Constraining the Lorentz-Violating Bumblebee Vector Field with Big Bang Nucleosynthesis and Gravitational Baryogenesis

TL;DR

This paper investigates how a Lorentz-violating vector field in a bumblebee gravity model affects early universe processes, using observational data from Big Bang Nucleosynthesis and Baryogenesis to constrain the model parameters.

Contribution

It introduces constraints on the bumblebee vector field's vacuum expectation value and evolution rate based on cosmological observations, advancing understanding of Lorentz violation in gravity.

Findings

Constraints on the Lorentz-violating vector field from BBN data

Limits on the evolution rate of the bumblebee field from Baryogenesis

Bounds on Lorentz violation parameters in the early universe

Abstract

By keeping the cosmological principle i.e., an isotropic and homogeneous universe, we consider the cosmology of a vector-tensor theory of gravitation known as the \textit{bumblebee} model. In this model a single Lorentz-violating timelike vector field with a nonzero vacuum expectation value (VEV) couples to the Ricci tensor and scalar, as well. Taking the ansatz $B(t)\sim t^\beta$ for the time evolution of the vector field we derive the relevant dynamic equations of the Universe, where $\beta$ is a free parameter. In particular, by employing observational data coming from the Big Bang Nucleosynthesis (BBN) and the matter-antimatter asymmetry in the Baryogenesis era, we impose some constraints on the VEV of the bumblebee timelike vector field i.e., $\xi b^2$, and the exponent parameter $\beta$. The former and the latter limit the size of Lorentz violation, and the rate of the time evolution of the background Lorentz-violating bumblebee field, respectively.