Detecting a Lorentz-Violating Field in Cosmology

TL;DR

This paper investigates the Einstein-aether theory's cosmological implications, showing that while scalar perturbations match general relativity, tensor perturbations differ with smaller amplitude, affecting CMB and matter spectra.

Contribution

It provides a covariant, gauge-invariant perturbation analysis of Einstein-aether cosmology, revealing unique tensor perturbation signatures and their effects on cosmological observations.

Findings

Scalar power spectrum matches general relativity.

Tensor power spectrum has smaller amplitude.

CMB and matter spectra are modified but degenerate with other parameters.

Abstract

We consider cosmology in the Einstein-aether theory (the generally covariant theory of gravitation coupled to a dynamical timelike Lorentz-violating vector field) with a linear aether-Lagrangian. The 3+1 spacetime splitting approach is used to derive covariant and gauge invariant perturbation equations which are valid for a general class of Lagrangians. Restricting attention to the parameter space of these theories which is consistent with local gravity experiments, we show that there are tracking behaviors for the aether field, both in the background cosmology and at linear perturbation level. The primordial power-spectrum of scalar perturbations in this model is shown to be the same that predicted by standard general relativity. However, the power-spectrum of tensor perturbation is different from that in general relativity, but has a smaller amplitude and so cannot be detected at present. We also study the implications for late-time cosmology and find that the evolution of photon and neutrino anisotropic stresses can source the aether field perturbation during the radiation and matter dominated epochs, and as a result the CMB and matter power spectra are modified. However these effects are degenerate with respect to other cosmological parameters, such as neutrino masses and the bias parameter in the observed galaxy spectrum.