On the Tensor/Scalar Ratio in Inflation with UV Cutoff

TL;DR

This paper examines how introducing a minimal length cutoff in spacetime affects the tensor/scalar ratio in inflationary cosmology, revealing cutoff-dependent variations through numerical solutions of perturbation equations.

Contribution

It demonstrates the impact of a UV cutoff on the tensor/scalar ratio in inflation, highlighting an ambiguity in the action choice due to boundary term non-invariance.

Findings

The tensor/scalar ratio depends on the UV cutoff.

Numerical solutions show cutoff-induced variations during inflation.

Boundary term non-invariance affects perturbation analysis.

Abstract

Anisotropy of the cosmic microwave background radiation (CMB) originates from both tensor and scalar perturbations. To study the characteristics of each of these two kinds of perturbations, one has to determine the contribution of each to the anisotropy of CMB. For example, the ratio of the power spectra of tensor/scalar perturbations can be used to tighten bounds on the scalar spectral index. We investigate here the implications for the tensor/scalar ratio of the recent discovery (noted in astro-ph/0410139) that the introduction of a minimal length cutoff in the structure of spacetime does not leave boundary terms invariant. Such a cutoff introduces an ambiguity in the choice of action for tensor and scalar perturbations, which in turn can affect this ratio. We numerically solve for both tensor and scalar mode equations in a near-de-sitter background and explicitly find the cutoff dependence of the tensor/scalar ratio during inflation.