# Life of cosmological perturbations in MDR models, and the prospect of travelling primordial gravitational waves

## TL;DR

This paper investigates how primordial cosmological perturbations evolve under modified dispersion relations, highlighting conditions for observable gravitational waves that could signal quantum gravity effects in MDR models.

## Contribution

It analyzes the evolution of scalar and tensor modes in MDR models, identifying conditions for their transition from trans-Planckian to observable regimes and proposing potential observational signatures.

## Key findings

- Scalar modes satisfy the horizon crossing condition in MDR models.
- Tensor modes may produce travelling gravitational waves detectable by future experiments.
- PeV-scale quantum gravity could allow observable travelling primordial gravitational waves.

## Abstract

We follow the life of a generic primordial perturbation mode (scalar or tensor) subject to modified dispersion relations (MDR), as its proper wavelength is stretched by expansion. A necessary condition ensuring that travelling waves can be converted into standing waves is that the mode starts its life deep inside the horizon and in the trans-Planckian regime, then leaves the horizon as the speed of light corresponding to its growing wavelength drops, to eventually become cis-Planckian whilst still outside the horizon, and finally re-enter the horizon at late times. We find that scalar modes in the observable range satisfy this condition, thus ensuring the viability of MDR models in this respect. For tensor modes we find a regime in which this does not occur, but in practice it can only be realised for wavelengths in the range probed by future gravity wave experiments if the quantum gravity scale experienced by gravity waves goes down to the PeV range. In this case travelling---rather than standing---primordial gravity waves could be the tell-tale signature of MDR scenarios.