CMB Power Spectrum in the Emergent Universe with K-Essence

The emergent universe provides a possible method to avoid the Big Bang singularity by considering that the universe stems from a 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. Furthermore, 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.

Automated summary

The emergent universe provides an alternative to the Big Bang singularity by proposing that the universe originates from a stable Einstein static universe. This concept suggests that relics from the Einstein static universe may be detected in the CMB power spectrum. In this study, the stability conditions for the Einstein static universe in general relativity with k-essence are analyzed in terms of both scalar and tensor perturbations. Additionally, the emergent universe can be successfully realized by introducing a scalar potential and an equation of state parameter.