# One-loop corrections to the primordial tensor spectrum from massless isocurvature fields

## TL;DR

This paper calculates one-loop quantum corrections to primordial tensor fluctuations caused by massless isocurvature fields, revealing a logarithmic running that impacts the tensor spectrum in early universe cosmology.

## Contribution

It provides the first detailed analysis of one-loop effects from various massless spectator fields on tensor perturbations during inflation.

## Key findings

- Logarithmic running of tensor spectrum corrections identified
- Quantum corrections depend on the Hubble parameter and renormalization scale
- Results apply to scalar, fermion, and gauge field isocurvature modes

## Abstract

We study one-loop corrections to the two-point correlation function of tensor perturbations in primordial cosmology induced by massless spectator matter fields. Using the Schwinger-Keldysh formalism in cosmological perturbation theory, we employ dimensional regularization and cutoff regularization to study the finite quantum corrections at one-loop arising from isocurvature fields of the massless scalar, fermion and abelian gauge field which are freely propagating on the FRW spacetime. For all cases, we find a logarithmic running of the form $\frac{C}{q^3} \, \frac{H^4}{M^4_p} \log \left( \frac{H}{\mu } \right)$ where $C$ is a negative constant related to the beta function, $H$ is the Hubble parameter at horizon exit and $\mu$ is the renormalization scale.