Where does Cosmological Perturbation Theory Break Down?

TL;DR

The paper analyzes the regime of validity for cosmological perturbation theory during inflation by embedding higher-dimensional, generally covariant operators into an effective field theory of the metric–inflaton system. Using the in-in formalism, it shows that tree-level corrections from these operators induce momentum-dependent modifications to tensor and scalar two-point functions, with a breakdown scale Λ ~ M_p^2/H, far above the Planck scale when H ≪ M_p. The leading corrections scale with powers of k_ph/M_p and H/M_p, and the breakdown occurs once k_ph approaches Λ, beyond which the EFT ceases to be predictive. These results imply trans-Planckian effects in the primordial spectrum are likely suppressed and that the standard perturbative treatment remains valid up to surprisingly high momenta, shaping how we interpret potential high-energy signatures in cosmological data.

Abstract

We apply the effective field theory approach to the coupled metric-inflaton system, in order to investigate the impact of higher dimension operators on the spectrum of scalar and tensor perturbations in the short-wavelength regime. In both cases, effective corrections at tree-level become important when the Hubble parameter is of the order of the Planck mass, or when the physical wave number of a cosmological perturbation mode approaches the square of the Planck mass divided by the Hubble constant. Thus, the cut-off length below which conventional cosmological perturbation theory does not apply is likely to be much smaller than the Planck length. This has implications for the observability of "trans-Planckian" effects in the spectrum of primordial perturbations.