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

Abstract

We compute the full one-loop corrections to the primordial tensor power spectrum in an inflationary scenario with a {non-canonical 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.

12 pages, 5 figures, accepted by JCAP