Distinctive signatures of space-time diffeomorphism breaking in EFT of inflation

TL;DR

This work develops an EFT of inflation that breaks both time and space diffeomorphisms, introducing two Goldstone modes $\pi$ and $\sigma$ and predicting new couplings among scalar and tensor fluctuations. Through a decoupling-limit analysis, it derives scalar and tensor power spectra with log-enhanced corrections from $\pi$–$\sigma$ mixing and shows that spatial-diffeomorphism breaking can yield a blue tensor tilt. The paper then computes squeezed-limit bispectra, revealing angular-dependent (monopole plus quadrupole) contributions in the scalar sector and explicit tensor-scalar-scalar bispectra that violate single-field consistency relations with additional log-enhanced terms, offering potential observational tests in CMB and LSS surveys. Overall, the EFTI framework proves capable of capturing distinctive signatures of space-time diffeomorphism breaking and provides concrete pathways to constrain such symmetry breaking with current and future data.

Abstract

The effective field theory of inflation is a powerful tool for obtaining model independent predictions common to large classes of inflationary models. It requires only information about the symmetries broken during the inflationary era, and on the number and nature of fields that drive inflation. In this paper, we consider the case for scenarios that simultaneously break time reparameterization and spatial diffeomorphisms during inflation. We examine how to analyse such systems using an effective field theory approach, and we discuss several observational consequences for the statistics of scalar and tensor modes. For example, examining the three point functions, we show that this symmetry breaking pattern can lead to an enhanced amplitude for the squeezed bispectra, and to a distinctive angular dependence between their three wavevectors. We also discuss how our results indicate prospects for constraining the level of spatial diffeomorphism breaking during inflation.

Figures (3)

• Figure 1: Leading diagram for computing the symmetry breaking contributions to $\left\langle \pi^{2}\right\rangle$.
• Figure 2: Leading diagram for computing the symmetry breaking contributions to $\langle\mathcal{R}^3\rangle$.
• Figure 3: Leading consistency violating contributions to the TSS bispectrum $\langle \gamma \pi\pi\rangle$