What spectators do during inflation

TL;DR

This paper derives the inflaton's equation of motion with one-loop radiative corrections from spectator fields, analyzing particle production during slow roll inflation and challenging the reliability of phenomenological friction models.

Contribution

It provides explicit solutions for the inflaton's evolution including radiative corrections, introduces a generalized optical theorem for cosmology, and develops a non-perturbative mean field theory.

Findings

Inflaton evolution is significantly affected by radiative corrections from spectators.

Total spectator particle number grows exponentially with the number of e-folds.

Phenomenological friction terms are shown to be unreliable for modeling inflaton dynamics.

Abstract

The inflaton equation of motion including one loop radiative corrections from spectator fields is obtained. We consider a massless scalar conformally coupled to gravity and a massless fermion Yukawa coupled to the inflaton as models for spectators that \emph{do not feature} gravitational particle production, their production during slow roll is solely a consequence of their coupling to the inflaton. The one-loop self energy and the fully renormalized equation of motion of the inflaton are obtained and solved explicitly for an inflaton potential $m^2\varphi^2/2$. The solution features Sudakov-type logarithmic secular terms, which are resumed via the dynamical renormalization group and compared to the solutions with a phenomenological friction term. During $N_e$ e-folds of slow roll inflation the inflaton evolves as $\varphi^{(0)}_{Isr}(t)\,e^{\frac{m^2\Gamma}{9H^3}\,N_e(t)}$ for the phenomenological friction term $\Gamma$ and $\varphi^{(0)}_{Isr}(t)\,e^{\Upsilon N^2_e}$ with $\Upsilon = -\frac{\lambda^2}{24\pi^2 H^2} ; \frac{y^2_R}{12\pi^2}$ for the radiative corrections from bosonic and fermionic spectators respectively where $\varphi^{(0)}_{Isr}(t)$ is the slow roll solution in absence of interactions, showing that a phenomenological friction term is not reliable. A generalization of the optical theorem to a finite time domain and cosmological expansion is introduced to obtain the distribution function $f(k,t)$ and total number of spectators produced \emph{during slow roll}. $f(k,t)$ is peaked at superhorizon scales and the total number of particles grows $\propto e^{3N_e}$. A non-perturbative mean field theory is introduced to describe the self-consistent evolution of the inflaton coupled to spectators, its linearized version reproduces the self-energy, the inflaton equation of motion and the results on particle production.