Observing Trans-Planckian Signatures in the Cosmic Microwave Background

We examine the constraints cosmological observations can place on any trans-Planckian corrections to the primordial spectrum of perturbations underlying the anisotropies in the Cosmic Microwave Background. We focus on models of trans-Planckian physics which lead to a modulated primordial spectrum. Rather than looking at a generic modulated spectrum, our calculations are based on a specific model, and are intended as a case study for the sort of constraints one could hope to apply on a well-motivated model of trans-Planckian physics. We present results for three different approaches -- a grid search in a subset of the overall parameter space, a Fisher matrix estimate of the likely error ellipses, and a Monte Carlo Markov Chain fit to a simulated CMB sky. As was seen in previous analyses, the likelihood space has multiple peaks, and we show that their distribution can be reproduced via a simple semi-analytic argument. All three methods lead to broadly similar results. We vary 10 cosmological parameters (including two related to the trans-Planckian terms) and show that the amplitude of the tensor perturbations is directly correlated with the detectability of any trans-Planckian modulation. We argue that this is likely to be true for any trans-Planckian modulation in the paradigm of slow-roll inflation. For the specific case we consider, we conclude that if the tensor to scalar ratio, $r \sim 0.15$, the ratio between the inflationary Hubble scale $H$, and the scale of new physics $M$ has to be on the order of 0.004 if the modulation is detectable at the 2$\sigma$ level. For a lower value of $r$, the bound on $H/M$ becomes looser.