Friedmann Robertson Walker Cosmological Model Research Articles

Observable features of tachyon-dominated cosmology

A Friedmann–Robertson–Walker cosmological model dominated by tachyonic — faster-than-light — dark matter can exhibit features similar to those of a standard dark energy/dark matter or [Formula: see text]CDM model. It can undergo expansion which decelerates to a minimum rate, passes through a “cosmic jerk,” then accelerates. But some features of a tachyon-dominated model are sufficiently distinct from those of the Standard Model that the two possibilities might be distinguished observationally. As a demonstration of concept, the distance-redshift relation of such a model is compared here with some observations of Type Ia supernovae. Other measures of the third time derivative of the cosmic scale factor — the true cosmic jerk — might be found to test a tachyonic-dark-matter hypothesis.

Complete noncommutativity in a cosmological model with radiation

In order to try explaining the present accelerated expansion of the universe, we consider the most complete noncommutativity, of a certain type, in a Friedmann–Robertson–Walker cosmological model, coupled to a perfect fluid. We use the ADM formalism in order to write the gravitational Hamiltonian of the model and the Schutz’s formalism in order to write the perfect fluid Hamiltonian. The noncommutativity is introduced by four nontrivial Poisson brackets between all geometrical as well as matter variables of the model. Each nontrivial Poisson bracket is associated with a noncommutative parameter. We recover the description in terms of commutative variables by introducing four variables transformations that depend on the noncommutative parameters. Using those variables transformations, we rewrite the total noncommutative Hamiltonian of the model in terms of commutative variables. From the resulting Hamiltonian, we obtain the scale factor dynamical equations for a generic perfect fluid. In order to solve these equations, we restrict our attention to a model where the perfect fluid is radiation. The solutions depend on six parameters: the four noncommutative parameters, a parameter associated with the fluid energy C, and the curvature parameter k. They also depend on the initial conditions of the model variables. We compare the noncommutative solutions to the corresponding commutative ones and determine how the former ones differ from the latter ones. The comparison shows that the noncommutative model is very useful for describing the accelerated expansion of the universe. We also obtain estimates for one of the noncommutative parameters.

The non-minimal coupling constant and the primordial de Sitter state

Dynamical systems methods are used to investigate dynamics of a flat Friedmann–Robertson–Walker cosmological model with the non-minimally coupled scalar field and a potential function. Performed analysis distinguishes the value of non-minimal coupling constant parameter xi =frac{3}{16}, which is the conformal coupling in five dimensional theory of gravity. It is shown that for a monomial potential functions at infinite values of the scalar field there exist generic de Sitter and Einstein–de Sitter states. The de Sitter state is unstable with respect to expansion of the Universe for potential functions which do not change faster than linearly. This leads to a generic cosmological evolution without the initial singularity.

Exact solutions of a full causal bulk viscous FRW cosmological model with variable G and Λ through factorization

We study the classical flat full causal bulk viscous Friedmann–Robertson–Walker cosmological model with variable gravitational and cosmological constants through the factorization method. The method allows us to find some new exact parametric solutions. The assumptions made lead us to study two approaches. We find, in the studied cases, that the Universe ends in an accelerating era except in the case of a particular solution where the Universe could be noninflationary for all times. In both approaches the cosmological constant is a decreasing function of time, while the gravitational constant behaves as a growing or decreasing time function depending on the sign of Λ. By taking into account recent observations that indicate that Λ must be positive, we conclude that G increases with time except in the first solution where both “constants” tend asymptotically in the large time limit to a constant value. We also present a new factorization scheme that allows us to generate new solutions to a kind of variable-coefficient, nonlinear, second-order, ordinary differential equation.

Scenario of a two-fluid FRW cosmological model with dark energy

In this paper we carry out an investigation of the equation of state parameter for dark energy in the spatially homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model with barotropic fluid and dark energy. To get a deterministic model, we have assumed that the deceleration parameter (q) is a linear function of the Hubble parameter (H), i.e., \(q=\alpha + \beta H\), which yields the scale factor \(a= e^{\frac{1}{\beta}\sqrt{2\beta t+k_{1}}}\), where \(k_{1}\) is constant. The equation of state parameter for dark energy is a decreasing function of cosmic time in both interacting and non-interacting cases, and is always varying in the quintessence region for all cases. We have also discussed the jerk parameter for our models, and its value approaches that of the \(\Lambda\) CDM model at late times.

Chameleon scalar field in LRS Bianchi type I cosmological model

We consider an anisotropic cosmological model with cold dark matter and a scalar field, where one component of the scale factor is taken in the framework of (i) a logamediate scenario (ii) an intermediate scenario, and (iii) an emergent scenario. In all cases we find expressions for the Chameleon field, Chameleon potential, the statefinder diagnostic pair, i.e., the {r, s} parameters, and the slow-roll parameters. All physical parameters are calculated and discussed in all three cases. It is also shown how the Chameleon field is directly affected by the role of curvature of space time. At large times (t→∞) the models tend asymptotically to an isotropic Friedmann–Robertson–Walker cosmological model.

Holographic dark energy model with quintessence in general class of Bianchi cosmological models

In this paper, we study the general class of Bianchi cosmological models with holographic dark energy component. We have discussed three types of solutions of the average scale factor for the general class of Bianchi cosmological models by using a special law for the deceleration parameter, which is linear in time with a negative slope. The exact solutions to the corresponding field equations are also obtained. All the physical parameters are calculated and discussed in each physically viable cosmological model. For large time (i.e., t → ∞) the models tend asymptotically to an isotropic Friedmann–Robertson–Walker cosmological model. Quintessence scalar field and quintessence potential are also obtained for three different scenarios of scale factor.

General class of anisotropic cosmological models with dilaton and magnetic fields

The Einstein–Maxwell dilaton field equations are considered for four-dimensional anisotropic Bianchi models. The general solutions have been obtained and their properties have been discussed. The exact solutions to the corresponding field equations are obtained for two different physical viable cosmologies. The cosmological parameters have been discussed in detail and it is also shown that the solutions tend asymptotically to isotropic Friedmann–Robertson–Walker cosmological model.

Homotopy Perturbation Method for Solving a Spatially Flat FRW Cosmological Model

In the present paper, we study a homogeneous cosmological model in Friedmann-Robertson-Walker (FRW) space-time by means of the so-called Homotopy Perturbation Method (HPM). First, we briefly recall the main equations of the cosmological model and the basic idea of HPM. Next we consider the test example when the exact solution of the model is known, in order to approbate the HPM in cosmology and present the main steps in solving by this method. Finally, we obtain a solution for the spatially flat FRW model of the universe filled with the dust and quintessence when the exact solution cannot be found. A comparison of our solution with the corresponding numerical solution shows that it is of a high degree of accuracy.

An interacting two-fluid scenario for dark energy in anisotropic cosmological model

The open anisotropic cosmological model of the early Universe is considered. We study the evolution of the dark energy parameter within anisotropic Bianchi type-V cosmological model filled with barotropic fluid and dark energy. The solutions have been obtained for power law and exponential forms of the expansion parameter. (They correspond to constant deceleration parameter in general relativity.) For large time (i.e., t → ∞), the models tend asymptotically to an isotropic Friedmann–Robertson–Walker cosmological model under certain conditions.

FRW Cosmological Model with Modified Chaplygin Gas and Dynamical System

The Friedmann-Robertson-Walker (FRW) model with dynamical Dark Energy (DE) in the form of modified Chaplygin gas (MCG) has been investigated. The evolution equations are reduced to an autonomous system on the two dimensional phase plane and it can be interpreted as the motion of the particle in an one dimensional potential. Also the dynamical system analysis has been extended to examine the critical points at infinity with will exist provided the equation of state parameter \(\omega<-\frac{1}{3}\). Finally, theoretical points are asymptotically stable or unstable.

DARK ENERGY IN SOME INTEGRABLE AND NONINTEGRABLE FRW COSMOLOGICAL MODELS

One of the greatest challenges in today's cosmology to determine the nature of dark energy, the sourse of the observed present acceleration of the universe. Besides the vacuum energy, various dark energy models have been suggested. The Friedmann–Robertson–Walker (FRW) spacetime plays an important role in modern cosmology. In particular, the most popular models of dark energy work in the FRW spacetime. In this work, a new class of integrable FRW cosmological models is presented. These models induced by the well-known Painlevé equations. Some nonintegrable FRW models are also considered. These last models are constructed with the help of Pinney, Schrödinger and hypergeometric equations. Scalar field description and two-dimensional generalizations of some cosmological models are presented. Finally some integrable and nonintegrable F(R) and F(G) gravity models are constructed.

On Dynamics of Brans–Dicke Theory of Gravitation

We study longstanding problem of cosmological clock in the context of Brans–Dicke theory of gravitation. We present the Hamiltonian formulation of the theory for a class of spatially homogeneous cosmological models. Then, we show that formulation of the Brans–Dicke theory in the Einstein frame allows how an identification of an appropriate cosmological time variable, as a function of the scalar field in the theory, can be emerged in quantum cosmology. The classical and quantum results are applied to the Friedmann–Robertson–Walker cosmological models.

Structural instability of Friedmann–Robertson–Walker cosmological models

Cosmological singularity and asymptotic behaviour of scale factor of generalized cosmological models are analyzed in respect of their structural stability. It is shown, that cosmological singularity is structurally unstable for the majority of models with barotropic perfect fluid with strong energy condition. Inclusion of Lambda-term extends the set of structurally stable cosmological models.

Interacting cosmic fluids in power-law Friedmann–Robertson–Walker cosmological models

We provide a detailed description for power-law scaling Friedmann–Robertson–Walker cosmological scenarios dominated by two interacting perfect fluid components during the expansion. As a consequence of the mutual interaction between the two fluids, neither component is conserved separately and the energy densities are proportional to 1/t2. It is shown that in flat FRW cosmological models there can exist interacting superpositions of two perfect fluids (each of them having a positive energy density) which accelerate the expansion of the universe. In this family there also exist flat power-law cosmological scenarios where one of the fluids may have a “cosmological constant” or “vacuum energy” equation of state (p=−ρ) interacting with the other component; this scenario exactly mimics the behavior of the standard flat Friedmann solution for a single fluid with a barotropic equation of state. These possibilities of combining interacting perfect fluids do not exist for the non-interacting mixtures of two perfect cosmic fluids, where the general solution for the scale factor is not described by power-law expressions and has a more complicated behavior. In this study is considered also the associated single fluid model interpretation for the interaction between two fluids.

On the integrability of Friedmann–Robertson–Walker models with conformally coupled massive scalar fields

In this paper, we use a nonintegrability theorem by Morales and Ramis to analyse the integrability of Friedmann–Robertson–Walker cosmological models with a conformally coupled massive scalar field. We answer the long-standing question of whether these models with a vanishing cosmological constant and non-self-interacting scalar field are integrable: by applying Kovacic's algorithm to the normal variational equations, we prove analytically and rigorously that these equations and, consequently, the Hamiltonians are nonintegrable. We then address the models with a self-interacting massive scalar field and cosmological constant and show that, with the exception of a set of measure zero, the models are nonintegrable. For the spatially curved cases, we prove that there are no additional integrable cases other than those identified in the previous work based on the non-rigorous Painlevé analysis. In our study of the spatially flat model, we explicitly obtain a new possibly integrable case.

Mass Parameter Quantization in the FRW Cosmological Model

Using the canonical quantum theory apply to spherically symmetric pure gravitational systems, we present the study of the closed Friedmann-Robertson-Walker (FRW) cosmological model filled with pressureless matter (dust) content as a toy model. The Wheeler-DeWitt equation is view as the Schrodinger equation for the linear harmonic oscillator with energy E. We show that such type of universe has a quantized masses of the order of the Planck mass and harmonic oscillator wave functions, where a dual symmetry emerge among the quantum parameters.

The structure of the big bang from higher-dimensional embeddings

We give relations for the embedding of spatially-flat Friedmann–Robertson–Walker cosmological models of Einstein's theory in flat manifolds of the type used in Kaluza–Klein theory. We present embedding diagrams that depict different 4D universes as hypersurfaces in a higher-dimensional flat manifold. The morphology of the hypersurfaces is found to depend on the equation of state of the matter. The hypersurfaces possess a line-like curvature singularity infinitesimally close to the t = 0+ 3-surface, where t is the time expired since the big bang. The family of timelike comoving geodesics on any given hypersurface is found to have a caustic on the singular line, which we conclude is the 5D position of the point-like big bang.

COASTING COSMOLOGIES WITH TIME DEPENDENT COSMOLOGICAL CONSTANT

The effect of a time dependent cosmological constant is considered in a family of scalar-tensor theories. Friedmann–Robertson–Walker cosmological models for vacuum and perfect fluid matter are found. They have a linear expansion factor, the so-called coasting cosmology, the gravitational "constant" decreases inversely with time; that is these models satisfy the Dirac Hypotheses. The cosmological "constant" decreases inversely with the square of time, therefore we can have a very small value for it at present time.

Cosmological models

Two of the most common terms employed in discussing cosmological models are open and closed. They are occasionally misused either by not recognizing or by not making it clear that each term may be used to characterize, independently and simultaneously, both the dynamic behavior and spatial geometric structure of the model under discussion. In addition, the spatial geometric structure implied by the terms open and closed is itself often either misunderstood or misused. Lastly, the role played by the cosmological constant is often improperly slighted. This paper is intended to give several examples of the abuse of terminology and clarify the distinction by means of a brief, elementary overview of Friedmann–Robertson–Walker cosmological models.