Geometric and thermodynamic properties in Gauss-Bonnet gravity

In this paper, the generalized second law (GSL) of thermodynamics and entropy is revisited in the context of cosmological models in Gauss-Bonnet gravity with the boundary of the universe is assumed to be enclosed by the dynamical apparent horizon. The model is best fitted with the observational data for distance modulus. The best fitted geometric and thermodynamic parameters such as equation of state parameter, deceleration parameter and entropy are derived. To link between thermodynamic and geometric parameters, the “entropy rate of change multiplied by the temperature” as a model independent thermodynamic state parameter is also derived. The results show that the model is in good agreement with the observational analysis.     

Plane symmetric inhomogeneous perfect fluid universe with electromagnetic field in Lyra geometry

A new class of plane-symmetric inhomogeneous cosmological models of perfect fluid distribution with electro-magnetic field based on Lyra’s geometry is obtained by considering a time dependent displacement field. The source of the magnetic field is due to an electric current produced along the z-axis. Only F ₁₂ is a non-vanishing component of electromagnetic field tensor. To get the deterministic solutions, the free gravitational field is assumed to be of Petrov type-II non-degenerate. It has been found that the displacement vector β(t) behaves like cosmological term Λ which is consistent with the recent observations of type Ia supernovae. It is also observed that β(t) affects entropy. Some geometric and physical behaviour of the models are also discussed in presence of magnetic field.      

Cyclical cosmo-thermodynamics

In this work, which is a supplemental to previous one, we undertake to establish some cosmological thermodynamic equations in the context of the cyclical universe as the scenario in which the universe itself is considered like an adiabatic thermodynamical system enclosed in physical volume characterized by periodic reversible transitions. Our model is based on the combination of local and global cosmological time-dependent temperatures {T ₀(τ ₀),T(τ)} and volumes {V ₀(τ ₀),V(τ)} instead of the critical temperature T _c and volume V _c; and the infinitesimal relative variations {dT/T,dV/V}, which are mainly due to the cosmological chaotic fluctuations that are generally ignored in certain oscillating models. By taking into account all these factors, certain equations in the form of d ℓ/ℓ=±η d τ/τ _H have been established and from them we derive some others to provide a mechanism that is responsible for the thermodynamic evolution of the cyclical universe.     

Time dependent viscous string cloud cosmological models

Bianchi type-I string cosmological models are studied in Saez-Ballester theory of gravitation when the source for the energy momentum tensor is a viscous string cloud coupled to gravitational field. The bulk viscosity is assumed to vary with time and is related to the scalar expansion. The relationship between the proper energy density ρ and string tension density λ are investigated from two different cosmological models.     

Anisotropic cosmological models with bulk viscosity for variable <Emphasis Type="Italic">G</Emphasis> and Λ

In this paper we have considered axially symmetric Bianchi-I, Kantowski Sachs and Bianchi-III space-time models with bulk viscosity, where the gravitational constant G and the cosmological term Λ vary with time. In Einstein equations this variation in G and Λ are taken in such a way as to preserve the energy momentum tensor. Solutions are obtained with the cosmological term varying inversely with square of time.     

Bianchi type-V cosmological model with perfect fluid using negative constant deceleration parameter in a scalar tensor theory based on Lyra Manifold

An exact Bianchi type-V perfect fluid cosmological model is obtained in a scalar tensor theory proposed by Sen (Z. Phys. 149:311, 1957) based on Lyra Manifold in case of β is a constant and it is shown that this cosmological model exists only in the case of Radiation Universe (ρ=3p) if β is a function of ‘t’ using negative constant deceleration parameter. Some physical and geometrical properties of these models are discussed.     

Accelerating universe with time variation of G and Λ

We study a gravitational model in which scale transformations play the key role in obtaining dynamical G and Λ. We take a non-scale invariant gravitational action with a cosmological constant and a gravitational coupling constant. Then, by a scale transformation, through a dilaton field, we obtain a new action containing cosmological and gravitational coupling terms which are dynamically dependent on the dilaton field with Higgs type potential. The vacuum expectation value of this dilaton field, through spontaneous symmetry breaking on the basis of anthropic principle, determines the time variations of G and Λ. The relevance of these time variations to the current acceleration of the universe, coincidence problem, Mach’s cosmological coincidence and those problems of standard cosmology addressed by inflationary models, are discussed. The current acceleration of the universe is shown to be a result of phase transition from radiation toward matter dominated eras. No real coincidence problem between matter and vacuum energy densities exists in this model and this apparent coincidence together with Mach’s cosmological coincidence are shown to be simple consequences of a new kind of scale factor dependence of the energy momentum density as ρ∼a ⁻⁴. This model also provides the possibility for a super fast expansion of the scale factor at very early universe by introducing exotic type matter like cosmic strings.     

Bianchi type I two-fluid cosmological models with a variable G and Λ

This paper presents anisotropic, homogeneous two-fluid cosmological models in a Bianchi type I space–time with a variable gravitational constant G and cosmological constant Λ. In the two-fluid model, one fluid represents the matter content of the universe and another fluid is chosen to model the CMB radiation. We find a variety of solutions in which the cosmological parameter varies inversely with time t. We also discuss in detail the behavior of associated fluid parameters and kinematical parameters. This paper pictures cosmic history when the radiation and matter content of the universe are in an interactive phase. Here, Ω is closing to 1 throughout the cosmic evolution.      

Cosmological models with time-varying gravitational and cosmological “constants”

The evolution and dynamics of a locally-rotationally-symmetric (LRS) Bianchi type-V space-time cosmological models are discussed with variable gravitational and cosmological “constants” in context of the particle creation. We present the exact solutions of Einstein field equations by using a power-law form of the average scale factor of the metric in the case of the particle creation and in the absence of particle creation. The solution describes the particle and entropy generation in the anisotropic cosmological models. The particle creation rate is uniquely determined by the variation of gravitational and cosmological “constants”. We observe that the variable gravitational constant does not necessarily imply particle creation. In a generic situation, models can be interpolated between different phases of the universe. The dynamical behaviors of the solutions and kinematical parameters of the model are discussed in detail.     

Full Causal Bulk Viscous LRS Bianchi I With Time Varying Constants

In this paper we study the evolution of a LRS Bianchi I Universe, filled with a bulk viscous cosmological fluid in the presence of time varying constants “but” taking into account the effects of a c-variable into the curvature tensor. We find that the only physical models are those which “constants” G and c are growing functions on time t, while the cosmological constant Λ is a negative decreasing function. In such solutions the energy density obeys the ultrastiff matter equation of state i.e. ω = 1.     

Entropy of viscous Universe models

The cosmological event horizon entropy and the apparent horizon entropy of the ΛCDM and the Bianchi type I Universe model with viscosity has been calculated numerically, and analytically in the large time limit. It is shown that for these Universe models the cosmological event horizon entropy increases with time and for large times it approaches a finite maximum value. The effect of viscosity upon the entropy is also studied and we have found that its role is to decrease the entropy. The bigger the viscosity coefficient is the less the entropy will be. Furthermore, the radiation entropy for the ΛCDM Universe model with and without viscosity is investigated, and together with the cosmological event horizon entropy are used to examine the validity of the generalized second law of thermodynamics, which states that the total rate of change of entropy of the Universe is never negative, in this Universe model.     

Cosmological scalar fields that mimic the ΛCDM cosmological model

We look for cosmologies with a scalar field (dark energy without cosmological constant), which mimic the standard ΛCDM cosmological model yielding exactly the same large-scale geometry described by the evolution of the Hubble parameter (i.e. photometric distance and angular diameter distance as functions on z). Asymptotic behavior of the field solutions is studied in the case of spatially flat Universe with pressureless matter and separable scalar field Lagrangians; the cases of power-law kinetic term and power-law potential are considered. Exact analytic solutions are found in some special cases. A number of models have the field solutions with infinite behavior in the past or even singular behavior at finite redshifts. We point out that introduction of the cosmological scalar field involves some degeneracy leading to lower precision in determination of Ω _m . To remove this degeneracy additional information is needed besides the data on large-scale geometry. The article is published in the original.     

(An)Isotropic models in scalar and scalar-tensor cosmologies

We study how the constants G and Λ may vary in different theoretical models (general relativity with a perfect fluid, scalar cosmological models (“quintessence”) with and without interacting scalar and matter fields and a scalar-tensor model with a dynamical Λ) in order to explain some observational results. We apply the program outlined in section II to study three different geometries which generalize the FRW ones, which are Bianchi V, VII₀ and IX, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we arrive at the conclusion that the solutions are isotropic and noninflationary while the cosmological constant behaves as a positive decreasing time function (in agreement with the current observations) and the gravitational constant behaves as a growing time function.     

Qualitative analysis of string cosmology with loop corrections. I

Homogeneous and Isotropic cosmological models of low-energy, string gravitation with loop corrections to the dilaton coupling functions are investigated by methods of the qualitative theory of dynamical systems. An ideal fluid with a barotropic equation of state is considered as the nongravitational source. In the general case of curved models, the cosmological equations are represented in the form of a third-order, autonomous, dynamical system. Phase portraits for different coupling functions are constructed for flat models. The asymptotic behavior of the general solution in limiting regions is investigated. The stabilization of the dilaton is analyzed using the Damour-Polyakov mechanism. Translated from Astrofizika, Vol. 42, No. 1, pp. 117–136, January–March, 1999.     

Massive cosmic strings in Bianchi type II

We study a massive cosmic strings with BII symmetries cosmological models in two contexts. The first of them is the standard one with a barotropic equation of state. In the second one we explore the possibility of taking into account variable “constants” (G and Λ). Both models are studied under the self-similar hypothesis. We put special emphasis in calculating the numerical values for the equations of state. We find that for ω∈(0,1], G, is a growing time function while Λ, behaves as positive decreasing time function. If ω=0, both “constants”, G and Λ, behave as true constants.     

Constraints on big bang models from structure formation

I review the constraints on standard big bang model arising from considerations related to structure formation. I will focus on two specific series of models though similar analysis can be performed for a wider class of models. The first one is a Ω = 1 model with non-zero cosmological constant and the second one is a Ω < 1 model with zero cosmological constant. The observational constraints which I shall discuss include the measurement of the Hubble’s constant, the ages of globular clusters, the abundance of rich clusters, the baryon content of galaxy clusters and the abundance of high redshift objects. These constraints limit the allowed range of the cosmological parameters and allow. for only a small region to survive. In particular, the aesthetically pleasing model with Ω = 1 and zero cosmological constant is ruled out by the observations. It seems necessary to fine-tune the theoretical parameters if they have to fall within the available space. This talk is based on the work in Baglaet al. (1996).     

Early Cosmological Models with Bulk Viscosity in Brans-Dicke Theory

The effect of time dependent bulk viscosity on the evolution of Friedmann models with zero curvature in Brans-Dicke theory is studied. The solutions of the field equations with ‘gamma-law’ equation of state p = (γ-1) ρ, where γ varies continuously as the Universe expands, are obtained by using the power-law relation φ = bR ⁿ , which lead to models with constant deceleration parameter. We obtain solutions for the inflationary period and radiation dominated era of the universe. The physical properties of cosmological solutions are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

A new class of bulk viscous universe with time dependent deceleration parameter and Λ-term

A new class of exact solutions of Einstein’s field equations with a bulk viscous fluid for an LRS Bianchi type-Ia obtained by using a time dependent deceleration parameter and cosmological term Λ. The coefficient of bulk viscosity is assumed to be a power function of mass density (ξ=ξ ₀ ρ ⁿ ). We have obtained a general solution of the field equations from which six models of the universe are derived: exponential, polynomial and sinusoidal form respectively. The behaviour of these models of the universe are also discussed in the frame of reference of recent supernovae Ia observations.      

Large-scale structure formation in cosmology with classical and tachyonic scalar fields

The evolution of scalar perturbations is studied for 2-component (non-relativistic matter and dark energy) cosmological models at the linear and non-linear stages. The dark energy is assumed to be the scalar field with either classical or tachyonic Lagrangian and constant equation-of-state parameter w. The fields and potentials were reconstructed for the set of cosmological parameters derived from observations. The comparison of the calculated within these models and observational large-scale structure characteristics is made. It is shown that for w = const such analysis can’t remove the existing degeneracy of the dark energy models. The article is published in the original.     

Dark energy models with anisotropic fluid in Bianchi Type-VI 0 space-time with time dependent deceleration parameter

We present two dark energy (DE) models with an anisotropic fluid in Bianchi type-VI ₀ space-time by considering time dependent deceleration parameter (DP). The equation of state (EoS) for dark energy ω is found to be time dependent and its existing range for derived models is in good agreement with the recent observations. Under the suitable condition, the anisotropic models approach to isotropic scenario. We also find that during the evolution of the universe, the EoS parameter for DE changes from ω>−1 to ω=−1 in first model whereas from ω>−1 to ω<−1 in second model which is consistent with recent observations. The cosmological constant Λ is found to be a positive decreasing function of time and it approaches a small positive value at late time (i.e. the present epoch) which is corroborated by results from recent type Ia supernovae observations. The cosmic jerk parameter in our derived models is also found to be in good agreement with the recent data of astrophysical observations. The physical and geometric aspects of both the models are also discussed in detail.