Quantum Slow Roll

TL;DR

This paper investigates how quantum effects from fermions coupled to a scalar field in de Sitter space induce a slow roll behavior in the scalar perturbations, affecting the power spectrum.

Contribution

It introduces a method to compute the nonlocal quantum effective action in curved spacetime and demonstrates quantum-induced slow roll with a red tilt in a classically de Sitter background.

Findings

Quantum nonlocality modifies scalar mode expansion.

Scalar power spectrum exhibits a red tilt proportional to Yukawa coupling squared.

Quantum effects induce slow roll behavior in a classical de Sitter spacetime.

Abstract

We consider a scalar field coupled to massless fermions through Yukawa couplings, such as the Higgs field, in a Robertson-Walker spacetime. We compute the nonlocal quantum effective action as a functional of the background scalar field and the scale factor at one loop order by integrating the Weyl anomaly resulting from the fermions in the loop. We show that the mode expansion of the scalar field is modified by the quantum nonlocality and the power spectrum of scalar perturbations exiting the horizon exhibits a slow roll with a red tilt proportional to the square of the Yukawa coupling even though the classical spacetime is exactly de Sitter. We comment on possible implications for cosmology.