Curvature Inspired Cosmological Scenario

Using modified gravity with non-linear terms of curvature, R ² and R ^(2+r) (with r being a positive real number and R being the scalar curvature), cosmological scenario, beginning at the Planck scale, is obtained. Here a unified picture of cosmology is obtained from f(R)-gravity. In this scenario, universe begins with power-law inflation followed by deceleration and acceleration in the late universe as well as possible collapse of the universe in future. It is different from f(R)-dark energy models with non-linear curvature terms assumed as dark energy. Here, dark energy terms are induced by linear as well as non-linear terms of curvature in Friedmann equation being derived from modified gravity. It is also interesting to see that, in this model, dark radiation and dark matter terms emerge spontaneously from the gravitational sector. It is found that dark energy, obtained here, behaves as quintessence in the early universe and phantom in the late universe. Moreover, analogous to brane-tension in brane-gravity inspired Friedmann equation, a tension term λ arises here being called as cosmic tension, It is found that, in the late universe, Friedmann equation (obtained here) contains a term −ρ ²/2λ (ρ being the phantom energy density) analogous to a similar term in Friedmann equation with loop quantum effects, if λ>0 and brane-gravity correction when λ<0.     

Phantom cosmology with non-minimally coupled real scalar field

We find that the expansion of the universe is accelerating by analyzing the recent observation data of type Ia supernova (SN-Ia). It indicates that the equation of state of the dark energy might be smaller than -1, which leads to the introduction of phantom models featured by its negative kinetic energy to account for the regime of equation of state parameter w < -1. In this paper the possibility of using a non-minimally coupled real scalar field as phantom to realize the equation of state parameter w < -1 is discussed. The main equations which govern the evolution of the universe are obtained. Then we rewrite them with the observable quantities.     

D = 1 Supergravity and Quantum Cosmology

Using a D = 1 supergravity framework I construct a super-Friedmann equation for an isotropic and homogenous universe including dynamical scalar fields. In the context of quantum theory this becomes an equation for a wave function of the universe of spinorial type, the Wheeler–DeWitt–Dirac equation. It is argued that a cosmological constant breaks a certain chiral symmetry of this equation, a symmetry in the Hilbert space of universe states, which could protect a small cosmological constant from being affected by large quantum corrections.

     

The Solution of Tachyon Inflation in Curved Universe

In this paper, we have considered the curved universe which is filled by tachyonic field. We have found the exact solutions for the field, pressure, density, and scale factor and some cosmological parameters. In such universe, we have investigated the role of tachyonic field in different stages of k for the evolution of the universe. Finally we draw the graphs for the scale factor, Hubble’s parameter, energy density, pressure, acceleration parameter, equation of state and potential for the different values of k. Also we obtained the exact form of field which shows that the tachyonic field has the kink form.     

New mechanism to cross the phantom divide

Recently, type Ia supernova data appear to support a dark energy whose equation of state w crosses −1, which is a much more amazing problem than the acceleration of the universe. We show that it is possible for the equation of state to cross the phantom divide by a scalar field in gravity with an additional inverse power-law term of the Ricci scalar in the Lagrangian. The necessary and sufficient condition for a universe in which the dark energy can cross the phantom divide is obtained. Some analytical solutions with w<−1 or w>−1 are obtained. A minimally coupled scalar with different potentials, including quadratic, cubic, quantic, exponential and logarithmic potentials are investigated via numerical methods, respectively. All these potentials lead to the crossing behavior. We show that it is a robust result which is hardly dependent on the concrete form of the potential of the scalar.     

Holographic Dark Energy in a Non-flat Universe with Granda-Oliveros Cut-off

Motivated by Granda and Oliveros (GO) model, we generalize their work to the non-flat case. We obtain the evolution of the dark energy density, the deceleration and the equation of state parameters for the holographic dark energy model in a non-flat universe with GO cut-off. In the limiting case of a flat universe, i.e. k=0, all results given in GO model are obtained.     

Investigation of the problem of singularities in general relativity

Recently Addy and Datta have obtained a linearized solution for isentropic motions of a perfect fluid by assigning Cauchy data on the hypersurfacex ⁴=0 and by imposing a restriction on the equation of state. In the present paper we pursue this study and discuss the problem of singularities from the standpoint of a local observer for which a singularity is defined as a state with an infinite proper rest mass density. It is shown that for a closed universe with any distribution of matter whatsoever there occurred a singularity in the past in the nonrotating parts of the universe and it must recur in the future. Furthermore, the collapse of a rotating fluid to a singularity seems inevitable when the relativistic equation of state is considered.     

Study of Thermodynamic Quantities in Generalized Gravity Theories

In this work, we have studied the thermodynamic quantities like temperature of the universe, heat capacity and squared speed of sound in generalized gravity theories like Brans-Dicke, Hořava-Lifshitz and f(R) gravities. We have considered the universe filled with dark matter and dark energy. Also we have considered the equation of state parameters for open, closed and flat models. We have observed that in all cases the equation of state behaves like quintessence. The temperature and heat capacity of the universe are found to decrease with the expansion of the universe in all cases. In Brans-Dicke and f(R) gravity theories the squared speed of sound is found to exhibit increasing behavior for open, closed and flat models and in Hořava-Lifshitz gravity theory it is found to exhibit decreasing behavior for open and closed models with the evolution of the universe. However, for flat universe, the squared speed of sound remains constant in Hořava-Lifshitz gravity.     

Growing Classical and Quantum Entropies in the Early Universe

Following the idea that the global and local arrow of time has a cosmological origin, we define an entropy in the classical and in the quantum periods of the universe evolution. For the quantum period a semi-classical approach is adopted, modelling the universe with Wheeler-De Witt equation and using WKB. By applying the self-induced decoherence to the state of the universe it is proved that the quantum universe becomes a classical one. This allows us to define a conditional entropy which, in our simplified model, is proportional to e ^{2γ t} where γ is the dumping factor associated with the interaction potential of the scalar fields. Finally we find both Gibbs and thermodynamical entropy of the universe based in the conditional entropy.     

Quantization of closed mini-superspace models as bound states

The Wheeler-DeWitt equation is applied to closedk>0 Friedmann-Robertson-Walker metric with various combination of cosmological constant and matter (e.g., radiation or pressureless gas). It is shown that if the universe ends in the matter dominated era (e.g., radiation or pressureless gas) with zero cosmological constant, then the resulting Wheeler-DeWitt equation describes a bound state problem. As solutions of a nondegenerate bound state system, the eigen-wave functions are real (Hartle-Hawking). Furthermore, as a bound state problem, there exists a quantization condition that relates the curvature of the three space with the various energy densities of the universe. If we assume that our universe is closed, then the quantum number of our universe isN(Gk)^–110¹²². The largeness of this quantum number is naturally explained by an early inflationary phase which resulted in a flat universe we observe today. It is also shown that if there is a cosmological constant >0 in our universe that persists for all time, then the resulting Wheeler-DeWitt equation describes a non-bound state system, regardless of the magnitude of the cosmological constant. As a consequence, the wave functions are in general complex (Vilenkin).     

Bianchi type-V model with a perfect fluid and A-term

A self-consistent system of gravitational field with a binary mixture of perfect fluid and dark energy given by a cosmological constant has been considered in Bianchi Type-V universe. The perfect fluid is chosen to be obeying either the equation of state p=γρ with γ ε |0,1| or a van der Waals equation of state. The role of A-term in the evolution of the Bianchi Type-V universe has been studied.     

充满物质的Friedmann-Robertson-Walker宇宙的稳定性

研究了在含有宇宙(学)常数的Friedmann-Robertson-Walker宇宙模型中,充满、满足p=(γ-1)ρ物质宇宙的稳定性.通过计算引力波的扰动,以及dp/dp=γ-1的扰动,得到对于ε=-1,Λ<0,满足Einstein场方程的宇宙只要γ≥0是不稳定的. 关键词： 充满物质的Friedmann-Robertson-Walker宇宙 虫洞 时空稳定性     

Brans-Dicke cosmological exact solution in a radiation-filled Robertson-Walker universe

Considering a Robertson-Walker line element, exact solutions are obtained for radiation-filled cosmological differential equations of Brans-Dicke theory with the assumption that the radius of curvatureQ of the universe varies directly as thenth power of time. The solution is found to be valid for closed space only and the coupling constantw of the scalar tensor theory is necessarily negative. The radius of curvature of increases linearly with respect to the age of the universe, while the gravitational constantk varies directly as the square of the radius of the universe. The solution obtained is in contradiction to Dirac's hypothesis, in which the gravitational constant should decrease with time in an expanding universe.     

Stochastic evolution of cosmological parameters in the early universe

We develop a stochastic formulation of cosmology in the early universe, after considering the scatter in the redshift-apparent magnitude diagram in the early epochs as an observational evidence for the non-deterministic evolution of early universe. We consider the stochastic evolution of density parameter in the early universe after the inflationary phase qualitatively, under the assumption of fluctuating w factor in the equation of state, in the Fokker-Planck formalism. Since the scale factor for the universe depends on the energy density, from the coupled Friedmann equations we calculated the two variable probability distribution function assuming a flat space geometry.     

Bianchi type III models with anisotropic dark energy

The general form of the anisotropy parameter of the expansion for Bianchi type-III metric is obtained in the presence of a single diagonal imperfect fluid with a dynamically anisotropic equation of state parameter and a dynamical energy density in general relativity. A special law is assumed for the anisotropy of the fluid which reduces the anisotropy parameter of the expansion to a simple form (D μ H^-2V^-2{\Delta\propto H^{-2}V^{-2}}, where Δ is the anisotropy parameter, H is the mean Hubble parameter and V is the volume of the universe). The exact solutions of the Einstein field equations, under the assumption on the anisotropy of the fluid, are obtained for exponential and power-law volumetric expansions. The isotropy of the fluid, space and expansion are examined. It is observed that the universe can approach to isotropy monotonically even in the presence of an anisotropic fluid. The anisotropy of the fluid also isotropizes at later times for accelerating models and evolves into the well-known cosmological constant in the model for exponential volumetric expansion.     

Bubble dynamics in the expanding universe

Using the Gauss-Codazzi equations, the behavior of a singular hypersurface, which divides the universe into two Friedmann-Robertson-Walker space-time regionsV ⁺ andV ^–, is investigated. The equation of motion for a spherical bubble in the expanding universe is presented and the physical meaning of the equation is clarified. The equations of state for fluids inV ^± and on the boundary shell, which should be determined by microscopic physics, are arbitrary in the present geometrical approach. The derived equations are quite similar to those for a shell in a vacuum and can be applied to the case that one ofV ^± or both are Schwarzschild-de Sitter space-time too.     

Emergent Scenario and Different Anisotropic Models

In this work, Emergent Universe scenario has been developed in general homogeneous anisotropic model and for the inhomogeneous LTB model. In the first case, it is assumed that the matter in the universe has two components—one is perfect fluid with barotropic equation of state p=ωρ (ω, a constant) and the other component is a real or phantom (or tachyonic) scalar field. In the second case, the universe is only filled with a perfect fluid and possibilities for the existence of emergent scenario has been examined.     

Classical stochastic approach to cosmology revisited

The classical stochastic model of cosmology recently developed by us is reconsidered. In that approach the parameterw defined by the equation of statep = wp was taken to be fluctuating with mean zero and we compared the theoretical probability distribution function (PDF) for the Hubble parameter with observational data corresponding to a universe with matter and vacuum energy. Even though qualitative agreement between the two was obtained, an attempt is herein made to introduce a more realistic assumption for the mean ofw and use it for the calculations. In the present theory the mean values of bothp andw are taken to be nonzero. The theoretical and observational PDFs are compared for different epochs and values of the Hubble parameter. The corresponding values of the diffusion constantD obtained are approximately constant. We use the scatter in the observed redshift-magnitude data of Type Ia supernova to place limits on the stochastic variation in expansion rate and consequently, on the stochastic variation of the equation of state.     

Emergent Universe in Einstein-Gauss-Bonnet Theory

In this work, Emergent Universe scenario has been developed in Einstein-Gauss-Bonnet (EGB) theory. The universe is chosen as homogeneous and isotropic FRW model and the matter in the universe has two components—the first one is a perfect fluid with barotropic equation of state p=ω ρ (ω, a constant) and the other component is a real or phantom (or tachyonic) scalar field. Various possibilities for the existence of emergent scenario has been discussed and the results are compared with those in Einstein gravity.