Where does Cosmological Perturbation Theory Break Down?

TL;DR

This paper uses effective field theory to determine where standard cosmological perturbation theory breaks down at high energies, especially near the Planck scale, affecting the potential observation of trans-Planckian effects.

Contribution

It identifies the energy scales and conditions under which cosmological perturbation theory becomes invalid due to higher dimension operators.

Findings

Breakdown occurs when Hubble parameter approaches Planck mass

Effective corrections become significant at high wave numbers

The cutoff length is smaller than the Planck length

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.