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A new Lagrangian framework has recently been proposed to describe
interactions between relativistic perfect fluids and scalar fields. In this
paper we investigate the Einstein static universe in this new class of
theories, which have been named Scalar-Fluid theories. The stability of the
static solutions to both homogeneous and inhomogeneous pertur...
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... the case of an open universe k = 1, we are unable to find solution which are stable to all perturbations. An example plot is shown in Fig. 3, where regions of stability for different values of q are shown for the case w = − 1 / 2. It is found that increasing q stops the regions of stability overlapping, and for large enough q the stable regions disappear ...
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... The stability of the ESU can be studied using different methods like homogeneous, inhomogeneous perturbations and also in terms of dynamical systems. Some of these methods are well described in Ref. [6][7][8][9][10][11][12][13][14][15][16][17]. Emergent cosmology is an alternative approach to address the issue of the initial singularity, as a non-singular inflationary Universe, succeeding an ever-existing ESU. ...
Non-singular cosmological models, particularly the idea of emergent cosmology have been explored to describe the non-singular origin of the Universe. Recently, zero-point length cosmology has shown some positive insights into some non-singular aspects of the early Universe. In addition, topological defects are well-known for their major impact on the early Universe and may play a significant role by its presence as a part of the energy content of the Universe. We investigate the stability of the Einstein static phase of the emergent Universe scenario in a generalized framework of zero-point length cosmology in the presence of topological defects in the very early Universe. We derive the modified Friedmann equations, where the energy momentum tensor includes an extra energy density term arising from n-dimensional topological defects. We study the possibility of graceful exit of the Einstein Static Universe (ESU) into the standard inflationary cosmology and its stability on the basis of dynamical system analysis. We also study the stability of the ESU against homogeneous scalar perturbation and also its possible graceful exit mechanism. We analyse the stability of the ESU against density, vector and tensor perturbations. Through the stability analysis, it has been shown that indeed the model parameters associated with zero-point length setting and n-dimensional topological defects play a visible role in the graceful exit mechanism of the ESU to the standard inflationary Universe. Also, interestingly it is found that there exists a mutual interplay between the zero-point length parameter, and the dimension of topological defect on the stability of the ESU on the basis of inhomogeneous density perturbation. Finally, the stability is also tested against vector and tensor perturbation, which shows that the ESU is stable against such perturbations.
... The stability analysis for a stable ESU can be done in terms of different methods like homogeneous, inhomogeneous perturbations and also in terms of dynamical systems. Some of these methods are well described in Ref. [8][9][10][11][12][13][14][15][16][17][18][19]. Emergent cosmology is an approach to address the problem of the big-bang singularity, with a modification of the standard inflationary Universe, with an ever-existing phase of ESU, with a radius greater than Planck's scale to avoid the quantum gravity era. ...
... 2 Setting C > 0 or C < 0 would not have any effect on the stability regions as observed from (19). We may choose C > 0 conventionally. ...
... However, due to the generic nature of the perturbation equations, we may use them to study the evolution of the matter density contrast in the ESU as well. In the same context, Bohmer et al investigated the stability of ESU under perturbations in the Newtonian gauge in theories with scalar fluids [19]. ...
In this paper, in an FLRW background and a perfect fluid equation of state, we explore the possibility of the realization of an emergent scenario in a 4D regularized extension of Einstein-Gauss-Bonnet gravity, with the field equations particularly expressed in terms of scalar-tensor degrees of freedom. By assuming non-zero spatial curvature (k = ± 1), the stability of the Einstein static universe (ESU) and its subsequent exit into the standard inflationary scenario is tested through different approaches. In terms of dynamical systems, a spatially closed universe rather than an open universe shows appealing behaviour to exhibit a graceful transition from the ESU to standard cosmological history. We found that under linear homogeneous perturbations, for some constraints imposed on the model parameters, the ESU is stable under those perturbations. Moreover, it is noted that for a successful graceful transition, the equation of state ω must satisfy the conditions −1 < ω < 0 and ω < − 1 for closed and open universes, respectively. Furthermore, the ESU is seen to be neutrally stable under matter perturbation in the Newtonian gauge.
... However, the original model of the emergent universe is unsuccessful since the Einstein static solution in general relativity with quintessence is unstable against inhomogeneous scalar perturbations [14]. Subsequently, a large amount of efforts have gone into theories of modified gravity, and the stable Einstein static universe against homogeneous and inhomogeneous scalar perturbations was found in Mimetic gravity [13], scalarfluid theory [15], non-minimal derivative coupling model [16,17], braneworld model [18], Jordan-Brans-Dicke theory [19], Eddington-inspired Born-Infeld theory [20], hybrid metric-Palatini gravity [21], GUP theory [22], f(R,T) gravity [23], f(R,T,Q) gravity [24], and massive gravity [25]. ...
The emergent universe provides a possible method to avoid the Big Bang singularity by considering that the universe stems from a stable Einstein static universe rather than the singularity. Since the Einstein static universe exists before inflation, it may leave some relics in the CMB power spectrum. In this paper, we analyze the stability condition for the Einstein static universe in general relativity with k-essence against both the scalar and tensor perturbations. Furthermore, we find the emergent universe can be successfully realized by constructing a scalar potential and an equation of state parameter. Solving the curved Mukhanov–Sasaki equation, we obtain the analytical approximation for the primordial power spectrum, and then depict the TT-spectrum of the emergent universe. The results show that both the primordial power spectrum and CMB TT-spectrum are suppressed on large scales.
... Bohmer et al. [57] investigated the stability of static solutions against homogeneous and inhomogeneous perturbations in the framework of scalar-fluid theory. They found that stable solutions existed against inhomogeneous perturbations, but homogeneous perturbations yielded unstable solutions. ...
The main objective of this article is to examine the stability of Einstein static universe using inhomogeneous perturbations in the context of energy–momentum squared gravity. For this purpose, we used FRW spacetime with perfect matter distribution and formulated static as well as perturbed field equations. We took a minimal model of this theory to investigate the stable regions of the Einstein universe for conserved and non-conserved energy–momentum tensors. We found that stable modes of the Einstein universe appeared in both conserved and non-conserved cases for all values of the equation of state and model parameters corresponding to both open and closed cosmic models. We found that stable solutions in this modified theory were obtained for a broader ω-region compared to other modified theories.
... Therefore, these Lagrangians cannot generally be used to describe the same fluid, thus implying that prior knowledge of their appropriate form may be crucial for a correct characterization of the overall dynamics. This is also true in the presence of an NMC between different physical matter components even in the absence of an NMC to gravity [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. ...
... for any possible value of µ, ν and i. Notice that Eq. (29) implies ...
In the context of general relativity, both energy and linear momentum constraints lead to the same equation for the evolution of the speed of free localized particles with fixed proper mass and structure in a homogeneous and isotropic Friedmann-Lema\^itre-Robertson-Walker universe. In this paper we extend this result by considering the dynamics of particles and fluids in the context of theories of gravity nonminimally coupled to matter. We show that the equation for the evolution of the linear momentum of the particles may be obtained irrespective of any prior assumptions regarding the form of the on-shell Lagrangian of the matter fields. We also find that consistency between the evolution of the energy and linear momentum of the particles requires that their volume-averaged on-shell Lagrangian and energy-momentum tensor trace coincide (). We further demonstrate that the same applies to an ideal gas composed of many such particles. This result implies that the two most common assumptions in the literature for the on-shell Lagrangian of a perfect fluid ( and , where and are the proper density and pressure of the fluid, respectively) do not apply to an ideal gas, except in the case of dust (in which case ).
... The stable regimes in the modified Gauss-Bonnet theory against homogenous and inhomogeneous perturbations have been studied in [19]. The stability of EU in scalar-field theories has been investigated in [20] and found the stable as well as unstable regions corresponding to homogeneous and inhomogeneous perturbations. ...
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 (R, T2)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.Weconclude that stable regions in this modified theory are large as compared to other modified theories of gravity.
... The stable regimes in the modified Gauss-Bonnet theory against homogenous and inhomogeneous perturbations have been studied in [19]. The stability of EU in scalar-field theories has been investigated in [20] and found the stable as well as unstable regions corresponding to homogeneous and inhomogeneous perturbations. ...
... Therefore, it was suggested to study Einstein static cosmos beyond the Einstein gravity. In this respect, the stability of EU has been investigated in several cosmological perspectives such as braneworld gravity (Gergely and Maartens 2002), loop quantum cosmology (Mulryne et al. 2005), Einstein Cartan scenario (Atazadeh 2014) and scalar fluid theories (Böhmer et al. 2015). The gravitational modified theories have become significant approaches to derive stable Einstein solutions. ...
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 Einstein regions exist for both closed as well as open FLRW universe models for an appropriate choice of parameters. We conclude that this theory is efficient for presenting such cosmological solutions leading to emergent universe scenario.
... Gauss-Bonnet gravity [68,69], Brans-Dicke theory [70][71][72][73], Horava-Lifshitz theory [74][75][76], brane world scenario [77][78][79], Einstein-Cartan theory [80], f (R, T ) gravity [81], Eddingtonginspired Born-Infeld theory [82], Horndeski theory [83,84], hybrid metric-Palatini gravity [85] and so on [86][87][88][89][90][91][92]. We refer to e.g. ...
We consider alternative inflationary cosmologies in massive gravity with degenerate reference metrics and study the feasibilities of the emergent universe scenario, bouncing and cyclic universes. We focus on the construction of the Einstein static universe, classes of exact solutions of bouncing and cyclic universes in degenerate massive gravity. We further study the stabilities of the Einstein static universe against both homogeneous and inhomogeneous scalar perturbations and give the parameters region for a stable Einstein static universe.
... The same authors 31 also established the unstable solutions for open universe and stable regions for closed universe in Gauss-Bonnet gravity. Böhmer et al. 32 examined the stability modes against homogeneous as well as inhomogeneous perturbations in scalar-fluid theories and obtained stable and unstable results corresponding to inhomogeneous and homogeneous perturbations, respectively. Darabi and his collaborators 33 studied the existence of EU and its stability in the framework of Lyra geometry using scalar, vector and tensor perturbations with suitable choice of parameters. ...
This paper investigates the existence and stability of Einstein universe in the context of f(R, T, Q) gravity, where Q = Rμν Tμν. Considering linear homogeneous perturbations around scale factor and energy density, we formulate static as well as perturbed field equations. We parametrize 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, stable regions of the Einstein universe are obtained which indicates that the big bang singularity can be avoided successfully by the emergent mechanism in non-minimal matter-curvature coupled gravity.
