Cosmological constraints on Lorentz invariance violation in the neutrino sector

TL;DR

This paper derives constraints on Lorentz invariance violation in the neutrino sector using cosmological data, finding no evidence for such violation and highlighting potential improvements with future experiments.

Contribution

It introduces a modified Boltzmann equation for massive neutrinos with deformed dispersion relations and constrains the deformation parameter using cosmological observations.

Findings

No evidence for Lorentz invariance violation in neutrinos.

Deformation parameter is degenerate with dark matter density.

Future Planck data could tighten constraints.

Abstract

We derive the Boltzmann equation in the synchronous gauge for massive neutrinos with a deformed dispersion relation. Combining the 7-year WMAP data with lower-redshift measurements of the expansion rate, we give constraints on the deformation parameter and find that the deformation parameter is strong degenerate with the physical dark matter density instead of the neutrino mass. Our results show that there is no evidence for Lorentz invariant violation in the neutrino sector. The ongoing Planck experiment could provide improved constraints on the deformation parameter.