1/N Resolution to Inflationary eta-Problem

TL;DR

This paper shows that in models with many light scalar fields, quantum loop corrections to the inflationary eta parameter are suppressed by 1/N, resolving the eta-problem in such inflationary scenarios.

Contribution

It demonstrates that the one-loop quantum corrections to the eta parameter are suppressed by 1/N in models with many scalar fields, providing a solution to the eta-problem.

Findings

Quantum corrections to the graviton propagator scale with N.

The Rφ_a^2 term coefficient is suppressed by 1/N.

The eta-problem is absent in N-flation and M-flation models.

Abstract

We observe that the dominant one loop contribution to the graviton propagator in the theory of N (N>>1) light scalar fields \phi_a (with masses smaller than M_{pl}/\sqrt{N}) minimally coupled to Einstein gravity is proportional to N while that of graviton-scalar-scalar interaction vertex is N independent. We use this to argue that the coefficient of the R\phi_a^2 term appearing at one loop level is 1/N suppressed. This observation provides a resolution to the \eta-problem, that the slow-roll parameter \eta receives order one quantum loop corrections for inflationary models built within the framework of scalar fields minimally coupled to Einstein gravity, for models involving large number of fields. As particular examples, we employ this to argue in favor of the absence of \eta-problem in M-flation and N-flation scenarios.