  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 $\eta_t = \eta_{max}$.

General Relativity and Quantum Cosmology