How to obtain a class of emergent universes with a general form of dissipation?

TL;DR

This paper explores how a flat universe with a specific dissipative mechanism can lead to emergent universe scenarios, identifying conditions under which such universes can form without initial singularities.

Contribution

It introduces a general form of dissipation proportional to H^{2k+1} and demonstrates that an exponential Hubble parameter can produce emergent universes under certain conditions.

Findings

Emergent universes can arise with dissipation proportional to H^{2k+1}.

The condition γk ≤ 0 is sufficient for emergent universe formation.

Emergent universes are possible without the inequality being necessary.

Abstract

In this paper, we have assumed a flat Friedmann-Lemaitr\'e-Robertson-Walker universe endowed with a general form of dissipation. The source of dissipation is considered to be a bulk viscous pressure $\Pi$ which leads to an adiabatic creation of particles induced by the gravitational field. Further, the cosmic substratum is assumed to satisfy the equation of state $p=(\gamma -1)\rho$ and $\Pi$ is considered to be proportional to $H^{2k+1}$, where $H$ is the Hubble parameter and $k$ is the index of dissipation. This choice of dissipation is consistent with the pioneering works by Barrow and Clifton. Finally, by assuming an exponential form for $H$ given by $H=e^{m(t-t_0)}$, where $m$ is a positive real parameter and which bears all the signatures of an emergent universe, we have been able to establish that the sufficiency of the inequality $\gamma k \leq 0$ can produce a class of emergent universes. However, this condition is by no means necessary for the existence of an emergent universe.