On the cosmological evolution of alpha and mu and the dynamics of dark energy

Abstract

We study the cosmological evolution of the fine structure constant, $α$, and the proton-to-electron mass ratio, $μ=m_p/m_e$, in the context of a generic class of models where the gauge kinetic function is a linear function of a quintessence-type real scalar field, $ϕ$, described by a Lagrangian with a standard kinetic term and a scalar field potential, $V(ϕ)$. We further assume that the scalar field potential is a monotonic function of $ϕ$ and that the scalar field is always rolling down the potential. We show that, for this class of models, low-redshift constrains on the evolution of $α$ and $μ$ can provide very stringent limits on the corresponding variations at high-redshift. We also demonstrate that these limits may be relaxed by considering more general models for the dynamics of $α$ and $μ$. However, in this case, the ability to reconstruct the evolution of the dark energy equation of state using varying couplings could be seriously compromised.

5 pages