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

TL;DR

The paper investigates the impact of a large number N of light scalar fields on early-universe cosmology, distinguishing participator and spectator fields and exploring both stochastic/eternal inflation and quantum loop corrections. Using the Schwinger-Keldysh in-in formalism, it analyzes two regimes: N spectator fields with a single inflaton, where one-loop corrections yield a bound $N \lesssim \frac{M_p^2}{H^2}\frac{1}{\epsilon}$, and N participator fields (N-flation), where loop corrections do not scale with N and the dynamics can be recast as an effective single-field theory. The results show that a large N of spectator fields can modestly affect the power spectrum yet remain subdominant, while a large N of participator fields leaves leading-order corrections independent of N, allowing an effectively composite inflaton. Overall, the work clarifies how many light scalars interact with inflationary dynamics and lays out methodological refinements for loop calculations in the in-in formalism.

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.

Figures (2)

• Figure 1: Feynman diagrams for the three- and four-point one-loop correction for the $I$ field correlator. With $N$ participator fields, the first two terms apparently scale as $N$, due to the summation of $J$, but each loop is suppressed by $\epsilon/N$, arising from the extra coupling. At leading order in slow roll, the third term only has contributions from the self-interaction $I=J$ term, so the corrections do not blow up as $N$ becomes large. Here we have denoted $I$ fields by a solid lines while dotted lines represent $J$ fields.
• Figure 2: The non-self-interaction four-point loops factor into a vacuum fluctuation piece times a propagator. The ellipses indicate contractions which lead to polynomial divergences.