields (N is large). We find a spherically symmetric self-consistent solution of the metric

g_{μ ν}

and the state

| ψ ⟩

. Here,

g_{μ ν}

is locally

A d S_{2} \times S^{2}

geometry, and

| ψ ⟩

provides

⟨ ψ | T_{μ ν} | ψ ⟩ = ⟨ 0 | T_{μ ν} | 0 ⟩ + T_{μ ν}^{(ψ)}

, where

| 0 ⟩

is the ground state of the matter fields in the metric and

T_{μ ν}^{(ψ)}

consists of the excitation of s-waves that describe the collapsing matter and Hawking radiation with the ingoing negative energy flow. This object is supported by a large tangential pressure

⟨ 0 | {T^{θ}}_{θ} | 0 ⟩

due to the vacuum fluctuation of the bound modes with large angular momenta

l ≫ 1

. This describes the interior of the black hole when the back reaction of the evaporation is taken into account. In this picture, the black hole is a compact object with a surface (instead of horizon) that looks like a conventional black hole from the outside and eventually evaporates without a singularity. If we count the number of configurations

{| ψ ⟩}

that satisfy the self-consistent equation, we reproduce the area law of the entropy. This tells that the information is carried by the s-waves inside the black hole.

| ψ ⟩

also describes the process that the negative ingoing energy flow created with Hawking radiation is superposed on the collapsing matter to decrease the total energy while the total energy density remains positive. Finally, as a special case, we consider conformal matter fields and show that the interior metric is determined by the matter content of the theory, which leads to a new constraint to the matter contents for the black hole to evaporate. Full article

(This article belongs to the Section Gravitation)

► Show Figures

Figure 1

19 pages, 348 KiB

Open AccessArticle

Symmetries, a Systematic Construction of Invariant Fields and AdS Backgrounds

by George Papadopoulos

Universe 2020, 6(6), 76; https://doi.org/10.3390/universe6060076 - 4 Jun 2020

Cited by 1 | Viewed by 1814

Abstract

We give a systematic local description of invariant metrics and other invariant fields on a spacetime under the action of a (non-abelian) group. This includes the invariant fields in a neighbourhood of a principal and a special orbit. The construction is illustrated with [...] Read more.

We give a systematic local description of invariant metrics and other invariant fields on a spacetime under the action of a (non-abelian) group. This includes the invariant fields in a neighbourhood of a principal and a special orbit. The construction is illustrated with examples. We also apply the formalism to give the R-symmetry invariant metrics of some AdS backgrounds and comment on applications to Kaluza-Klein theory. Full article

(This article belongs to the Section Field Theory)

10 pages, 313 KiB

Open AccessArticle

Invisible QCD as Dark Energy

by Andrea Addazi, Stephon Alexander and Antonino Marcianò

Universe 2020, 6(6), 75; https://doi.org/10.3390/universe6060075 - 31 May 2020

Cited by 3 | Viewed by 1984

Abstract

We account for the late time acceleration of the Universe by extending the Quantum Chromodynamics (QCD) color to a

S U (3)

invisible sector (IQCD). If the Invisible Chiral symmetry is broken in the early universe, a condensate of dark pions [...] Read more.

We account for the late time acceleration of the Universe by extending the Quantum Chromodynamics (QCD) color to a

S U (3)

invisible sector (IQCD). If the Invisible Chiral symmetry is broken in the early universe, a condensate of dark pions (dpions) and dark gluons (dgluons) forms. The condensate naturally forms due to strong dynamics similar to the Nambu–Jona-Lasinio mechanism. As the Universe evolves from early times to present times the interaction energy between the dgluon and dpion condensate dominates with a negative pressure equation of state and causes late time acceleration. We conclude with a stability analysis of the coupled perturbations of the dark pions and dark gluons. Full article

(This article belongs to the Special Issue Shedding Light to the Dark Sides of the Universe: Cosmology from Strong Interactions)

► Show Figures

Figure 1

15 pages, 275 KiB

Open AccessArticle

Semi-Classical Einstein Equations: Descend to the Ground State

by Zbigniew Haba

Universe 2020, 6(6), 74; https://doi.org/10.3390/universe6060074 - 29 May 2020

Viewed by 1845

Abstract

The time-dependent cosmological term arises from the energy-momentum tensor calculated in a state different from the ground state. We discuss the expectation value of the energy-momentum tensor on the right hand side of Einstein equations in various (approximate) quantum pure as well as [...] Read more.

The time-dependent cosmological term arises from the energy-momentum tensor calculated in a state different from the ground state. We discuss the expectation value of the energy-momentum tensor on the right hand side of Einstein equations in various (approximate) quantum pure as well as mixed states. We apply the classical slow-roll field evolution as well as the Starobinsky and warm inflation stochastic equations in order to calculate the expectation value. We show that, in the state concentrated at the local maximum of the double-well potential, the expectation value is decreasing exponentially. We confirm the descent of the expectation value in the stochastic inflation model. We calculate the cosmological constant Λ at large time as the expectation value of the energy density with respect to the stationary probability distribution. We show that

Λ ≃ γ^{\frac{4}{3}}

where γ is the thermal dissipation rate. Full article

(This article belongs to the Section Cosmology)

11 pages, 952 KiB

Open AccessArticle

Obscuration and Scattering in Narrow-Line Seyfert 1s

by Xiang Pan, Hongyan Zhou and Peng Jiang

Universe 2020, 6(6), 73; https://doi.org/10.3390/universe6060073 - 28 May 2020

Cited by 1 | Viewed by 1861

Abstract

Narrow-line Seyfert 1s (NLS1s) observed at large inclinations from face-on are important for understanding this amazing AGN subclass. However, progress is slowly being made in the huntings and studies of highly obscured (E_B–V ≥ 1) NLS1s. Recently, we discovered that multi-wavelength [...] Read more.

Narrow-line Seyfert 1s (NLS1s) observed at large inclinations from face-on are important for understanding this amazing AGN subclass. However, progress is slowly being made in the huntings and studies of highly obscured (E_B–V ≥ 1) NLS1s. Recently, we discovered that multi-wavelength photometric and polarimetric analysis can be of great help in identifying and studying highly obscured NLS1s. This paper presents an intercomparison study of three typical highly obscured NLS1s. By joint analysis of extinction, absorption lines, and scattered AGN radiation, properties of the nucleus (disk and broad emission line regions) are measured. Physical and geometrical conditions about circum-nucleus obscuring/scattering clouds are also estimated. In addition, the host galaxies which are usually difficult to observe in such high luminosity NLS1s are also revealed in these targets. The results show that obscuration and scattering can be powerful probes to obscured NLS1s. Analogues of these obscured NLS1s are found to widely exist. In addition, they will be followed up in our future works, so as to understand the nuclei, circum-nucleus clouds, and host galaxies of NLS1s. Full article

(This article belongs to the Special Issue Seyfert Galaxies Astrophysics)

► Show Figures

Figure 1

17 pages, 2791 KiB

Open AccessArticle

Numerical Investigation for Periodic Orbits in the Hill Three-Body Problem

by Vassilis S. Kalantonis

Universe 2020, 6(6), 72; https://doi.org/10.3390/universe6060072 - 28 May 2020

Cited by 21 | Viewed by 2364

Abstract

The current work performs a numerical study on periodic motions of the Hill three-body problem. In particular, by computing the stability of its basic planar families we determine vertical self-resonant (VSR) periodic orbits at which families of three-dimensional periodic orbits bifurcate. It is [...] Read more.

The current work performs a numerical study on periodic motions of the Hill three-body problem. In particular, by computing the stability of its basic planar families we determine vertical self-resonant (VSR) periodic orbits at which families of three-dimensional periodic orbits bifurcate. It is found that each VSR orbit generates two such families where the multiplicity and symmetry of their member orbits depend on certain property characteristics of the corresponding VSR orbit’s stability. We trace twenty four bifurcated families which are computed and continued up to their natural termination forming thus a manifold of three-dimensional solutions. These solutions are of special importance in the Sun-Earth-Satellite system since they may serve as reference orbits for observations or space mission design. Full article

(This article belongs to the Section Gravitation)

► Show Figures

Figure 1

20 pages, 362 KiB

Open AccessArticle

Cosmic Analogues of Classic Variational Problems

by Valerio Faraoni

Universe 2020, 6(6), 71; https://doi.org/10.3390/universe6060071 - 27 May 2020

Cited by 3 | Viewed by 2885

Abstract

Several classic one-dimensional problems of variational calculus originating in non-relativistic particle mechanics have solutions that are analogues of spatially homogeneous and isotropic universes. They are ruled by an equation which is formally a Friedmann equation for a suitable cosmic fluid. These problems are [...] Read more.

Several classic one-dimensional problems of variational calculus originating in non-relativistic particle mechanics have solutions that are analogues of spatially homogeneous and isotropic universes. They are ruled by an equation which is formally a Friedmann equation for a suitable cosmic fluid. These problems are revisited and their cosmic analogues are pointed out. Some correspond to the main solutions of cosmology, while others are analogous to exotic cosmologies with phantom fluids and finite future singularities. Full article

(This article belongs to the Section Cosmology)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Universe, Volume 6, Issue 6 (June 2020) – 17 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI