Cosmological implications of a minimal length hypothesis

Abstract

One of the firm predictions of inflationary cosmology is the consistency relation between scalar and tensor spectra. It has been argued that such a relation — if experimentally confirmed — would offer strong support for the idea of inflation. We examine the possibility that trans-Planckian physics violates the consistency relation in the framework of inflation with a cutoff proposed in astro-ph/0009209. We find that despite the ambiguity that exists in choosing the action, Planck-scale physics modifies the consistency relation considerably. It also leads to the running of the spectral index. For modes that are larger than our current horizon, the tensor spectral index is positive. For a window of k values with amplitudes of the same order as the modes that are the precursors to structure formation, the behavior of the tensor spectral index is oscillatory about the standard Quantum field theory result, taking both positive and negative values. There is a hope that in the light of future experiments, this scenario of short distance physics, can be verified.PACS Nos.: 98.80.Cq , 98.80.-k, 98.80.Qc