Gravitational waves and large field inflation

TL;DR

This paper investigates whether non-detection of large tensor-to-scalar ratios can rule out large field inflation models and explores what measurements of $r$ reveal about the inflation scale, using $ ext{alpha}$-attractors as a testing framework.

Contribution

It clarifies the distinctions between different definitions of large field inflation and inflation scale, and analyzes their implications within the $ ext{alpha}$-attractor models.

Findings

Non-detection of tensor modes can constrain certain large field inflation models.

The relationship between $r$ and the inflation scale depends on the specific definitions used.

$ ext{alpha}$-attractors provide a versatile framework to test these theoretical considerations.

Abstract

According to the famous Lyth bound, one can confirm large field inflation by finding tensor modes with sufficiently large tensor-to-scalar ratio $r$. Here we will try to answer two related questions: Is it possible to rule out all large field inflationary models by not finding tensor modes with $r$ above some critical value, and what can we say about the scale of inflation by measuring $r$? However, in order to answer these questions one should distinguish between two different definitions of the large field inflation and three different definitions of the scale of inflation. We will examine these issues using the theory of cosmological $\alpha$-attractors as a convenient testing ground.