Emergent scenario in the Einstein-Cartan theory

Abstract

We study the emergent scenario, which is proposed to avoid the big bang singularity, in the Einstein-Cartan (EC) theory with a positive cosmological constant and a perfect fluid by analyzing the existence and stability of the Einstein static (ES) solutions. We find that there is no stable ES solution for a spatially flat or open universe. However, for a spatially closed universe, the stable ES solution does exist, and in the same existence parameter regions, there also exists an unstable one. With the slow decrease of the equation of state w of the perfect fluid, the stable and unstable critical points move close gradually and coincide once w reaches a critical value, so that the stable critical point becomes an unstable one. As a result, if w approaches a constant at t → −∞, the universe can stay at the stable ES state past eternally, and furthermore it can naturally exit from this state and evolve into an inflationary era if w decreases slowly as time goes forward. Therefore, the emergent scenario that avoids the big bang singularity can be successfully implemented in the EC theory of gravity.

Stability of the Einstein static universe in Eddington-inspired Born-Infeld theory

“…The homogeneous scalar perturbation corresponds to n = 0, namely k 2 = 0. The first inhomogeneous mode (n = 1) corresponds to a gauge degree of freedom related to a global rotation, which reflects the freedom to change the four-velocity of fundamental observers [31,35,39]. So, the physical inhomogeneous modes have n ≥ 2 and hence k 2 = n(n + 2) ≥ 8.…”

“…In GR, this was reconsidered, and it was found that the Einstein static universe can be stable against small inhomogeneous vector and tensor perturbations as well as adiabatic scalar density perturbations if the universe contains a perfect fluid with w = c 2 s > 1/5 [25,26,31]. Of course, the stability of the Einstein static universe has also been extensively studied in many modified gravities, for example, loop quantum cosmology [32], f (R) theory [33][34][35], f (T ) theory [36,37], modified Gauss-Bonnet gravity [38,39], Brans-Dicke theory [40][41][42][43], Horava-Lifshitz theory [44][45][46], massive gravity [47,48], braneworld scenario [49][50][51], Einstein-Cartan theory [52], f (R, T ) gravity [53], hybrid metric-Palatini gravity [54] and so on [55][56][57][58][59][60][61][62]. We refer to e.g.…”

Classical defocussing of world lines in higher dimensions

“…Ellis and Maartens [10], and Ellis, Murugan and Tsagas [11] proposed the emergent scenario in which the universe stays in a static past eternally and then evolves to a subsequent inflationary era, suggesting that the universe originates from Einstein static state rather than a big bang singularity. An emergent scenario has been made possible in the modified theories of gravity such as f (R) gravity, loop quantum gravity [12] and in Einstein -Cartan theory [13]. These studies motivate the consideration of higher dimensional gravity as a possible candidate for avoiding a singularity.…”

Emergent universe in theories with natural UV cutoffs

“…As time passes and the universe equation-of-state parameter decreases these critical points become unstable and are exchanged with their unstable counterpart Critical Point 4, offering a natural graceful exit from the Einstein static universe and an entering into the usual expanding thermal history (this procedure is more efficient for the closed geometry, since Critical Point 4 is always unstable for suitable values of α). This behavior is also achieved in complicated models of the emergent universe in some various modified gravities [38], however in the present scenario it is obtained solely from the quantum gravity deformation parameter α.…”

“…Similarly to the previous critical points, we can see that for suitable val-ues of α and w this point, which is the most interesting one concerning the successful realization of the emergent universe scenario, is stable. Let us verify the above results using the approach of [38][39][40], and express them in a more transparent way. We introduce the two variables x 1 = a and x 2 =ȧ, and therefore the linear perturbations of the Friedmann equation (9) around the Critical Points (13)- (16) leads tȯ…”