Scale-dependence in DHOST inflation

TL;DR

This paper explores how DHOST inflation models behave under different perturbations, finding that certain modifications lead to scale-invariant spectra while others produce scale-dependent spectra compatible with current observational constraints.

Contribution

It investigates the effects of breaking degeneracy and shift symmetry in DHOST theories on inflationary perturbations, highlighting conditions for scale invariance and potential observational signatures.

Findings

Power spectra are scale-invariant under derivative scordatura.

Small axion-like perturbations induce scale-dependent spectra.

Results align with current inflationary observational constraints.

Abstract

We study the inflationary consequences of Degenerate Higher Order Scalar Tensor (DHOST) theories in a de Sitter background. We perturb the de Sitter background by operators breaking either the degeneracy condition, i.e scordatura DHOST, or the shift symmetry in the scalar field. We first consider derivative scordatura and find that in all cases the power spectra of curvature perturbations are scale-invariant. We then investigate small perturbations by an axion-like potential, and show that in this scenario the power spectrum becomes scale-dependent. The modifications to the spectral index and its first two derivatives are compatible with the latest inflationary constraints. Moreover the tensor to scalar ratio and the non-Gaussianities of these models could be within reach of future experiments.