On what scale should inflationary observables be constrained?

Abstract

We examine the choice of scale at which constraints on inflationary observables are presented. We describe an implementation of the hierarchy of inflationary consistency equations which ensures that they remain enforced on different scales, and then seek to optimize the scale for presentation of constraints on marginalized inflationary parameters from WMAP3 data. For models with spectral index running, we find a strong variation of the constraints through the range of observational scales available, and optimize by finding the scale which decorrelates constraints on the spectral index nS and the running. This scale is k=0.017Mpc-1, and gives a reduction by a factor of more than four in the allowed parameter area in the nS-r plane (r being the tensor-to-scalar ratio) relative to k=0.002Mpc-1. These optimized constraints are similar to those obtained in the no-running case. We also extend the analysis to a larger compilation of data, finding essentially the same conclusions. © 2007 The American Physical Society.