Emergent universe from the Ho\v{r}ava-Lifshitz gravity

TL;DR

This paper investigates the stability of the Einstein static universe within Hořava-Lifshitz gravity, showing conditions under which the universe can avoid the big bang singularity and potentially undergo natural inflation.

Contribution

It introduces a stability analysis of Einstein static solutions in Hořava-Lifshitz gravity and its generalized form, revealing scenarios that avoid singularities and enable inflation.

Findings

Stable Einstein static universe exists with negative cosmological constant.

Universe can avoid big bang singularity and remain in a stable state.

Conditions for natural transition to inflation are identified.

Abstract

We study the stability of the Einstein static universe in the Ho\v{r}ava-Lifshitz (HL) gravity and a generalized version of it formulated by Sotiriou, Visser and Weifurtner. We find that, for the HL cosmology, there exists a stable Einstein static state if the cosmological constant $\Lambda$ is negative. The universe can stay at this stable state eternally and thus the big bang singularity can be avoided. However, in this case, the Universe can not exit to an inflationary era. For the Sotiriou, Visser and Weifurtner HL cosmology, if the cosmic scale factor satisfies certain conditions initially, the Universe can stay at the stable state past eternally and may undergo a series of infinite, nonsingular oscillations. Once the parameter of the equation of state $w$ approaches a critical value, the stable critical point coincides with the unstable one, and the Universe enters an inflationary era. Therefore, the big bang singularity can be avoided and a subsequent inflation can occur naturally.