Inflationary predictions of double-well, Coleman-Weinberg, and hilltop potentials with non-minimal coupling

TL;DR

This paper explores how non-minimal coupling between the inflaton and gravity influences inflationary predictions, showing that certain models can mimic Starobinsky predictions and identifying parameter regions compatible with observations.

Contribution

It provides a detailed analysis of inflation with double-well, Coleman-Weinberg, and hilltop potentials considering non-minimal coupling effects, highlighting conditions for observational consistency.

Findings

Inflationary predictions can resemble Starobinsky model under certain conditions.

Regions in the $v$-$\xi$ plane yield spectral index and tensor-to-scalar ratio compatible with observations.

Tensor-to-scalar ratio $r$ remains above 0.002 in the analyzed parameter space.

Abstract

We discuss how the non-minimal coupling $\xi\phi^2R$ between the inflaton and the Ricci scalar affects the predictions of single field inflation models where the inflaton has a non-zero vacuum expectation value (VEV) $v$ after inflation. We show that, for inflaton values both above the VEV and below the VEV during inflation, under certain conditions the inflationary predictions become approximately the same as the predictions of the Starobinsky model. We then analyze inflation with double-well and Coleman-Weinberg potentials in detail, displaying the regions in the $v$-$\xi$ plane for which the spectral index $n_s$ and the tensor-to-scalar ratio $r$ values are compatible with the current observations. $r$ is always larger than 0.002 in these regions. Finally, we consider the effect of $\xi$ on small field inflation (hilltop) potentials.