Quantum instability of the emergent universe
We perform a semi-classical analysis of the Emergent Universe scenario for inflation. Fixing the background, and taking the inflaton to be homogenous, we cast the inflaton’s evolution as a onedimensional quantum mechanics problem. The potential is taken to be flat or linear, as an approximation to the monotonic and slowly-varying asymptotic behavior of the Emergent Universe potential. We find that the tuning required over a long time scale for this inflationary scenario is unstable quantum mechanically. Considering the inflaton field value as a wavepacket, the spreading of the wavepacket destroys any chance of both starting and ending with a well-formed state. Thus, one cannot have an Einstein static universe to begin with that evolves into a well-defined beginning to inflation a long time later.