Decoherence problem in an ekpyrotic phase

Quantum decoherence and the transition to semiclassical behavior during inflation have been extensively considered in the literature. In this paper, we use a simple model to analyze the same process in ekpyrosis. Our result is that the quantum to classical transition would not happen during an ekpyrotic phase even for superhorizon modes, and therefore the fluctuations cannot be interpreted as classical. This implies the prediction of a scale-free power spectrum in an ekpyrotic/cyclic universe model requires more inspection.

Figure 1

The relation of coherence length and the conformal time for usual inflation. The horizontal axis is $k\eta$ and the vertical axis is normalized coherence length. The upper (red) line corresponds to no interaction, and the lower (blue) line corresponds to $c=0.15$. If there is an interaction, the coherence length starts decreasing and eventually becomes zero for the superhorizon modes.

Figure 2

The relation of coherence length and the conformal time for power law inflation. We choose $p=10$ in this plot. The upper (red) line corresponds to no interaction, and the lower (blue) line corresponds to $c=0.15$.

Figure 3

The relation of coherence length and the conformal time for ekpyrosis with $p=0.1$. The upper (red) line corresponds to no interaction, and the lower (blue) line corresponds to $c=0.15$. It is clear that even the modes go outside the horizon; the coherence length continues growing and approaches to a nonzero constant in the end.