Scale Invariance from Modified Dispersion Relations

TL;DR

This paper explores how modified dispersion relations in cosmology can produce scale-invariant primordial perturbation spectra, analyzing the dependence on background evolution and parameter choices.

Contribution

It provides a detailed analysis of the conditions under which scale invariance can be achieved with modified dispersion relations in cosmological models.

Findings

Multiple parameter regimes allow for scale-invariant spectra.

The relation between dispersion relation parameters and background evolution is clarified.

Conditions for scale invariance are identified for various z and p values.

Abstract

In this paper, inspired by the investigations on the theory of cosmological perturbations in Ho\v{r}ava-Liftshit cosmology, we calculated the spectrum of primordial perturbation leaded by a scalar field with modified dispersion relation \omega\sim k^z/a^{p-1}, in which z is the critical exponent and p is generally not equal to z. We discussed that for fixed z, if the spectrum is required to be scale invariant, how should p depend on the background evolution. We concluded that there is always a room of parameters for the generation of scale invariant spectrum.