Khronon inflation

TL;DR

This paper explores a symmetry-based approach to inflation, promoting time shift symmetry to full reparametrization invariance, which constrains scalar perturbations and allows potential violations of standard consistency relations.

Contribution

It introduces a model where the full time reparametrization invariance constrains inflationary perturbations and predicts possible deviations from standard consistency relations in the squeezed limit.

Findings

Scalar n-point functions are fixed by the symmetry and power spectrum.

Potential violation of consistency relations in the squeezed limit.

3-point function terms suppressed by 1/k_L, indicating deviations from local shape.

Abstract

We study the possibility that the approximate time shift symmetry during inflation is promoted to the full invariance under time reparametrization t \to \tilde t(t), or equivalently under field redefinition of the inflaton \phi \to \tilde\phi(\phi). The symmetry allows only two operators at leading order in derivatives, so that all n-point functions of scalar perturbations are fixed in terms of the power spectrum normalization and the speed of sound. During inflation the decaying mode only decays as 1/a and this opens up the possibility to violate some of the consistency relations in the squeezed limit, although this violation is suppressed by the (small) breaking of the field reparametrization symmetry. In particular one can get terms in the 3-point function that are only suppressed by 1/k_L in the squeezed limit k_L \to 0 compared to the local shape.