CMB power spectrum in the emergent universe with k-essence

TL;DR

This paper explores how an emergent universe model with k-essence can avoid the big bang singularity and leave observable relics in the CMB power spectrum, especially on large scales.

Contribution

It provides a stability analysis of the Einstein static universe with k-essence and derives an analytical approximation for the primordial power spectrum and CMB TT-spectrum.

Findings

Primordial power spectrum is suppressed on large scales.

CMB TT-spectrum shows suppression on large scales.

Emergent universe can be realized with specific scalar potential and equation of state.

Abstract

The emergent universe provides a possible method to avoid the big bang singularity by considering that the universe stems from an 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. And 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.