Effective theories of single field inflation when heavy fields matter
Ana Achucarro, Jinn-Ouk Gong, Sjoerd Hardeman, Gonzalo A. Palma, Subodh P. Patil
TL;DR
The paper develops a covariant EFT for single-field inflation that emerges when heavy fields in a multi-field parent theory are integrated out, with a focus on how turns in field space induce a reduced, time-dependent speed of sound $c_s$. Through both a Minkowski toy model and a full FRW treatment with gravity, the authors show that all EFT couplings are controlled by $c_s$ and generalized adiabaticity conditions, allowing transient strong coupling without violating the derivative expansion. They derive the effective actions for the adiabatic curvature perturbation $\mathcal{R}$ and the Goldstone mode $\pi$, revealing distinctive cubic interactions that imprint signatures in the primordial bispectrum and potential features in the power spectrum. The results provide a robust framework to connect UV multi-field inflationary dynamics to low-energy observables, with clear discriminants from other models like DBI inflation and concrete implications for CMB/LSS data analysis.
Abstract
We compute the low energy effective field theory (EFT) expansion for single-field inflationary models that descend from a parent theory containing multiple other scalar fields. By assuming that all other degrees of freedom in the parent theory are sufficiently massive relative to the inflaton, it is possible to derive an EFT valid to arbitrary order in perturbations, provided certain generalized adiabaticity conditions are respected. These conditions permit a consistent low energy EFT description even when the inflaton deviates off its adiabatic minimum along its slowly rolling trajectory. By generalizing the formalism that identifies the adiabatic mode with the Goldstone boson of this spontaneously broken time translational symmetry prior to the integration of the heavy fields, we show that this invariance of the parent theory dictates the entire non-perturbative structure of the descendent EFT. The couplings of this theory can be written entirely in terms of the reduced speed of sound of adiabatic perturbations. The resulting operator expansion is distinguishable from that of other scenarios, such as standard single inflation or DBI inflation. In particular, we re-derive how certain operators can become transiently strongly coupled along the inflaton trajectory, consistent with slow-roll and the validity of the EFT expansion, imprinting features in the primordial power spectrum, and we deduce the relevant cubic operators that imply distinct signatures in the primordial bispectrum which may soon be constrained by observations.