SOLUTIONS OF COSMOLOGICAL MODELS WITH VARYING SPEED OF LIGHT

In recent years, there has been some renewed interest in cosmological models in which the constants of nature vary with time. In one of these, one supposes a dependence on the redshift of the fine structure constant as suggested by some astronomical observations of quasars. This has led, among others, to the proposal that the speed of light varies with the cosmological time. A Varying Speed of Light (VSL) would be able to solve some long standing problems of the standard cosmological model, without the need for inflation. In this work we study two models in which (1) c varies according to a power law of the scale factor c(t) ∝ a-r and (2) c is proportional to the Hubble parameter c(t) ∝ Hu. We present solutions for these two types of VSL cosmologies. We find that for a flat (k = 0) Friedmann–Robertson–Walker (FRW) universe, the variation of c is coupled to a cosmological Λ-term and both singular and non-singular solutions are possible.