Isotropic Cosmological Models Research Articles

Exact solutions and particle creation for nonconformal scalar fields in homogeneous isotropic cosmological models

The problem is solved of describing scale factors of a homogeneous isotropic spaces-time such that the exact solution for the scalar field with a nonconformal coupling to curvature can be obtained from solutions for the conformally coupled field by redefining the mass and momentum. Explicit expressions for dependence of time from the large-scale factor are presented in the form of Abelian integrals in these cases. The exact solution for a scalar field with Gauss-Bonnet type coupling with curvature is received and it is shown that the corresponding nonconformal additions can dominate at the particles creation by gravitational field.

Bianchi Type II, VIII, and IX Perfect Fluid Dark Energy Cosmological Models in Saez-Ballester and General Theory of Gravitation

The paper deals with spatially homogeneous anisotropic Bianchi type II, VIII , and IX dark energy cosmological models filled with perfect fluid in the framework of Saez-Ballester (1986) theory, and Einstein's general relativity. Assuming that the two sources interact minimally and therefore their energy momentum tensors are conserved separately, we have considered different cases and presented anisotropic as well as isotropic cosmological models. Some important physical and geometrical features of the models, thus obtained, have been discussed.

Why Noether Symmetry of F(R) Theory Yields Three-Half Power Law?

Noether symmetry of F(R) theory of gravity in vacuum or in matter dominated era yields three-half power law of R. We show that this particular curvature invariant term is very special in the context of isotropic and homogeneous cosmological model as it makes the first fundamental form cyclic. As a result, it allows a unique power law solution, typical for this particular fourth order theory of gravity, both in the vacuum and in the matter dominated era. This power law solution has been found to be quite good to explain the early stage but not so special and useful to explain the late stage of cosmological evolution. The usefulness of Palatini variational technique in this regard has also been discussed.

Is there correlation between fine structure and dark energy cosmic dipoles?

We present a detailed analysis (including redshift tomography) of the cosmic dipoles in the Keck+VLT quasar absorber and in the Union2 SnIa samples. We show that the fine structure constant cosmic dipole obtained through the Keck+VLT quasar absorber sample at $4.1\sigma$ level is anomalously aligned with the corresponding dark energy dipole obtained through the Union2 sample at $2\sigma$ level. The angular separation between the two dipole directions is $11.3^\circ \pm 11.8^\circ$. We use Monte Carlo simulations to find the probability of obtaining the observed dipole magnitudes with the observed alignment, in the context of an isotropic cosmological model with no correlation between dark energy and fine structure constant $\alpha$. We find that this probability is less than one part in $10^6$. We propose a simple physical model (extended topological quintessence) which naturally predicts a spherical inhomogeneous distribution for both dark energy density and fine structure constant values. The model is based on the existence of a recently formed giant global monopole with Hubble scale core which also couples non-minimally to electromagnetism. Aligned dipole anisotropies would naturally emerge for an off-centre observer for both the fine structure constant and for dark energy density. This model smoothly reduces to \lcdm for proper limits of its parameters. Two predictions of this model are (a) a correlation between the existence of strong cosmic electromagnetic fields and the value of $\alpha$ and (b) the existence of a dark flow on Hubble scales due to the repulsive gravity of the global defect core (`Great Repulser') aligned with the dark energy and $\alpha$ dipoles. The direction of the dark flow is predicted to be towards the spatial region of lower accelerating expansion. Existing data about the dark flow are consistent with this prediction.

Conformal invariance, dark energy, and CMB non-gaussianity

In addition to simple scale invariance, a universe dominated by dark energy naturally gives riseto correlation functions possessing full conformal invariance. This is due to the mathematicalisomorphism between the conformal group of certain three dimensional slices of de Sitter spaceand the de Sitter isometry group SO(4,1). In the standard homogeneous, isotropic cosmologicalmodel in which primordial density perturbations are generated during a long vacuum energydominated de Sitter phase, the embedding of flat spatial ℝ3 sections in de Sitterspace induces a conformal invariant perturbation spectrum and definite prediction for the shapeof the non-Gaussian CMB bispectrum. In the case in which the density fluctuations are generatedinstead on the de Sitter horizon, conformal invariance of the \U0001d54a2 horizon embeddingimplies a different but also quite definite prediction for the angular correlations of CMB non-Gaussianityon the sky. Each of these forms for the bispectrum is intrinsic to the symmetries of de Sitter space,and in that sense, independent of specific model assumptions. Each is different from the predictionsof single field slow roll inflation models, which rely on the breaking of de Sitter invariance. Wepropose a quantum origin for the CMB fluctuations in the scalar gravitational sector from theconformal anomaly that could give rise to these non-Gaussianities without a slow roll inflaton field,and argue that conformal invariance also leads to the expectation for the relation nS−1 = nTbetween the spectral indices of the scalar and tensor power spectrum. Confirmation of this predictionor detection of non-Gaussian correlations in the CMB of one of the bispectral shape functions predictedby conformal invariance can be used both to establish the physical origins of primordial density fluctuations,and distinguish between different dynamical models of cosmological vacuum dark energy.

Bulk Viscosity and Decaying Vacuum Density in Friedmann Universe

We present an isotropic and homogeneous flat cosmological model for bulk viscous fluid distribution. We consider the vacuum density proportional to Hubble expansion parameter and time dependent bulk viscosity related to the velocity and acceleration of universe. The behaviour of resulting solutions are in accordance with recent astronomical observations. The model obtained evolves with a decelerating expansion followed by late time acceleration. Cosmological term Λ being very large at initial epoch relaxes to a genuine cosmological constant asymptotically. Presence of bulk viscosity prevents the matter density to vanish asymptotically and the matter density continues to be of the order of vacuum density after a finite time. Thus, we obtain a universe having the possibility of cosmic coincidence.

Qualitative study of perfect-fluid Friedmann-Lemaître-Robertson-Walker models with a cosmological constant

The evolution of spatially homogeneous and isotropic cosmological models containing a perfect fluid with equation of state p = wρ and a cosmological constant Λ is investigated for arbitrary combinations of w and Λ, using standard qualitative analysis borrowed from classical mechanics. This approach allows one to consider a large variety of situations, appreciating similarities and differences between models, without solving the Friedmann equation, and is suitable for an elementary course in cosmology.

Scalar field potentials for closed and open cosmological models

We develop a technique for the reconstruction of the potential for a scalar field or a tachyon field, reproducing a given cosmological evolution in a closed and open isotropic cosmological models. Such potentials are explicitly written down for the cases of the evolutions driven by a generic barotropic fluid and by radiation plus a cosmological constant, for the case of a scalar field. For tachyon and pseudo-tachyon fields the potentials are reconstructed for some special cases, corresponding to particular values of the barotropic index.

Evolution of homogeneous and isotropic scalar-tensor cosmological models

Homogeneous and isotropic cosmological models are considered in the framework of general scalar-tensor theories of gravity with arbitrary coupling function and scalar potential. Nonlinear approximate equations are derived for the regime close to the so-called limit of general relativity where the local observational constraints are satisfied. Approximate solutions in cosmological time are presented for the potential dominated era and for the era when the energy density of ordinary matter dominates over the energy density of scalar potential.

YANG-MILLS CONDENSATES IN COSMOLOGY

We discuss homogeneous and isotropic cosmological models driven by SU(2) gauge fields in the framework of Einstein gravity. There exists a Yang-Mills field configuration, parametrized by a single scalar function, which consists of parallel electric and magnetic fields and has the stress tensor mimicking an homogeneous and isotropic fluid. The unique SU(2) gauge theory with spontaneous symmetry breaking sharing the same property is the Yang-Mills coupled to the complex doublet Higgs, this exists only in the case of the closed universe. This model contains an intrinsic mechanism for inflation due to the Higgs potential. Our second goal is to show that a successful inflation can be achieved also within the pure Yang-Mills theory adding an appropriate theta-term.

Backreaction: directions of progress

Homogeneous and isotropic cosmological models with ordinary matter and gravity predict slower expansion and shorter distances than observed. It is possible that this failure is due the known breakdown of homogeneity and isotropy related to structure formation, rather than new fundamental physics. We review this backreaction conjecture, concentrating on topics on which there has been progress as well as open issues.

Scalar Field in Cosmology: Potential for Isotropization and Inflation

The important role of scalar field in cosmology was noticed by a number of authors. Due to the fact that the scalar field possesses zero spin, it was basically considered in isotropic cosmological models. If considered in an anisotropic model, the linear scalar field does not lead to isotropization of expansion process. One needs to introduce scalar field with nonlinear potential for the isotropization process to take place. In this paper the general form of scalar field potentials leading to the asymptotic isotropization in case of Bianchi type-I cosmological model, and inflationary regime in case of isotropic space-time is obtained. In doing so we solved both direct and inverse problem, where by direct problem we mean to find metric functions and scalar field for the given potential, whereas, the inverse problem means to find the potential and scalar field for the given metric function. The scalar field potentials leading to the inflation and isotropization were found both for harmonic and proper synchronic time.

A spatially homogeneous and isotropic Einstein–Dirac cosmology

We consider a spatially homogeneous and isotropic cosmological model where Dirac spinors are coupled to classical gravity. For the Dirac spinors we choose a Hartree–Fock ansatz where all one-particle wave functions are coherent and have the same momentum. If the scale function is large, the universe behaves like the classical Friedmann dust solution. If however the scale function is small, quantum effects lead to oscillations of the energy-momentum tensor. It is shown numerically and proven analytically that these quantum oscillations can prevent the formation of a big bang or big crunch singularity. The energy conditions are analyzed. We prove the existence of time-periodic solutions which go through an infinite number of expansion and contraction cycles.

Modelling background radiation in isotropic cosmologies

Using explicit perturbations of isotropic cosmological models which describe simple gravitational waves, an isotropic tensor having the algebraic symmetries of the Bel-Robinson tensor is derived as a model of cosmic background gravitational radiation and this is used to provide an answer to the question: in what sense can an energy-momentum-stress tensor similar to that describing the cosmic microwave background radiation (neglecting anisotropies) be associated with an isotropic background of gravitational radiation?

On a wave-particle in closed and open isotropic universes

The Klein–Gordon equation satisfied by the wave function in general relativity is solved for the metric of the closed and open universe corresponding to Einstein–De Sitter–Friedmann isotropic cosmological model. The angular dependences are specified by spherical harmonics for the longitude and latitude, and for the hyperlatitude by modified spherical harmonics having as variable circular functions for the closed universe and hyperbolic functions for the open universes. The time dependence of the probabilistic wave function is similar for the closed and open universes and is obtained in the following three cases: (I) constant Hubble parameter, (II) constant decceleration parameter, and (III) uniform matter and energy distribution, which corresponds to the Hubble parameter a linear function of time. Thus six solutions are obtained, namely, the three cases I–III each for closed and open isotropic universes. For each of these six solutions is considered: (i) the existence of singularities in space–time including asymptotic time in the future or past, (ii) the square integrability of the wave function over the full extent of the four-dimensional space–time, and (iii) the existence or otherwise of a positive probability density associated with the wave function.

W-cosmological singularities

In this paper we characterize barotropic index singularities of homogeneous isotropic cosmological models [M. P. Da\ifmmode \mbox{\c{}}\else \c{}\fi{}browski and T. Denkiewicz, Phys. Rev. D 79, 063521 (2009).]. They are shown to appear in cosmologies for which the scale factor is analytical with a Taylor series in which the linear and quadratic terms are absent. Though the barotropic index of the perfect fluid is singular, the singularities are weak, as it happens for other models for which the density and the pressure are regular.

FRW Cosmological Models with Bulk-Viscosity in Barber’s Second Self-Creation Theory

We have studied the evolution of spatially homogeneous and isotropic FRW cosmological model with bulk-viscosity in the frame work of Barber’s (Gen. Relativ. Gravit. 14: 117, 1982) second self-creation theory of gravitation. The cosmological models are obtained with the help of special law of variation for Hubble parameter proposed by Bermann (Nuovo Cimento 74B: 182, 1983). Physical parameters of the models have been discussed in case of false vacuum model, Zel’dovich fluid and radiation dominated fluid.

Zero mass scalar field with bulk viscous cosmological solutions in Lyra geometry

In this paper, we have investigated spatially homogeneous isotropic Friedmann cosmological model with bulk viscosity and zero-mass scalar field in Lyra manifold. The cosmological models are obtained with the help of the special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983) and power law relation. Some physical properties of the models are discussed.

ACCELERATED EXPANSION OF THE UNIVERSE THROUGH INTERACTIONS IN THE COSMIC SUBSTRATUM

Various homogeneous and isotropic cosmological models which describe the present stage of accelerated expansion of the Universe, like the ΛCDM model or (generalized) Chaplygin gas models, can be seen as specific realizations of a holographic dark energy cosmology if an interaction within the cosmic substratum is admitted. The corresponding interaction strength parameter determines the cosmological constant. The transition from decelerated to accelerated expansion arises as a pure interaction phenomenon. Different from the "standard" ΛCDM and Chaplygin gas models, the interaction based approach is characterized by non-adiabatic pressure perturbations.

F(R) Cosmology with torsion

f(R)-gravity with geometric torsion (not related to any spin fluid) is considered in a cosmological context. We derive the field equations in vacuum and in the presence of perfect-fluid matter and discuss the related cosmological models. Torsion vanishes in vacuum for almost all arbitrary functions f(R) leading to standard general relativity. Only for f(R)=R2, torsion gives a contribution in the vacuum leading to accelerated behavior. When material sources are considered, we find that the torsion tensor is different from zero even with spinless material sources. This tensor is related to the logarithmic derivative of f′ (R), which can be expressed also as a nonlinear function of the trace of the matter energy–momentum tensor Σμν. We show that the resulting equations for the metric can always be arranged to yield effective Einstein equations. When the homogeneous and isotropic cosmological models are considered, terms originated by torsion can lead to accelerated expansion. This means that, in f(R)-gravity, torsion can be a geometric source for acceleration.