One-Loop Tensor Power Spectrum from a Non-Minimally Coupled Spectator Field during Inflation

TL;DR

This paper calculates one-loop quantum corrections to the primordial tensor power spectrum during inflation with a non-minimally coupled spectator field, revealing potential large enhancements in tensor-to-scalar ratio under certain couplings.

Contribution

It provides the first semi-analytic computation of one-loop tensor corrections in this inflationary scenario with specific coupling models.

Findings

Model G yields about 1-fold correction to $r_{eff}$

Model O can increase $r_{eff}$ by several orders of magnitude

Primordial gravitational wave energy density is below detection thresholds of planned experiments

Abstract

We compute the full one-loop corrections to the primordial tensor power spectrum in an inflationary scenario with a non-minimally coupled spectator field, using the in-in formalism. We derive semi-analytic results for the scalar-sourced one-loop tensor spectrum and the effective tensor-to-scalar ratio, $r_{\mathrm{eff}}$ . We consider two representative coupling functions: a localized Gaussian dip (Model G), which leads to moderate loop corrections, and a rapidly oscillatory coupling (Model O), which can yield much larger loop contributions. For Model G, we find a $\mathcal{O}(1)$ correction to $r_{\mathrm{eff}}$ while Model O can significantly enhance $r_{\mathrm{eff}}$ by several orders of magnitude (relative to the tree-level value). We further calculate the energy density of primordial gravitational waves. Assuming that primordial black holes with mass $10^{-12}M_{\odot}$ generated in this scenario, constitute all of the dark matter, we find that the results are several orders of magnitude lower than the sensitivities of Taiji/TianQin/LISA.