Constraining the Lorentz-violating bumblebee vector field with big bang nucleosynthesis and gravitational baryogenesis
Mohsen Khodadi, Gaetano Lambiase, Ahmad Sheykhi
Abstract
Abstract By assuming the cosmological principle i.e., an isotropic and homogeneous universe, we consider the cosmology of a vector-tensor theory of gravitation known as the 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 $$B(t)\sim t^\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>∼</mml:mo> <mml:msup> <mml:mi>t</mml:mi> <mml:mi>β</mml:mi> </mml:msup> </mml:mrow> </mml:math> for the time evolution of the vector field, where $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> is a free parameter, we derive the relevant dynamic equations of the Universe. 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., $$\xi b^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:msup> <mml:mi>b</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> , and the exponent parameter $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> . 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.