Viscous cosmology in the Weyl-type f(Q, T) gravity

Bulk viscosity is the only viscous influence that can change the background dynamics in a homogeneous and isotropic universe. In the present work, we analyze the bulk viscous cosmological model with the bulk viscosity coefficient of the form $$\zeta =\zeta _0+\zeta _1H+\zeta _2\left( \frac{\dot{H}}{H}+H\right) $$ ζ = ζ 0 + ζ 1 H + ζ 2 H ˙ H + H where, $$\zeta _0$$ ζ 0 , $$\zeta _1$$ ζ 1 and $$\zeta _2$$ ζ 2 are bulk viscous parameters, and H is the Hubble parameter. We investigate the impact of the bulk viscous parameter on dynamics of the universe in the recently proposed Weyl-type f(Q, T) gravity, where Q is the non-metricity, and T is the trace of the matter energy–momentum tensor. The exact solutions to the corresponding field equations are obtained with the viscous fluid and the linear model of the form $$f(Q, T)=\alpha Q+\frac{\beta }{6\kappa ^2}T$$ f ( Q , T ) = α Q + β 6 κ 2 T , where $$\alpha $$ α and $$\beta $$ β are model parameters. Further, we constrain the model parameters using the 57 points Hubble dataset the recently released 1048 points Pantheon sample and the combination Hz + BAO + Pantheon, which shows our model is good congeniality with observations. We study the possible scenarios and the evolution of the universe through the deceleration parameter, the equation of state (EoS) parameter, the statefinder diagnostics, and the Om diagnostics. It is observed that the universe exhibits a transition from a decelerated to an accelerated phase of the universe under certain constraints of model parameters.

Stability Analysis of Bulk Viscous Cosmology

In this paper, we study phase space analysis of FRW universe model by taking a power-law model for bulk viscosity coefficient. An autonomous system of equations is developed by defining normalized dimensionless variables. We find corresponding critical points for di.erent values of the parameters to investigate stability of the system. It is found that the presence of power-law model of bulk viscosity appears as an e.ective ingredient to enhance the stability of the respective universe model.

Continuum perspective of bulk viscosity in compressible fluids

Kinetic theory and acoustic measurements have proven that the bulk viscosity associated with the expansion or compression effect cannot be ignored in compressible fluids except for monatomic gases. A new theoretical formula for the bulk viscosity coefficient (BVC) $\unicode[STIX]{x1D701}$ is derived by the continuum medium methodology, which provides a further understanding of the bulk viscosity, i.e. $\unicode[STIX]{x1D701}$ is equal to the product of the bulk modulus $K$ and the relaxation time $\unicode[STIX]{x1D70F}$ ($\unicode[STIX]{x1D701}=K\unicode[STIX]{x1D70F}$). The continuum and kinetic theories present consistent results from macro- and microperspectives respectively, only differing in terms of a coefficient. The theoretical predictions of the BVC in diatomic molecules, such as $\text{N}_{2}$, $\text{O}_{2}$ and CO, show good agreement with the experimental data over a wide range of temperature. In addition, the vibrational contributions to $\unicode[STIX]{x1D701}$ are controlled by a rapid exponential decrease at high temperatures, while at low temperatures a slow linear increase proceeds for the rotational cases. The relaxation time $\unicode[STIX]{x1D70F}$, collision number $Z$, BVC $\unicode[STIX]{x1D701}$ and ratio of bulk-to-shear viscosities $\unicode[STIX]{x1D701}/\unicode[STIX]{x1D707}$ in the vibrational mode are found to be several orders of magnitude larger than those in the rotational mode.

Thermodynamics of viscous matter and radiation in the early universe

Assuming that the background geometry is filled with a free gas consisting of matter and radiation and that no phase transitions are occurring in the early universe, we discuss the thermodynamics of this closed system using classical approaches. We find that essential cosmological quantities, such as the Hubble parameter H, scale factor a, and curvature parameter k, can be derived from this simple model. On one hand, it obeys the laws of thermodynamics entirely. On the other hand, the results are compatible with the Friedmann–Lemaitre–Robertson–Walker model and the Einstein field equations. The inclusion of a finite bulk viscosity coefficient derives important changes in all of these cosmological quantities. The thermodynamics of the viscous universe is studied and a conservation law is found. Accordingly, our picture of the evolution of the early universe and its astrophysical consequences seems to be the subject of radical revision. We find that the parameter k, for instance, strongly depends on the thermodynamics of the background matter. The time scale, at which a negative curvature might take place, depends on the relation between the matter content and the total energy. Using quantum and statistical approaches, we assume that the size of the universe is given by the volume occupied by one particle and one photon. Different types of interactions between matter and photon are taken into account. In this quantum treatment, expressions for H and a are also introduced. Therefore, the expansion of the universe turns out to be accessible.

Thermodynamics in the viscous early universe

Assuming that the matter in the background geometry is a free gas and that no phase transitions were occurring in the early Universe, we discuss the thermodynamics of this closed system using classical approaches. We find that essential cosmological quantities, such as the Hubble parameter H, the scaling factor a, and the curvature parameter k, can be derived from this simple model, which on one hand fulfills and entirely obeys the laws of thermodynamics, and on the other hand, its results are compatible with the Friedmann–Robertson–Walker model and the Einstein field equations. Including a finite bulk viscosity coefficient leads to important changes in all these cosmological quantities. Accordingly, our picture about the evolution of the Universe and its astrophysical consequences seems to undergoing a radical revision. We find that k strongly depends on the thermodynamics of background matter. The time scale at which negative curvature might take place depends on the relation between the matter content and the total energy. Using quantum and statistical approaches, we introduce expressions for H and the bulk viscosity coefficient ξ.

VISCOUS CARDASSIAN UNIVERSE

The viscous Cardassian cosmology is discussed, assuming that there is a bulk viscosity in the cosmic fluid. The dynamical analysis indicates that there exists a singular curve in the phase diagram of the viscous Cardassian model. In the viscous PL model, the equation-of-state parameter wk is no longer a constant and it can cross the cosmological constant divide wΛ = -1, in contrast with the same problem of the ordinary PL model. Other models possess similar characteristics. For MP and exp models, wk evolves more near -1 than the case without viscosity. The bulk viscosity also affects the virialization process of a collapse system in the universe: R vir /R ta is increasingly large when the bulk viscosity is increasing. In other words, the bulk viscosity retards the progress of the collapse system. In addition, we fit the viscous Cardassian models to current type Ia supernova data and give the best fit value of the model parameters, including the bulk viscosity coefficient τ.

FULL CAUSAL DISSIPATIVE COSMOLOGIES WITH STIFF MATTER

The general solution of the gravitational field equations for a full causal bulk viscous stiff cosmological fluid, with bulk viscosity coefficient proportional to the energy density to the power 1/4, is obtained in the flat Friedmann–Robertson–Walker geometry. The solution describes a non-inflationary Universe, which starts its evolution from a singular state. The time variation of the scale factor, deceleration parameter, viscous pressure, viscous pressure-thermodynamic pressure ratio, co-moving entropy and Ricci and Kretschmann invariants is considered in detail.