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arXiv · 2203.06447

Analytical approximations for primordial power spectra in a spatially closed emergent universe

Qihong Huang·Kaituo Zhang·Zhenxing Fang·Feiquan Tu
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Abstract

The emergent universe scenario was proposed to solve the big bang singularity by suggesting that the universe originates from an Einstein static state and then evolves into a subsequently inflationary era. Thus, to find the relic of the existence of the Einstein static state becomes a crucial work. In this paper, we derive analytical approximation of the primordial power spectra and analyze the CMB TT-spectra for the spatially closed emergent universe. After analyzing the CMB TT-spectrum of the emergent universe scenario, we find that both the CMB TT-spectra produced by the Einstein static state followed by the ultraslow-roll inflationary epoch (method I) and by a special evolution of the scale factor in the emergent scenario as $a=a_{0}+A e^{H_{0}t}$(method II) are suppressed at $l<30$, and their spectra are nearly identical. Additionally, by comparing the spectra of the emergent universe scenario with the ones of the ultraslow-roll inflationary model in the closed universe, we find that the CMB TT-spectrum of the emergent universe is similar to the one of the inflationary model with the special case $η_t = η_{max}$.

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Qihong Huang, Kaituo Zhang, Zhenxing Fang, Feiquan Tu. 2022-10-30. Analytical approximations for primordial power spectra in a spatially closed emergent universe. https://doi.org/10.1016/j.dark.2022.101124

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