Theoretical bounds on the tensor-to-scalar ratio in the cosmic microwave background

TL;DR

This paper establishes new, stronger theoretical bounds on the tensor-to-scalar ratio in the cosmic microwave background, enhancing our understanding of inflationary signatures.

Contribution

It generalizes the Lyth bound, introduces a new absolute upper bound on tensors, and compares with existing relationships, advancing theoretical constraints in cosmology.

Findings

New bounds are at least 100 times stronger than previous ones.

Derived a universal upper limit on tensor modes using de Sitter entropy.

Clarified the relationship between existing bounds and new theoretical limits.

Abstract

Tensor modes in the cosmic microwave background are one of the most robust signatures of inflation. We derive theoretical bounds on the tensor fraction, as a generalization of the well-known Lyth bound. Under reasonable assumptions, the new bounds are at least two orders of magnitude stronger than the original one. We comment on a previously derived generalization, the so-called Efstathiou-Mack relationship. We also derive a new absolute upper bound on tensors using de Sitter entropy bounds.