Emergent universe in brane world scenario with Schwarzschild–de Sitter bulk

Abstract

A model of an emergent universe is obtained in brane world. Here the bulk energy is in the form of cosmological constant, while the brane consists of a fluid satisfying an equation of state of the form p b = 1 3 ρ b , which is effectively a radiation equation of state at high energies. It is shown that with the positive bulk cosmological constant, one of our models represents an emergent universe.The search for singularity free inflationary models in the context of Classical General Relativity has recently led to the development of emergent universes.Harrison [1] obtained a model of the closed universe containing radiation, which approaches the state of an Einstein static model asymptotically, i.e. as t → −∞. This kind of model has so far been discovered subsequently by several workers in the recent past such as that of Ellis and Maartens [2], Ellis et al. [3]. They obtained closed universes with a minimally coupled scalar field φ with a special form for self interacting potential and possibly some ordinary matter with equation of state p = ωρ where − 1 3 ≤ ω ≤ 1. However, exact analytic solutions were not presented in these models, although their behaviour alike that of an emergent universe was highlighted. An emergent universe is a model universe in which there is no timelike singularity, is ever existing and having almost static behaviour in the infinite past (t → −∞) as is mentioned earlier. The model eventually evolves into an inflationary stage. In fact, the emergent universe scenario can be said to be a modern version and extension of the original Lemaitre-Eddington universe. Mukherjee et al. [4] obtained solutions for Starobinsky model for flat FRW space time and studied the features of

Emergent universe by tunneling

“…However, recently, models that escape this conclusion has been studied in Refs. [11][12][13][14][15][16][17][18]. These models do not satisfy the geometrical assumptions of these theorems.…”

“…[11][12][13][14][15][16][17][18] consider closed models in which k = +1 and H can become zero, so that both assumptions i) and ii) of the inflationary singularity theorems are violated. In these models the universe is initially in a past eternal classical Einstein static (ES) state which eventually evolves into a subsequent inflationary phase.…”

“…Normally in the Emergent Universe scenario, the universe is positively curved and initially it is in a past eternal classical Einstein static state which eventually evolves into a subsequent inflationary phase, see [11][12][13][14][15][16][17][18].…”

Tunneling and the Emergent Universe scheme in a JBD Theory

“…This theorem was developed in 2003 by Arvind Borde, Alan Guth and Alex Vilenkin [8].Vilenkin's arguments demonstrate that null and time-like geodesics are generally incomplete in inflationary models, regardless of whether energy conditions are maintained, provided that the average expansion condition (H > 0) is maintained throughout of these geodesics directed towards the past. The search for cosmological models without initial singularities has led to the development of emergent universes models (UE) [9,10,11,12,13,14,15,16]. However, most simple models developed in a context of General Relativity suffer from instabilities, associated with the instability of Einstein's static universe [17].…”

Observational constraints on EoS parameters of emergent universe

“…The modified Gauss-Bonnet gravity as gravitational alternative for dark energy is however considered by Nojiri and Oddintsov [19]. It is also shown recently that EU model can be successfully implemented in Brane world gravity [20,21], Brans-Dicke theory [22]. A number of cosmological models are obtained with different cosmological fluids and fields [14,[23][24][25][26] where initial singularity problem is addressed.…”