Modified dispersion relations, inflation and scale invariance

TL;DR

This paper explores how modified dispersion relations can produce scale-invariant quantum fluctuations during inflation, emphasizing the importance of background dynamics and showing that high Hubble rate inflation can achieve near scale-invariance.

Contribution

It demonstrates that non-trivial pre-inflationary dynamics, such as high Hubble rate inflation, are necessary for scale-invariance in modified dispersion relation scenarios, extending previous models.

Findings

Scale-invariance requires specific background evolution before standard cosmology.

High Hubble rate inflation can produce nearly scale-invariant fluctuations for any power-law dispersion.

Slow-roll conditions further enhance scale-invariance in these models.

Abstract

For a certain type of modified dispersion relations, the vacuum quantum state for very short wavelength cosmological perturbations is scale-invariant and it has been suggested that this may be the source of the scale-invariance observed in the temperature anisotropies in the cosmic microwave background. We point out that for this scenario to be possible, it is necessary to redshift these short wavelength modes to cosmological scales in such a way that the scale-invariance is not lost. This requires non-trivial background dynamics before the onset of standard radiation-dominated cosmology; we demonstrate that one possible solution is inflation with a sufficiently large Hubble rate, for this slow roll is not necessary. In addition, we also show that if the slow-roll condition is added to inflation with a large Hubble rate, then for any power law modified dispersion relation quantum vacuum fluctuations become nearly scale-invariant when they exit the Hubble radius.