This paper analyzes the stability of the closed Einstein static universe by using linear homogeneous perturbations in the framework of energy-momentum squared gravity. This newly developed proposal resolves the primordial singularity and yields feasible cosmological results in the early times. For this purpose, we consider the closed Friedmann-Robertson-Walker universe with isotropic matter configuration and adopt small perturbations on the matter parameters and scale factor. Further, we establish equations of motion for static as well as perturbed systems and analyze the stable regions for particular $f(\mathcal{R},\mathbf{T}^{2})$ models corresponding to both conserved and non-conserved energy-momentum tensor. The graphical interpretation demonstrates that stable regions of the Einstein cosmos exist for all values of the model parameters and equation of state variable. We conclude that stable regions in this modified theory are large as compared to other modified theories of gravity.
We study the cosmological models in which an extended Chaplygin gas universe is merged with the braneworld scenario. In particular, we examine the realization of Einstein static universe on the brane embedded in a non-constant curvature bulk space and perform a detailed perturbation analysis. We extract the stability conditions and find their impacts on the geometric equation of state parameter and the spatial curvature of the universe.
We report a symmetry property of the Einstein-Friedmann equations for spatially flat Friedmann-Lemaître-Robertson-Walker universes filled with a perfect fluid with any constant equation of state. The symmetry transformations form a one-parameter Abelian group.
We investigate stability of the Einstein static solution against homogeneous scalar, vector and tensor perturbations in the context of Rastall theory of gravity. We show that this solution in the presence of perfect fluid and vacuum energy originating from conformally-invariant fields is stable. Using the fix point method and taking linear homogeneous perturbations, we find that the scale factor of Einstein static universe for closed deformed isotropic and homogeneous FLRW universe depends on the coupling parameter $λ$ between the energy-momentum tensor and the gradient of Ricci scalar. Thus, …
We investigate stability of the Einstein static universe against the scalar, vector and tensor perturbations in the context of induced matter brane gravity. It is shown that in the framework of this model, the Einstein static universe has a positive spatial curvature. In contrast to the classical general relativity, it is found that a stable Einstein static universe against the scalar perturbations does exist provided that the variation of time dependent geometrical equation of state parameter is proportional to the minus of the variation of the scale factor, $δω_{g}(t)=-Cδa(t)$. We obtain neu…
We study the stability of Einstein static Universe, with FLRW metric, by considering linear homogeneous perturbations in the kinetic coupled gravity. By taking linear homogeneous perturbations, we find that the stability of Einstein static Universe, in the kinetic coupled gravity with quadratic scalar field potential, for closed ($K=1$) isotropic and homogeneous FLRW Universe depends on the coupling parameters $κ$ and $\varepsilon$. Specifically, for $κ=L_P^2$ and $\varepsilon=1$ we find that the stability condition imposes the inequality $a_0>\sqrt{3}L_P$ on the initial size $a_0$ of the clos…
This paper explores stability of the Einstein universe against linear homogeneous perturbations in the background of $f(\mathcal{G},T)$ gravity. We construct static as well as perturbed field equations and investigate stability regions for the specific forms of generic function $f(\mathcal{G},T)$ corresponding to conserved as well as non-conserved energy-momentum tensor. We use the equation of state parameter to parameterize the stability regions. The graphical analysis shows that the suitable choice of parameters lead to stable regions of the Einstein universe.
This paper investigates the existence and stability of Einstein universe in the context of $f(R,T,Q)$ gravity, where $Q=R_{μν}T^{μν}$. Considering linear homogeneous perturbations around scale factor and energy density, we formulate static as well as perturbed field equations. We parameterize the stability regions corresponding to conserved as well as non-conserved energy-momentum tensor using linear equation of state parameter for particular models of this gravity. The graphical analysis concludes that for a suitable choice of parameters, the stable regions of the Einstein universe are obtain…
Stability of the Einstein static universe versus the linear scalar, vector and tensor perturbations is investigated in the context of deformed Hořava-Lifshitz cosmology inspired by entropic force scenario. A general stability condition against the linear scalar perturbations is obtained. Using this general condition, it is shown that there is no stable Einstein static universe for the case of flat universe, $k=0$. For the the special case of large values of running parameter of HL gravity $ω$, in a positively curved universe $k>0$, the domination of the quintessence and phantom matter fields w…
The purpose of this paper is to analyze the existence of static stable Einstein universe using inhomogeneous linear perturbations in the context of $f(R,T)$ gravity ($R$ and $T$ denote the scalar curvature and trace of the stress-energy tensor, respectively). The static and perturbed field equations are constructed for perfect fluid parameterized by linear equation of state parameter. We obtain solutions manifesting the Einstein static state by considering peculiar $f(R,T)$ forms for vanishing and non-vanishing conservation of the stress-energy tensor. It is observed that stable static Einstei…
We present a time-dependent solution of the Maxwell equations in the Einstein universe, whose electric and magnetic fields, as seen by the stationary observers, are aligned with the Clifford parallels of the $3$-sphere $S^3$. The conformal equivalence between Minkowski's spacetime and (a region of) the Einstein cylinder is then exploited in order to obtain a knotted, finite energy, radiating solution of the Maxwell equations in flat spacetime. We also discuss similar electromagnetic fields in expanding closed Friedmann models, and compute the matter content of such configurations.
Hybrid metric-Palatini gravity is a recent and novel approach to modified theories of gravity, which consists of adding to the metric Einstein-Hilbert Lagrangian an f(R) term constructed a la Palatini. It was shown that the theory passes local tests even if the scalar field is very light, and thus implies the existence of a long-range scalar field, which is able to modify the dynamics in galactic and cosmological scales, but leaves the Solar System unaffected. In this work, motivated by the possibility that the Universe may have started out in an asymptotically Einstein static state in the inf…
In the present paper we investigate the effects caused by the modification of the dispersion relation obtained by solving the Klein-Gordon equation in the closed Einstein's universe in the context of rainbow's gravity models. Thus, we analyse how the quantum vacuum fluctuations of the scalar field are modified when compared with the results obtained in the usual General Relativity scenario. The regularization, and consequently the renormalization, of the vacuum energy is performed adopting the Epstein-Hurwitz and Riemann's zeta functions.
The emergent mechanism provides a possible way to resolve the big bang singularity problem by assuming that our universe originates from the Einstein static (ES) state. Thus, the existence of a stable ES solution becomes a very crucial prerequisite for the emergent scenario. In this paper, we study the stability of an ES universe in gravity theory with a non-minimal coupling between the kinetic term of a scalar field and the Einstein tensor. We find that the ES solution is stable under both scalar and tensor perturbations when the model parameters satisfy certain conditions, which indicates th…
We study the static cosmological solutions and their stability at background level in the framework of massive bigravity theory with Friedmann-Robertson-Walker (FRW) metrics. By the modification proposed in the cosmological equations subject to a perfect fluid we obtain new solutions interpreted as the Einstein static universe. It turns out that the non-vanishing size of initial scale factor of Einstein static universe depends on the non-vanishing three-dimensional spatial curvature of FRW metrics and also the graviton's mass. By dynamical system approach and numerical analysis, we find that t…
The type D Kasner vacuum solution of general relativity is reviewed, highlighting the little-known, intriguing property that it can describe both an anisotropic cosmology and the spacetime deep within a black hole, these two descriptions linked by a reversal of the time-ordering of the solution. The flexible nature of solutions of Einstein's equations is emphasised, and a brief discussion of the arrow of time in modern physics is presented.
In order to bypass the big bang singularity, we develop an emergent universe scenario within a covariant extension of General Relativity known as \emph{"Energy-Momentum Squared Gravity"}. The extra terms of the model emerge in the high energy regime. Considering dynamics in a Friedmann-Lemaître-Robertson-Walker background, critical points, representing stable Einstein static states of the phase space, result as solutions. It then turns out that as the equation of state parameter $ω$ gradually declines from a constant value as $t\rightarrow-\infty$, eventually some of the static past eternal so…
The complete theory of cosmological evolution's macroscopic description is constructed with a help of self-consistent field. The theory includes a subsystem of linear equations of perturbations' evolution and nonlinear macroscopic Einstein equations and equations of a scalar field. We provide examples of system's solution which show the principal difference of the cosmological models of the early Universe built on homogenous and locally fluctuating scalar fields. {\bf Keywords}: macroscopic gravitation, self-consistent field, cosmological model, scalar fields, averaging of local fluctuations, …
We report a new symmetry of the Einstein-Friedmann equations for spatially flat Friedmann- Lemaître-Robertson-Walker universes. We discuss its application to barotropic perfect fluids and its use as a solution-generating technique for scalar field universes.
By presenting a relation between average energy of the ensemble of probe photons and energy density of the Universe, in the context of {\it gravity's rainbow} or {\it doubly general relativity} scenario, we introduce a rainbow FRW Universe model. By analyzing the fixed points in flat FRW model modified by two well known rainbow functions, we find that the finite time singularity avoidance (i.e. Big-Bang) may still remain as a problem. Then, we follow the "Emergent Universe" scenario in which there is no beginning of time and consequently there is no Big-Bang singularity. Moreover, we study the…
An interpretation is suggested that a spontaneous compactification of space-time can be regarded as a topological defect in a higher-dimensional Einstein-Yang-Mills (EYM) theory. We start with $D$-dimensional EYM theory in our present analysis. A compactification leads to a $D-2$ dimensional effective action of Abelian gauge-Higgs theory. We find a "vortex" solution in the effective theory. Our universe appears to be confined in a center of a "vortex", which has $D-4$ large dimensions. In this paper we show an example with $SU(2)$ symmetry in the original EYM theory, and the resulting solution…
The emergent scenario provides a possible way to avoid the big bang singularity by assuming that the universe originates from an Einstein static state. Therefore, an Einstein static universe stable under perturbations is crucial to a successful implementation of the emergent mechanism. In this paper, we analyze the stability of the Einstein static universe against the scalar perturbations in the mimetic theory and find that stable Einstein static solutions exist under certain conditions in this theory. In the original mimetic gravity, the Einstein static universe is unstable. Then, we find tha…
We consider the FLRW universe in a loop quantum cosmological model filled with the radiation, baryonic matter (with negligible pressure), dark energy and dark matter. The dark matter sector is supposed to be of Bose-Einstein condensate type. The Bose-Einstein condensation process in a cosmological context by supposing it as an approximate first order phase transition, has been already studied in the literature. Here, we study the evolution of the physical quantities related to the early universe description such as the energy density, temperature and scale factor of the universe, before, durin…
Scale-independent EMSG is a particular model of energy-momentum squared gravity (EMSG) in which the new terms in the Einstein field equations arising from the EMSG theory enter with the same power as the usual terms from Einstein-Hilbert part of the action. However, the model violates the local energy-momentum conservation and matter-current conservation in general and hence, permits a process of matter creation/annihilation in an expanding universe. Consequently, the scale factor dependencies of the energy densities are modified by the dimensionless model parameter $α$. We revisit some nostal…
We consider the existence and stability of the Einstein static universe under the Generalized Uncertainty Principle (GUP) effects. We show that this solution in the presence of perfect fluid with a minimal length is cyclically stable around a center equilibrium point. By taking linear homogeneous perturbations, we find that the scale factor of Einstein static universe for closed deformed isotropic and homogeneous FLRW universe depends on the GUP coupling parameter $α$. Thus, in the model by GUP effects, our universe can stay at the Einstein static state past-eternally, which means that the big…
We present some wormhole configurations using analytic and numerical solutions of the Euclidean field equations considering Einstein Gauss Bonnet dilaton coupled interaction in the Robertson Walker metric. Analytic solutions invoking slow-roll type approximation for some potentials yield identical wormholes in the early era. Eventually, in a later era, the universe enters to an expanding era much faster than usual inflation accompanied by oscillations with analytic continuation τ=it. The numerical solutions of wormholes in terms of the scale factor a(τ) are almost identical for some standard p…
