Inflating with Large Effective Fields

TL;DR

The paper develops a symmetry-based framework for large-field inflation within effective field theory, showing that pseudo-Goldstone inflatons and higher-dimensional moduli can yield robust large-field expansions protected from large quantum corrections. It demonstrates that both power-law and exponential potentials can drive slow-roll inflation compatible with current data, and derives key relations among observables, including the universal large-field behavior $r \approx \frac{8}{3} (1-n_s)$ for certain exponential potentials. It also investigates naturalness and UV completions, presenting explicit constructions in 4D supergravity and string-inspired settings (notably coset models like $SU(1,1)/U(1)$) and discussing moduli stabilization and the role of large decay constants. Collectively, the work provides a coherent path from high-energy symmetries to viable large-field inflationary scenarios with testable predictions in $n_s$ and $r$.

Abstract

We re-examine large scalar fields within effective field theory, in particular focussing on the issues raised by their use in inflationary models (as suggested by BICEP2 to obtain primordial tensor modes). We argue that when the large-field and low-energy regimes coincide the scalar dynamics is most effectively described in terms of an asymptotic large-field expansion whose form can be dictated by approximate symmetries, which also help control the size of quantum corrections. We discuss several possible symmetries that can achieve this, including pseudo-Goldstone inflatons characterized by a coset $G/H$ (based on abelian and non-abelian, compact and non-compact symmetries), as well as symmetries that are intrinsically higher dimensional. Besides the usual trigonometric potentials of Natural Inflation we also find in this way simple {\em large-field} power laws (like $V \propto φ^2$) and exponential potentials, $V(φ) = \sum_{k} V_k \; e^{-k φ/M}$. Both of these can describe the data well and give slow-roll inflation for large fields without the need for a precise balancing of terms in the potential. The exponential potentials achieve large $r$ through the limit $|η| \ll ε$ and so predict $r \simeq \frac83(1-n_s)$; consequently $n_s \simeq 0.96$ gives $r \simeq 0.11$ but not much larger (and so could be ruled out as measurements on $r$ and $n_s$ improve). We examine the naturalness issues for these models and give simple examples where symmetries protect these forms, using both pseudo-Goldstone inflatons (with non-abelian non-compact shift symmetries following familiar techniques from chiral perturbation theory) and extra-dimensional models.