In this work, we have considered the power law correction of entropy on the horizon. If the flat FRW Universe is filled with the n components fluid with interactions, the GSL of thermodynamics for apparent and event horizons have been investigated for equilibrium and non-equilibrium cases. If we consider a small perturbation around the de Sitter space-time, the general conditions of the validity of GSL have been found. Also if a phantom dominated Universe has a polelike type scale factor, the validity of GSL has also been analyzed. Further we have obtained constraints on the power-law parameter α in the phantom and quintessence dominated regimes. Finally we obtain conditions under which GSL breaks down in a cosmological background.
In the present work we investigate the Hojman symmetry in FRW cosmology. In particular, we use the Hojman symmetry to find conserved quantities of particular cosmological models. Next, we study the Hojman symmetry in the scalar-tensor cosmology and find corresponding exact forms of integrals of motion. Finally, the formalism of the Hojman symmetry is extended to dynamical systems with the higher-order equations of motion.
In this thesis we will focus on Einstein's interpretation of gravity. We will examine how the most famous equations in cosmology are derived from GR and also some results of cosmological significance. We will see how combining that with observational data forces us to consider some form of dark energy or vacuum energy. So we will conclude with some of the more well-known models for dark energy and examine how the dynamics of dark energy can lead us to the so-called cosmological inflation.
Within the scope of a FRW cosmological model we have studied the role of spinor field in the evolution of the Universe when it is non-minimally coupled to the gravitational one. We have considered a few types of nonlinearity. It was found that if the spinor field nonlinearity describes an ordinary matter such as radiation, the presence of non-minimality becomes essential and leads to the rapid expansion of the Universe, whereas if the spinor field nonlinearity describes a dark energy, the evolution of the Universe is dominated by it and the difference between the minimal and non-minimally coup…
Present paper deals with flat Friedmann - Robertson - Walker (FRW) model with two - fluid source in fractal cosmology. In this model one fluid represents matter content of the universe and another fluid is radiation field modeling the cosmic microwave background. To get the deterministic model, we have used the relation between pressure and density for matter through the gamma law equation of state $p_{m} = (γ-1)\, ρ_{m}, \,\, 1\leq γ\leq2$ . The solutions of fractal field equations are obtained in terms of Kummer's confluent hypergeometric function of the first kind. Some physical parameters …
In this paper we study the effects of including anisotropic scaling invariance in the minisuperspace Lagrangian for a universe modelled by the Friedman-Robertson-Walker metric, a massless scalar field and cosmological constant. We find that canonical quantization of this system leads to a Schroedinger type equation, thus avoiding the frozen time problem of the usual Wheeler-DeWitt equation. Furthermore, we find numerical solutions for the classical equations of motion, and we also find evidence that under some conditions the big bang singularity is avoided in this model.
In this work, we present a phase space analysis of a spatially flat Friedmann $-$Robertson$-$Walker (FRW) model in which the dark matter fluid is modeled as an imperfect fluid having bulk viscosity. The bulk viscosity is governed by the Maxwell$-$Cattaneo approach. The rest of the components of the model: radiation and dark energy are treated as perfect fluids. Imposing a complete cosmological dynamics and taking into account a recent constraint on the dark matter equation of state (EOS), we obtain bound on the bulk viscosity. The results point towards the possibility of describing not only th…
A flat Fiedmann-Robertson-Walker (FRW) multi-scalar field cosmology is studied with a particular potential of the form $ \rm V(ϕ,σ)=V_0 e^{-λ_1 ϕ-λ_2 σ}$, which emerges as a relation between the time derivatives of the scalars field momenta. Classically, by employing the Hamiltonian formalism of two scalar fields $\rm(ϕ,σ)$ with standard kinetic energy, exact solutions are found for the Einstein-Klein-Gordon (EKG) system for different scenarios specified by the parameter $\rmλ^2=λ_1^2+λ_2^2$, as well as the e-folding function $\rm N_{e}$ which is also computed. For the quantum scheme of this m…
In an accelerated expanding universe, one can expect the existence of an event horizon. It may be interesting to study the thermodynamics of the Friedmann-Robertson-Walker (FRW) universe at the event horizon. Considering the usual Hawking temperature, the first law of thermodynamics does not hold on the event horizon. To satisfy the first law of thermodynamics, it is necessary to redefine Hawking temperature. In this paper, using the redefinition of Hawking temperature and applying the first law of thermodynamics on the event horizon, the Friedmann equations are obtained in f(R) gravity from t…
In this paper, we considered the study of Friedmann-Robertson-Walker (FRW) model in the framework of $f(Q,T)$ gravity, an extension of symmetric teleparallel gravity, recently defined by Y. Xu et al. \cite{Xu}. The non-linear model $f(Q,T)=-αQ-βT^2$, where $α>0$ and $β>0$ are constants, is taken into account. The equation of state of perfect fluid is assumed and 31 points of Hubble data are used to constrain the value of model parameter. To explore the evolution of the universe, the numerical solutions of cosmological implications such as Hubble parameter, deceleration parameter, apparent magn…
In this paper, we find exact string cosmological solutions for FRW cosmology, by using Hojman symmetry approach. The string cosmology under consideration includes a scalar field $ψ(t)$ with the potential $W(ψ)$, and a totally antisymmetric field strength $H_{μνρ}$ which is specifically defined in terms of the scale factor $a(t)$. We show that for this string cosmology, Hojman conserved quantities exist using which new exact solutions for the scale factor and the scalar field are obtained for specific potentials $W(ψ)$ with some free parameters. The presence of these parameters, together with t…
We present simple solutions of IKKT-type matrix models describing a quantized homogeneous and isotropic cosmology with $k=-1$, finite density of microstates and a resolved Big Bang. At late times, a linear coasting cosmology $a(t) \propto t$ is obtained, which is remarkably close to observation. The solution consists of two sheets with opposite intrinsic chiralities, which are connected in a Euclidean pre-big bang era.
By applying the unified first law of thermodynamics on the apparent horizon of FRW universe, we get the entropy relation for the apparent horizon in quasi-topological gravity theory. Throughout the paper, the results of considering the Hayward-Kodama and Cai-Kim temperatures are also addressed. Our study shows that whenever, there is no energy exchange between the various parts of cosmos, we can get an expression for the apparent horizon entropy in quasi-topological gravity, which is in agreement with other attempts followed different approaches. The effects of a mutual interaction between the…
We analyze the quantum supersymmetric cosmological FRW model with a scalar field, with a conditional probability density and the scalar field identified as time. The Hilbert space has a spinorial structure and there is only one consistent solution, with a conserved probability density. The dynamics of the scale factor is obtained from its mean value. The uncertainty relations are fulfilled and the corresponding fluctuations are consistent with a semiclassical Universe. We give two examples which turn out to have negative potential.
The Cosmological Problem is considered in a five-dimensional (bulk) manifold with two time coordinates, obeying vacuum Einstein field equations. The evolution formalism is used there, in order to get a simple form of the resulting constraints. In the spatially flat case, this approach allows to find out the general solution, which happens to consist in a single metric. All the embedded Friedmann-Robertson-Walker (FRW) metrics can be obtained from this 'mother' metric ('M-metric') in the bulk, by projecting onto different four-dimensional hypersurfaces (branes). Having a time plane in the bulk …
In this paper, we will study the rainbow deformation of the FRW cosmology in both Einstein gravity and Gauss-Bonnet gravity. We will demonstrate that the singularity in the FRW cosmology can be removed because of the rainbow deformation of the FRW metric. We will obtain the general constraints required for the FRW cosmology to be free from singularities. It will be observed that the inclusion of Gauss-Bonnet gravity can significantly change the constraints required to obtain a nonsingular universes. We will use a rainbow functions motivated from the hard spectra of gamma-ray bursts to deform t…
We study the quantum cosmology of a quadratic $f(R)$ theory with a FRW metric, via one of its equivalent Horndeski type actions, where the dynamics of the scalar field is induced. The classical equations of motion and the Weeler-deWitt equation, in their exact versions, are solved numerically. From the choice of a free parameter in the action follow two cases, inflation + exit and inflation alone. The numerical solution of the Wheeler-DeWitt equation depends strongly on the boundary conditions, which can be chosen so that the resulting wave function of the universe seems to be normalizable and…
We assume the non-flat Friedmann-Robertson-Walker (FRW) Universe as a thermodynamical system. We assume the cosmological horizon as a inner trapping horizon which is treated as dynamical apparent horizon of FRW Universe. We write the dynamical apparent horizon radius and temperature on the apparent horizon. We assume that the fluid pressure as thermodynamical pressure of the system. Using Hayward's unified first law, Clausius relation and Friedmann equations with cosmological constant, we obtain the entropy on the apparent horizon. We assume that the cosmological constant provides the thermody…
In this paper, we propose extended Chaplygin gas equation of state for which it recovers barotropic fluid with quadratic equation of state. We use numerical method to investigate the behavior of some cosmological parameters such as scale factor, Hubble expansion parameter, energy density and deceleration parameter. We also discuss about the resulting effective equation of state parameter. Using density perturbations we investigate the stability of the theory.
The Friedmann equation in the Friedmann-Robertson-Walker(FRW) universe with any spatial curvature is derived from the first law of thermodynamics on the event horizon. The key idea is to redefine a Hawking temperature on the event horizon. Furthermore, we obtain the evolution equations of the universe including the quantum correction and explore the evolution of the universe in the $f(R)$ gravity. In addition, we also investigate the generalized second law of thermodynamics in Einstein gravity and the $f(R)$ gravity. This perspective also implies that the first law of thermodynamics on the eve…
The partial Hamiltonian analysis of the Hořava-type action presented in the paper by M. Chaichian, S. Nojiri, S. D. Odintsov, M. Oksanen, A. Tureanu (Class. Quant. Grav. 27 (2011) 185021) is incorrect; for the authors' choice of variables, a covariant shift, instead of a contravariant shift which is the one usually used in General Relativity (GR) in ADM variables, the true algebra of constraints differs from what they presented. The algebra of constraints for their choice of variables is explicitly given for GR and compared with the standard algebra.
