A geometrically-induced varying speed of light (VSL) and the accelerating universe

Abstract

We tackle the problem of the accelerating universe by reconsidering the most general form of the metric when the speed of light is allowed to evolve with time in a homogeneous and isotropic universe. A new varying speed of light (VSL) model naturally emerges. We find it unconvenient to perform a general coordinate transformation to obtain the usual constant $g_{tt}$ as such an operation would mask the relation existing between the evolution of the scale factor and the frequency shifts. In the model proposed the expansion rate and the acceleration of the universe turn out to be apparent effects induced by the evolution of the speed of light. The model is beneficial in that no sort of exotic (and so far unobserved) fluids, not even a cosmological constant, are needed for our solutions to be compatible with observations. Only dust and radiation are put into the energy-momentum tensor and these are found to be sufficient to reach the critical density for the model and therefore to obtain a spatially-flat universe. The field equations for the model are derived and solved. Among others, one fashinating possibility is that of an eternally bouncing universe. The relation with the varying-$\alpha_\textsc{em}$ results is discussed.