Multiple spectator condensates from inflation

TL;DR

This paper explores how multiple light spectator fields develop condensates during inflation, revealing new stationary solutions for asymmetric potentials and identifying critical couplings that influence condensate formation.

Contribution

It introduces novel stationary solutions for coupled spectator fields in inflation and establishes conditions for condensate formation and decoupling, supported by a new computational tool.

Findings

New stationary solutions for asymmetric potentials.

Critical inter-field coupling thresholds identified.

A publicly available Python tool for simulations.

Abstract

We investigate the development of spectator (light test) field condensates due to their quantum fluctuations in a de Sitter inflationary background, making use of the stochastic formalism to describe the system. In this context, a condensate refers to the typical field value found after coarse-graining using the Hubble scale $H$, which can be essential to seed the initial conditions required by various post-inflationary processes. We study models with multiple coupled spectators and for the first time we demonstrate that new forms of stationary solution exist (distinct from the standard exponential form) when the potential is asymmetric. Furthermore, we find a critical value for the inter-field coupling as a function of the number of fields above which the formation of stationary condensates collapses to $H$. Considering some simple two-field example potentials, we are also able to derive a lower limit on the coupling, below which the fluctuations are effectively decoupled, and the standard stationary variance formulae for each field separately can be trusted. These results are all numerically verified by a new publicly available python class (https://github.com/umbralcalc/nfield) to solve the coupled Langevin equations over a large number of fields, realisations and timescales. Further applications of this new tool are also discussed.