Lorentz-Violating Vector Fields Slow the Universe Down

TL;DR

This work examines a fixed-norm timelike vector field that violates local Lorentz invariance and couples to gravity. By deriving the field equations and analyzing both the Newtonian limit and cosmology, the authors show that the vector rescaless the observable Newton constant differently in the Solar System and in the expanding universe. They derive a Big Bang nucleosynthesis bound that limits the vector norm to be well below the Planck scale, with m ≲ 10^18 GeV for order-one beta parameters. The results provide robust constraints on Lorentz-violating extensions of gravity and point to possible signatures in inflation and CMB perturbations explored in companion work.

Abstract

We consider the gravitational effects of a single, fixed-norm, Lorentz-violating timelike vector field. In a cosmological background, such a vector field acts to rescale the effective value of Newton's constant. The energy density of this vector field precisely tracks the energy density of the rest of the universe, but with the opposite sign, so that the universe experiences a slower rate of expansion for a given matter content. This vector field similarly rescales Newton's constant in the Newtonian limit, although by a different factor. We put constraints on the parameters of the theory using the predictions of primordial nucleosynthesis, demonstrating that the norm of the vector field should be less than the Planck scale by an order of magnitude or more.