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CMB power spectrum in the emergent universe with k-essence

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arxiv 2210.16166 v3 pith:MRT46TFM submitted 2022-10-28 gr-qc

CMB power spectrum in the emergent universe with k-essence

classification gr-qc
keywords universeemergentpowerspectrumeinsteinstaticequationk-essence
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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