Squeezing of scalar and tensor primordial perturbations generated by modified dispersion relations

TL;DR

This paper investigates the absence of primordial squeezing in models with modified dispersion relations by analyzing the problem in a dual rainbow frame, revealing that gravity's behavior at sub-Planckian scales explains the phenomenon.

Contribution

It provides a novel analysis of primordial perturbations in a dual rainbow frame, clarifying why squeezing is absent in certain models with modified dispersion relations.

Findings

No primordial squeezing in the critical model with scale-invariant spectrum.

Squeezing occurs for non-critical models with red spectra.

Potential observational differences for blue spectrum gravitational waves.

Abstract

In recent work we analyzed the evolution of primordial perturbations satisfying Planck-scale-modified dispersion relations and showed that there is no cosmological "squeezing" in the critical model that produces perturbations with a scale invariant spectrum. Nevertheless, the perturbations reenter the horizon as standing waves with the correct temporal phase because of the late-time decay of the momentum mode. Here we shed light on the absence of primordial squeezing by re-examining the problem in the dual rainbow frame, where $c$ is set to 1, shifting the varying $c$ effects elsewhere. In this frame gravity switches off at sub-Planckian wavelengths, so that the fluctuations behave as if they were in Minkowski spacetime. This is ultimately why they are not squeezed. However, away from the critical model squeezing does occur if the fluctuations spectrum is red, as is the case for scalar perturbations. Should the primordial gravity waves have a blue spectrum, we predict that they might not reenter the horizon as standing waves, because the momentum mode would be enhanced in the primordial phase.