Abstract and Figures
We probe into universes filled with quark gluon plasma with non-zero viscosities. In particular, we study the evolution of a universe with non-zero shear viscosity motivated by the theoretical result of a non-vanishing shear viscosity in the quark gluon plasma due to quantum-mechanical effects. We first review the consequences of a non-zero bulk viscosity and show explicitly the non-singular nature of the bulk-viscosity-universe by calculating the cosmological scale factor which goes to zero only asymptotically. The cosmological model with bulk viscosity is extended to include a cosmological constant. The previous results are contrasted with the cosmology with non-zero shear viscosity. We first clarify under which conditions shear viscosity terms are compatible with the Friedmann–Lamaître–Robertson–Walker metric. To this end we use a version of the energy–momentum tensor from the Müller–Israel–Stewart theory which leads to causal Navier–Stoke equations. We then derive the corresponding Friedmann equations and show under which conditions the universe emerges to be non-singular.
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... Due to its length, we do not reproduce it here and refer the interested reader to the original publication. The second example can be found in Ref. [406], where the relaxation time τ π proportional to the shear viscosity parameter η was used to study the evolution of the universe filled with QGP with nonzero shear viscosity. The authors argue that in general relativity, the following modification of the shear-stress tensor π µν → π µν + τ π u α π µν ;α + 4 3 π µν ∇ α u α = 2η ∇ µ u ν , π µν ;α ≡ ∂ α π µν + Γ µ αβ π βν + Γ ν αβ π µβ , ...
... where π µν ;α is a covariant derivative of π µν and Γ µ αβ are the Christoffel symbols, makes the resulting Navier-Stokes equations causal. Using the FLRW metric and taking into account that the compatibility with the isotropy and homogeneity of the universe demands π µν to be diagonal, the solution of Equation (A15) reads [406] π 00 (t) = π 00 (t 0 ) a(t 0 ) a(t) 4 e − t−t 0 τπ , π ij (t) = π ij (t 0 ) a(t 0 ) a(t) 6 e − t−t 0 τπ δ ij . ...
... In the Friedmann equations, the effect of the traceless viscosity tensor shows up in the modification of the initial energy density (t 0 ) and in the behavior of the energy density at times t t 0 + τ π , which at later times goes over to the standard expression [406] (t) = (t 0 ) + π 00 (t 0 ) a(t 0 ) a(t) 4 − π 00 (t 0 ) a(t 0 ) a(t) 4 e − t−t 0 τπ . ...
The wealth of theoretical and phenomenological information about Quantum Chromodynamics at short and long distances collected so far in major collider measurements has profound implications in cosmology. We provide a brief discussion on the major implications of the strongly coupled dynamics of quarks and gluons as well as on effects due to their collective motion on the physics of the early universe and in astrophysics.
... Some other results can be found in Refs. [31,32], where the role of bulk viscosity is studied in other contexts such as the radial oscillation of relativistic stars and the cosmological implications for universes filled with Quark-Gluon plasma. Recent studies show that bulk viscous cosmologies are not ruled out by the observational data at all. ...
... Finally, for the causality parameter, we obtain the best-fit ϵ = 0.34 ± 0.04, which is a value strongly incompatible with the condition ϵ = 1 considered in many works in the relation between τ and ρ. This highlights the importance of the expression (5) and the conditions (30) and (32) in the Israel-Stewart theory, conditions that ensure the causality of the theory and also lead to unique solutions with local existence. ...
In this work, we test the ability of an exact solution, found in the framework of a nonlinear extension of the Israel–Stewart theory, to fit the supernovae Ia, gravitational lensing, and black hole shadow data. This exact solution is a generalization of one previously found for a dissipative unified dark matter model in the context of the near-equilibrium description of dissipative processes, where we do not have the full regime of the nonlinear picture. This generalized solution is restricted to the case where a positive entropy production is guaranteed and is tested under the condition that ensures its causality, local existence, and uniqueness. From the observational constraints, we found that this generalized solution is a good candidate in the description of the observational late-time data used in this work, with best-fit values of H0=73.2−0.9+0.8km/sMpc, q0=−0.41−0.03+0.03, ξ^0=0.88−0.17+0.09, ϵ=0.34−0.04+0.03, and k=0.27−0.20+0.37, at a 1σ(68.3%) of confidence level. We show that the nonlinear regime of the Israel–Stewart theory consistently describes the recent accelerated expansion of the universe without the inclusion of some kind of dark energy component and also provides a more realistic description of the fluids that make up the late universe.
... These effects have also been studied concerning singularities such as the Big Rip and Little Rip, across both classical and quantum regimes [69,71,73,[101][102][103][104][105][106][107][108]. Further research has investigated the role of bulk viscosity in the radial oscillations of relativistic stars as well as its cosmological implications for Quark-Gluon plasma-filled universes [109,110]. ...
In this paper, we revisit the extension of the classical non-standard cosmological model in which dissipative processes are considered through a bulk viscous term in the new field ϕ, which interacts with the radiation component during the early universe. Specifically, we consider an interaction term of the form Γϕρϕ, where Γϕ represents the decay rate of the field and ρϕ denotes its energy density and a bulk viscosity described by ξ=ξ0ρϕ1/2, within the framework of Eckart’s theory. This extended non-standard cosmology is employed to explore the parameter space for the production of Feebly Interacting Massive Particles (FIMPs) as Dark Matter candidates, assuming a constant thermal averaged Dark Matter production cross-section (〈σv〉), as well as a preliminary analysis of the non-constant case. In particular, for certain combinations of the model and Dark Matter parameters, namely (Tend,κ) and (mχ,〈σv〉), where Tend corresponds to the temperature at which ϕ decays, κ is the ratio between the initial energy density of ϕ and radiation, and mχ is the Dark Matter mass, we identify extensive new parameter regions where Dark Matter can be successfully established while reproducing the currently observed relic density, in contrast to the predictions of ΛCDM and classical non-standard cosmological scenarios.
... This effects have also been studied concerning singularities such as the Big Rip and Little Rip, across both classical and quantum regimes [71,73,75,[103][104][105][106][107][108][109][110]. Further research has investigated the role of bulk viscosity in the radial oscillations of relativistic stars as well as its cosmological implications for Quark-Gluon plasmafilled universes [111,112]. Finally, bulk viscosity has also been proposed as an alternative to mitigate some of the recent tensions in the ΛCDM model. For instance, a decaying DM scenario increases the expansion rate relative to ΛCDM, potentially alleviating the H 0 and σ 8 tensions [113]. ...
In this paper, we revisited the extension of the classical non-standard cosmological model in which dissipative processes are considered through a bulk viscous term in the new field , which interacts with the radiation component during the early universe. Specifically, we consider an interaction term of the form , where represents the decay rate of the field and denotes its energy density, and a bulk viscosity described by , within the framework of Eckart's theory. This extended non-standard cosmology is employed to examine the parameter space for the production of Feebly Interacting Massive Particles (FIMPs) as Dark Matter candidates. In particular, for certain combinations of the model and Dark Matter parameters, namely (,) and , we found large new regions in which it can establish the Dark Matter and reproduce the current observable relic density as compared with the CDM and the classical non-standard cosmological scenarios.
... Other scenarios of interest can be found in Refs. [107,108], where the role of bulk viscosity is studied in the radial oscillation of relativistic stars and their cosmological implications for universes filled with Quark-Gluon plasma, respectively. Last but not least, bulk viscosity was also considered as an alternative to alleviate some recent tensions in the ΛCDM model. ...
In this paper, we explored an extension of the classical non-standard cosmological scenario in which the new field, , which interacts with the radiation component in the early universe, experiences dissipative processes in the form of a bulk viscosity. Assuming an interaction term given by , where accounts for the decay rate of the field and corresponds to its energy density, and a bulk viscosity according to the expression in the framework of Eckart's theory, we apply this novel non-standard cosmology to study the parameters space for WIMPs Dark Matter candidate production. This parameter space shows deviations from the classical non-standard cosmological scenario, obtaining new regions to search for this candidate. In particular, for certain combinations of the free parameters, we found large regions in which the model can establish the DM and reproduce the current observable relic density.
... It is quite remarkable that all hypermomentum variables have canceled out in the first Friedmann equation and in the end it retained its usual form. Furthermore we see that the acceleration equation have received a viscous term [62][63][64][65] that is exactly the one appearing in viscous cosmologies! Note that the term κσ has a clear interpretation as the bulk viscosity coefficient (up to numerical factors) Furthermore, differentiating (8.34) with respect to t and on using also (8.35), plugging all back at (8.31) we find the evolution equation for σ: 26 ...
We explore a new action formulation of hyperfluids, fluids with intrinsic hypermomentum. Brown's Lagrangian for a relativistic perfect fluid is generalised by incorporating the degrees of freedom encoded in the hypermomentum tensor, namely by including connection-matter couplings. Quite interestingly, generic hyperfluids are imperfect, since hypermomentum induces such effects as bulk and shear viscosities as well as heat fluxes. The various coefficients that appear in the first order expansion of hydrodynamics can now be deduced from a Lagrangian formulation, given a geometrical interpretation and a suggested microscopic description in terms of hypermomentum. This connection between hypermomentum and dissipative fluids could shed new light on the physics of relativistic hydrodynamics. The applicability of the new formalism is demonstrated by exact cosmological solutions.
... Viscous cosmology plays a pivotal role within the scientific community in the evolution of the universe. A few studies and reviews on viscous cosmological analysis are presented in [109][110][111][112][113][114]. In this context, bulk viscosity is attributed to space isotropy and shear viscosity is linked to space anisotropy. ...
In this work, we report a study on bouncing cosmology with modified generalized Chaplygin Gas (mgCG) in a bulk viscosity framework. Reconstruction schemes were demonstrated in Einstein and modified f(T) gravity framework under the purview of viscous cosmological settings. We also took non-viscous cases into account. We studied the equation of state (EoS) parameter under various circumstances and judged the stability of the models through the sign of the squared speed of sound. We observed the mgCG behaving like avoidance of Big Rip in the presence of bulk viscosity at the turnaround point and in non-viscous cases, a phantom-like behavior appears. The turnaround point equation of state parameter crosses the phantom boundary, violating NEC. The role of the mgCG’s model parameters was also investigated before and after the bounce. A Hubble flow dynamics was carried out and, it was revealed that mgCG is capable of realizing an inflationary phase as well as an exit from inflation. An f(T) gravitational paradigm was also considered, where the mgCG density was reconstructed in the presence of bulk viscosity. The role of the parameters associated with the bouncing scale factor, describing how fast the bounce takes place, was also studied in this framework. Finally, the reconstructed mgCG turned out to be stable against small perturbations irrespective of the presence of bulk viscosity and modified gravity scenario. Finally, the reconstruction scheme was assessed using statistical analysis, Shannon entropy.
In this paper, we explore an extension of the classical non-standard cosmological scenario in which the new field, ϕ, which interacts with the radiation component in the early universe, experiences dissipative processes in the form of a bulk viscosity. Assuming an interaction term given by Γ ϕ ρ ϕ , where Γ ϕ accounts for the decay rate of the field and ρ ϕ corresponds to its energy density, and a bulk viscosity according to the expression ξ=ξ 0 ρ ϕ ϕ1/2 in the framework of Eckart's theory, we apply this novel non-standard cosmology to study the parameters space for WIMPs Dark Matter candidate production. This parameter space shows deviations from the classical non-standard cosmological scenario, obtaining new regions to search for this candidate. In particular, for certain combinations of the free parameters, we found large regions in which the model can establish the DM and reproduce the current observable relic density.
We study the homogeneous and anisotropic evolution of Bianchi type-I spacetime driven by perfect fluid with shear viscosity. We obtain exact solutions by considering the simplest form of the equation of state wherein the pressure and the shear stress are proportional to the energy density individually. A special case of our general solutions represent Bianchi type-VII cosmology. We analyse the singularity structure of the solutions and its connection with various energy conditions. We find that the initial singularity can be removed only for the Bianchi type-VII. We also analyse the late-time behaviour of the solutions and find that, compared to the usual Friedmann universe, the spacetime expands less rapidly and the energy density drops faster.
Fluid dynamics is traditionally thought to apply only to systems near local equilibrium. In this case, the effective theory of fluid dynamics can be constructed as a gradient series. Recent applications of resurgence suggest that this gradient series diverges, but can be Borel resummed, giving rise to a hydrodynamic attractor solution which is well defined even for large gradients. Arbitrary initial data quickly approaches this attractor via nonhydrodynamic mode decay. This suggests the existence of a new theory of far-from-equilibrium fluid dynamics. In this Letter, the framework of fluid dynamics far from local equilibrium for a conformal system is introduced, and the hydrodynamic attractor solutions for resummed Baier-Romatschke-Son-Starinets-Stephanov theory, kinetic theory in the relaxation time approximation, and strongly coupled N=4 super Yang-Mills theory are identified for a system undergoing Bjorken flow.
The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. As a result over the past two decades there has been a huge theoretical and observational effort into improving our understanding of the Universe. The cosmological equations describing the dynamics of a homogeneous and isotropic Universe are systems of ordinary differential equations, and one of the most elegant ways these can be investigated is by casting them into the form of dynamical systems. This allows the use of powerful analytical and numerical methods to gain a quantitative understanding of the cosmological dynamics derived by the models under study. In this review we apply these techniques to cosmology. We begin with a brief introduction to dynamical systems, fixed points, linear stability theory, Lyapunov stability, centre manifold theory and more advanced topics relating to the global structure of the solutions. Using this machinery we then analyse a large number of cosmological models and show how the stability conditions allow them to be tightly constrained and even ruled out on purely theoretical grounds. We are also able to identify those models which deserve further in depth investigation through comparison with observational data. This review is a comprehensive and detailed study of dynamical systems applications to cosmological models focusing on the late-time behaviour of our Universe, and in particular on its accelerated expansion. In self contained sections we present a large number of models ranging from canonical and non-canonical scalar fields, interacting models and non-scalar field models through to modified gravity scenarios. Selected models are discussed in details and interpreted in the context of late-time cosmology.
Self interacting dark matter (SIDM) provides us with a consistent solution to certain astrophysical observations in conflict with collision-less cold DM paradigm. In this work we estimate the shear viscosity and bulk viscosity of SIDM, within kinetic theory formalism, for galactic and cluster size SIDM halos. To that extent we make use of the recent constraints on SIDM crossections for the dwarf galaxies, LSB galaxies and clusters. We also estimate the change in solution of Einstein's equation due to these viscous effects and find that constraints on SIDM from astrophysical data provide us with sufficient viscosity to account for the observed cosmic acceleration at present epoch, without the need of any additional dark energy component. Using the estimates of dark matter density for galactic and cluster size halo we find that the mean free path of dark matter few Mpc. Thus the smallest scale at which the viscous effect start playing the role is cluster scale. Astrophysical data for dwarf, LSB galaxies and clusters also seems to suggest the same. The entire analysis is independent of any specific particle physics motivated model for SIDM.
From a hydrodynamicist’s point of view the inclusion of viscosity concepts in the macroscopic theory of the cosmic fluid would appear most natural, as an ideal fluid is after all an abstraction (exluding special cases such as superconductivity). Making use of modern observational results for the Hubble parameter plus standard Friedmann formalism, we may extrapolate the description of the universe back in time up to the inflationary era, or we may go to the opposite extreme and analyze the probable ultimate fate of the universe. In this review, we discuss a variety of topics in cosmology when it is enlarged in order to contain a bulk viscosity. Various forms of this viscosity, when expressed in terms of the fluid density or the Hubble parameter, are discussed. Furthermore, we consider homogeneous as well as inhomogeneous equations of state. We investigate viscous cosmology in the early universe, examining the viscosity effects on the various inflationary observables. Additionally, we study viscous cosmology in the late universe, containing current acceleration and the possible future singularities, and we investigate how one may even unify inflationary and late-time acceleration. Finally, we analyze the viscosity-induced crossing through the quintessence-phantom divide, we examine the realization of viscosity-driven cosmological bounces, and we briefly discuss how the Cardy–Verlinde formula is affected by viscosity.
In this paper, we analyze the effects of thermal fluctuations on a STU black hole. We observe that these thermal fluctuations can affect the stability of a STU black hole. We will also analyze the effects of these thermal fluctuations on the thermodynamics of a STU black hole. Furthermore, in the Jacobson formalism such a modification will produce a deformation of the geometry of the STU black hole. Hence, we use the AdS/CFT correspondence to analyze the effect of such a deformation on the dual quark–gluon plasma. So, we explicitly analyze the effect of thermal fluctuations on the shear viscosity to entropy ratio in the quark–gluon plasma, and we analyze the effects of thermal fluctuations on this ratio.
It has been known for some time that the cosmological Friedmann equation deduced from General Relativity can be also obtained within the Newtonian framework under certain assumptions. We use this result together with quantum corrections to the Newtonian potentials to derive a set a of quantum corrected Friedmann equations. We examine the behavior of the solutions of these modified cosmological equations paying special attention to the sign of the quantum corrections. We find different quantum effects crucially depending on this sign. One such a solution displays a qualitative resemblance to other quantum models like Loop Quantum Gravity or non-commutative geometry.
Cosmological perturbations of sufficiently long wavelength admit a fluid
dynamic description. We consider modes with wavevectors below a scale for
which the dynamics is only mildly non-linear. The leading effect of modes above
that scale can be accounted for by effective non-equilibrium viscosity and
pressure terms. For mildly non-linear scales, these mainly arise from momentum
transport within the ideal and cold but inhomogeneous fluid, while momentum
transport due to more microscopic degrees of freedom is suppressed. As a
consequence, concrete expressions with no free parameters, except the matching
scale , can be derived from matching evolution equations to standard
cosmological perturbation theory. Two-loop calculations of the matter power
spectrum in the viscous theory lead to excellent agreement with N-body
simulations up to scales Mpc. The convergence properties in the
ultraviolet are better than for standard perturbation theory and the results
are robust with respect to variations of the matching scale.
Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.
This paper presents cosmological results based on full-mission Planck observations of temperature and polarization anisotropies of the cosmic microwave background (CMB) radiation. Our results are in very good agreement with the 2013 analysis of the Planck nominal-mission temperature data, but with increased precision. The temperature and polarization power spectra are consistent with the standard spatially-flat 6-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations (denoted "base ΛCDM" in this paper). From the Planck temperature data combined with Planck lensing, for this cosmology we find a Hubble constant, H0 = (67.8 ± 0.9) km s⁻¹Mpc⁻¹, a matter density parameter Ωm = 0.308 ± 0.012, and a tilted scalar spectral index with ns = 0.968 ± 0.006, consistent with the 2013 analysis. Note that in this abstract we quote 68% confidence limits on measured parameters and 95% upper limits on other parameters. We present the first results of polarization measurements with the Low Frequency Instrument at large angular scales. Combined with the Planck temperature and lensing data, these measurements give a reionization optical depth of τ = 0.066 ± 0.016, corresponding to a reionization redshift of \hbox{}. These results are consistent with those from WMAP polarization measurements cleaned for dust emission using 353-GHz polarization maps from the High Frequency Instrument. We find no evidence for any departure from base ΛCDM in the neutrino sector of the theory; for example, combining Planck observations with other astrophysical data we find Neff = 3.15 ± 0.23 for the effective number of relativistic degrees of freedom, consistent with the value Neff = 3.046 of the Standard Model of particle physics. The sum of neutrino masses is constrained to â'mν < 0.23 eV. The spatial curvature of our Universe is found to be very close to zero, with | ΩK | < 0.005. Adding a tensor component as a single-parameter extension to base ΛCDM we find an upper limit on the tensor-to-scalar ratio of r0.002< 0.11, consistent with the Planck 2013 results and consistent with the B-mode polarization constraints from a joint analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP B-mode data to our analysis leads to a tighter constraint of r0.002 < 0.09 and disfavours inflationarymodels with a V(φ) φ² potential. The addition of Planck polarization data leads to strong constraints on deviations from a purely adiabatic spectrum of fluctuations. We find no evidence for any contribution from isocurvature perturbations or from cosmic defects. Combining Planck data with other astrophysical data, including Type Ia supernovae, the equation of state of dark energy is constrained to w =-1.006 ± 0.045, consistent with the expected value for a cosmological constant. The standard big bang nucleosynthesis predictions for the helium and deuterium abundances for the best-fit Planck base ΛCDM cosmology are in excellent agreement with observations. We also constraints on annihilating dark matter and on possible deviations from the standard recombination history. In neither case do we find no evidence for new physics. The Planck results for base ΛCDM are in good agreement with baryon acoustic oscillation data and with the JLA sample of Type Ia supernovae. However, as in the 2013 analysis, the amplitude of the fluctuation spectrum is found to be higher than inferred from some analyses of rich cluster counts and weak gravitational lensing. We show that these tensions cannot easily be resolved with simple modifications of the base ΛCDM cosmology. Apart from these tensions, the base ΛCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets.
Unlike crushing singularities, the so-called Type IV finite-time singularity
offers the possibility that the Universe passes smoothly through it, without
any catastrophic effects. Then the question is if the effects of a Type IV
singularity can be detected in the process of cosmic evolution. In this paper
we address this question in the context of F(R) gravity. As we demonstrate,
the effects of a Type IV singularity appear in the Hubble flow parameters,
which determine the dynamical evolution of the cosmological system. So we study
various inflation models incorporating a Type IV singularity, with the
singularity occurring at the end of inflation. Particularly we study a toy
model and a singular version of the gravity Hubble rate. As we evince,
some of the Hubble flow parameters become singular at the singularity, an
effect which indicates that at that point a dynamical instability occurs. This
dynamical instability eventually indicates the graceful exit from inflation. We
demonstrate that the toy model has an unstable de Sitter point at the
singularity, so indeed graceful exit could be triggered. In the case of the
singular inflation model, graceful exit proceeds in the standard way. In the
case of the singular inflation model, we found various scenarios for singular
evolution, most of which are compatible with observations, and only one leads
to severe instabilities. We also compare the ordinary Starobinsky with the
singular inflation model, and we point out the qualitative and quantitative
differences. Finally, we study the late-time dynamics of the toy model and of
the singular inflation model and we demonstrate that the unification of early
and late-time acceleration can be achieved. We also show that it is possible to
achieve late-time acceleration similar to the -Cold Dark Matter model.