Narrow Results

Using the proper time description and the usual cosmological observer field, it is possible to construct general space–time metrics representing a class of shearfree cosmological models.

Recent advances in string theory and inflationary cosmology have led to a surge of interest in the possible existence of an ensemble of cosmic regions, or "universes", among the members of which key physical parameters, such as the masses of elementary particles and the coupling constants, might assume different values. The observed values in our cosmic region are then attributed to an observer selection effect (the so-called anthropic principle). The assemblage of universes has been dubbed "the multiverse". In this paper we review the multiverse concept and the criticisms that have been advanced against it on both scientific and philosophical grounds.

Cosmological models in Lyra's geometry are constructed and investigated with the assumption of a minimal interaction of matter with the displacement vector field and the dynamical Λ-term. Exact solutions of the model equations are obtained for the different equations of state of the matter, that fills the universe, and for the certain assumptions on the decaying law for Λ.

We propose a model of the Universe based on Minkowski flat spacetime metric. In this model the spacetime does not evolve. Instead the matter evolves such that all the mass parameters increase with time. We construct a model based on unimodular gravity to show how this can be accomplished within the framework of flat spacetime. We show that the model predicts the Hubble law if the masses increase with time. Furthermore, we show that it fits the high z supernova data in a manner almost identical to the standard Big Bang model. Furthermore, we show that at early times the Universe is dominated by radiative energy density. The phenomenon of recombination also arises in our model and hence predicts the existence of CMBR. However, a major difference with respect to the standard Big Bang is that there is no initial singularity and the radiative temperature and energy density do not evolve in our model. Furthermore, we argue that the basic motivation for inflation is absent in our model.

Specific dark energy models, leading to the Little Rip (LR) cosmology in the far future, are investigated. Conditions for the occurrence of LR in terms of the parameters present in the proposed equation of state for the dark energy cosmic fluid are studied. Estimates about the time needed before the occurrence of the small singularity in the standard LR model in which the universe approaches the de Sitter spacetime asymptotically, are given.

We propose a new type of cosmological model derived from the fractional variational principle when it is applied to the gravitational sector of action functional. In contrast to the fractional cosmological model developed earlier by the author from a fractional total action, in our new model the continuity equation remains valid in its usual form. For this model, a lot of exact solutions are obtained from a specific ansatz which is proposed for the cosmological term in this paper. Several examples arising from the given variations of the Hubble parameter with time are provided. Besides, we suggest an original interpretation of the main equations for our model. It supposes that the effective cosmological term could arise as a result of kinematical induction through the nonzero Hubble parameter. With the help of particular example, we demonstrate how this approach could lead our model quite closer to the real behavior of the universe.

In this brief review, we present the results of the fractional differential approach in cosmology in the context of the exact models of cosmological accelerated expansion obtained by several authors to date. Most of these studies are devoted to the problem of introducing fractional derivatives or fractional integrals into the classical General Relativity (GR). There are several observational and theoretical motivations to investigate the modified or alternative theories of GR. Among other things, we cover General Relativity modified by a phenomenological approach dealing with fractional calculus. At the same time, a sufficiently large number of exact solutions of the cosmological equations modified by this approach were obtained. Some of these models may be especially relevant in the light of solving the problem of late accelerated expansion of the Universe. These studies are largely motivated by rapid progress in the field of observational cosmology that now allows, for the first time, precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole.

In this paper, we study the Chaplygin gas equation in curvature-matter coupling gravity to describe the observed expansion of the universe. We consider the Chaplygin gas equation of state in terms of the energy density $\rho$ and pressure $p$, by the relationship $p=-\frac{A}{\rho }$ and the curvature-matter coupling gravity as $f(R,T)$, where $A$ is a positive constant, $R$ and $T$ denote, respectively, the Ricci scalar and the trace of energy–momentum tensor. Considering the gravitational lagrangian in the form $f(R,T)=R+h(T)$, where we used two forms of $h(T)$ and by assuming a perfect fluid as matter source, we determined through the modified Friedmann equations, the corresponding energy and pressure for each model. By using the free parameters of our models, we performed the numerical results of the energy conditions to study its viability. Furthermore, we have derived some cosmological parameters like deceleration parameter and statefinder parameters and graphically investigated the nature of these parameters in Chaplygin gas model.

This study includes the cosmic evolution and the potential periodicity of the universe. It employs a periodic varying deceleration parameter (PVDP) within the framework of $f(R,T)$ theory of gravity, with a specific focus on the Bianchi-II model. We explore the dynamic nature of the universe, with physical and geometrical properties within this theoretical framework. We have also analyzed the cosmographic parameters, including jerk, snap, and lerk, for deeper insights into the universe’s evolution and behavior. Utilizing state finder diagrams and the Om diagnostic (which illustrates the variation of $\mathrm{\text{Om}}(z)$ with redshift) signifying a shift from matter dominance to a stronger influence of dark energy (DE), we construct a comprehensive map of the universe’s trajectory and behavior. By employing the Bianchi-II model within the $f(R,T)$ theory, our proposed model helps us in understanding the universe’s oscillatory patterns and underlying mechanisms. This research significantly contributes to our understanding of cosmic evolution and periodicity within the $f(R,T)$ theory.

It is shown that, with the only exception of n=2, the Einstein–Hilbert action in n+D+d dimensions, with n times, is invariant under the duality transformation and , where a is a Friedmann–Robertson–Walker scale factor in D dimensions and b a Brans–Dicke scalar field in d dimensions respectively. We investigate the (2+D+d)-dimensional cosmological model in some detail.

In this work, a cosmological model inspired by string theory with Gauss–Bonnet term coupled to the fermionic field is taken into consideration. The self-interaction potential is considered as a combination of the scalar and pseudoscalar invariants. Here the cosmological contribution of the coupling of Gauss–Bonnet term with a non-Dirac fermionic field — characterized by an interaction term — is investigated. It is observed that the new type of coupling plays a significant role in the accelerating behavior of the universe. Specifically, in addition to the late time acceleration for the universe, produces an early decelerating behavior. The behavior of the equation-of-state parameter (w) is such that it guarantees the stability of the theory.

In this work, a cosmological model inspired by string/M-theory with fermionic field is taken into consideration. Here it is investigated whether the introduction of a non-Dirac fermionic field — characterized by an interaction term — affects the cosmological evolution. The self-interaction potential is considered as a combination of the scalar and pseudoscalar invariants. It is observed that the fermionic field under consideration behaves like an inflation field for the early universe and later on, as a dark energy field. The late time acceleration becomes more prominent by the addition of the interaction term. There is a slight decrease for the inflation peak as well as for the energy density. We see that the addition of higher-order terms to the fermionic part of Lagrangian does not significantly change either the inflation or the late time acceleration behavior.

Within the scope of simple cosmological models we have studied the role of spinor field in the evolution of the Universe when it is non-minimally coupled to the gravitational one. 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 in FRW model, but this is not the case for LRSBI model. If the spinor field nonlinearity describes a dark energy the role non-minimal coupling becomes insignificant in both isotropic and anisotropic models.

A special law of variation for Hubble's parameter in anisotropic space–time models that yields a constant value of the deceleration parameter is presented. Also, a spatially homogeneous and anisotropic but locally rotationally symmetric (LRS) Bianchi type-II cosmological model is studied with a perfect fluid and constant deceleration parameter. Assuming the equation of state p = γρ, where 0≤γ≤1, and using a special law of variation for the Hubble parameter, we are able to construct many new solutions to Einstein's field equations of LRS Bianchi type-II for four different physical models (dust, radiation, Zel'dovich and vacuum). We discuss the solutions with power-law and exponential expansion and examine a particular class of models. A detailed study of kinematic, geometrical and observational properties is carried out.

For a class of viable cosmological models in f(R) gravity in which deviation from the Einstein gravity decreases as an inverse power law of the Ricci scalar R for large R, an analytic solution for density perturbations in the matter component during the matter-dominated stage is obtained in terms of hypergeometric functions. An analytical expression for the matter transfer function at scales much smaller than the present Hubble scale is also obtained.

Mounting observational data confirm that about 73% of the energy density consists of dark energy which is responsible for the current accelerated expansion of the Universe. We present observational evidences and dark energy projects. We then review various theoretical ideas that have been proposed to explain the origin of dark energy; they contain the cosmological constant, modified matter models, modified gravity models and the inhomogeneous model. The cosmological constant suffers from two major problems: one regarding fine-tuning and the other regarding coincidence. To solve them there arose modified matter models such as quintessence, k-essence, coupled dark energy and unified dark energy. We compare those models by presenting attractive aspects, new rising problems and possible solutions. Furthermore, we review modified gravity models that lead to late-time accelerated expansion without invoking a new form of dark energy; they contain f(R) gravity and the Dvali–Gabadadze–Porrati (DGP) model. We also discuss observational constraints on those models and on future modified gravity theories. Finally we review the inhomogeneous Lemaître–Tolman–Bondi (LTB) model that drops an assumption of the spatial homogeneity of the Universe. We also present basics of cosmology and scalar field theory, which are useful especially for students and novices to understand dark energy models.

We discuss recent developments related to certain blow-up methods suitable for the analysis of cosmological singularities and asymptotics. We review results obtained in a variety of currently popular themes and describe ongoing research about universes with various kinds of extreme states, higher-order gravity and certain models of braneworlds.

Much effort has been made in trying to solve or at least evade the inconsistencies that emerge from general relativity as the framework for a cosmological model. The extradimensional models rise as superb possibilities in this regard. In this work, I present cosmological solutions for Wesson’s space–time–matter theory of gravity. A relation between mass variation at cosmological scales and the expansion velocity of the universe is obtained. Such a relation yields novel features on space–time–matter theory of gravity, which are carefully discussed.

Stability analysis plays a major rule in our understanding of nature. For example it was shown that among empty flat spacetimes only those with a Lorentzian metric are stable [A. Yahalom, Found Phys.38 (2008) 489–497; Int. J. Mod. Phys. D18(4) (2009) 2155–2158]. However, the universe is not empty and the energy momentum tensor is metric dependent an thus effects stability. In this essay we concentrate on simple perturbations of the standard cosmological model with and without cosmological constant which is based on a uniform mass distribution. The results suggest that while Euclidean, open or closed section models are valid solutions, the choice of stable solutions is limited. In particular, the popular Lambda-CDM model is unstable.

Cosmic void as a cosmological probe is reviewed. We introduce the theoretical background and recent development in observations of cosmic voids, focusing on its potential to test theorists of gravity. Four observables about cosmic voids are introduced: void number counts, weak gravitational lensing, redshift-space distortions and ISW around voids. We discuss opportunities on their application to current and future galaxy surveys and highlight challenges for this subject.