Running of the Spectral Index and Violation of the Consistency Relation Between Tensor and Scalar Spectra from trans-Planckian Physics

TL;DR

This paper investigates how trans-Planckian physics can violate the inflationary consistency relation between scalar and tensor spectra, leading to observable effects like spectral index running and oscillatory tensor spectral index behavior.

Contribution

It demonstrates that Planck scale physics can significantly alter the inflationary consistency relation and induce spectral index running, challenging standard predictions.

Findings

Planck scale physics modifies the consistency relation.

Tensor spectral index can be positive or oscillate.

Spectral index running is induced by trans-Planckian effects.

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 cut-off 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 of the modes which are the precursor to structure formation, the behavior of 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, one can verify this scenario of short distance physics.