The Transplanckian Question and the Casimir Effect

Abstract

It is known that, through inflation, Planck scale phenomena should have left an imprint in the cosmic microwave background. The magnitude of this imprint is expected to be suppressed by a factor $\sigma^n$ where $\sigma\approx 10^{-5}$ is the ratio of the Planck length to the Hubble length during inflation. While there is no consensus about the value of $n$, it is generally thought that $n$ will determine whether the imprint is observable. Here, we suggest that the magnitude of the imprint may not be suppressed by any power of $\sigma$ and that, instead, $\sigma$ may merely quantify the amount of fine tuning required to achieve an imprint of order one. To this end, we show that the UV/IR scale separation, $\sigma$, in the analogous case of the Casimir effect plays exactly this role.