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, we base our calculations on a specific model, and they are intended as a case study for the sort of constraints one could hope to apply to 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 estimation 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 ten 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 similar to 0.15, the ratio between the inflationary Hubble scale H and the scale of new physics M has to be of 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.