Bounds on Generic High-Energy Physics Modifications to the Primordial Power Spectrum from Back-Reaction on the Metric

TL;DR

The paper investigates whether generic high-energy (trans-Planckian) modifications to the primordial power spectrum, modeled via boundary conditions in an effective field theory, can be observable without inducing prohibitive back-reaction on the metric. Using a boundary-state formalism, it computes how a dimension-four boundary perturbation parameterized by $\beta$ alters the stress-energy tensor through the symmetric two-point function, and derives quantitative back-reaction bounds that depend on $H$, $M$, and slow-roll parameters. The core result is a set of three inequalities limiting $\beta$ with increasing rigidity: $\beta < \frac{4\pi}{GM^2}(\frac{H}{M})^2$, $\beta < \epsilon \frac{8\pi}{5GM^2}(\frac{H}{M})^3$, and $\beta < \epsilon \eta \frac{8\pi}{15GM^2}(\frac{H}{M})^4$, indicating that realistic scenarios likely render trans-Planckian signatures unobservable via this back-reaction channel. The findings clarify the role of metric back-reaction in boundary EFT approaches to inflation and set stringent limits on the observational prospects of such high-energy modifications.

Abstract

Modifications to the primordial power spectrum of inflationary density perturbations have been studied recently using a boundary effective field theory approach. In the approximation of a fluctuating quantum field on a fixed background, the generic effect of new physics is encoded in parameters of order H/M. Here, we point out that the back-reaction on the metric can be neglected only when these parameters obey certain bounds that may put them beyond the reach of observation.