Cosmology With Many Light Scalar Fields: Stochastic Inflation and Loop Corrections

TL;DR

This paper investigates the effects of numerous light scalar fields during early universe inflation, analyzing stochastic behavior, eternal inflation scenarios, and quantum loop corrections, revealing that the number of participator fields does not bound the inflationary power spectrum.

Contribution

It introduces a detailed analysis of stochastic and quantum effects in multi-field inflation models, showing loop corrections do not limit the number of participator fields and addressing in-in formalism challenges.

Findings

Loop corrections are largest with spectator fields and a single participator.

Loop corrections do not scale with N, placing no upper bound on participator fields.

The theory behaves like a single scalar field at leading order.

Abstract

We explore the consequences of the existence of a very large number of light scalar degrees of freedom in the early universe. We distinguish between participator and spectator fields. The former have a small mass, and can contribute to the inflationary dynamics; the latter are either strictly massless or have a negligible VEV. In N-flation and generic assisted inflation scenarios, inflation is a co-operative phenomenon driven by N participator fields, none of which could drive inflation on their own. We review upper bounds on N, as a function of the inflationary Hubble scale H. We then consider stochastic and eternal inflation in models with N participator fields showing that individual fields may evolve stochastically while the whole ensemble behaves deterministically, and that a wide range of eternal inflationary scenarios are possible in this regime. We then compute one-loop quantum corrections to the inflationary power spectrum. These are largest with N spectator fields and a single participator field, and the resulting bound on N is always weaker than those obtained in other ways. We find that loop corrections to the N-flation power spectrum do not scale with N, and thus place no upper bound on the number of participator fields. This result also implies that, at least to leading order, the theory behaves like a composite single scalar field. In order to perform this calculation, we address a number of issues associated with loop calculations in the Schwinger-Keldysh "in-in" formalism.