  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.
