Asymptotic Analysis of Varying Light Speed Cosmologies

We investigate potential singularities in isotropic cosmological models featuring a time-varying speed of light and the gravitational constant. The governing field equations generally simplify into two-dimensional systems, subject to analysis through dynamical systems techniques within phase space and the application of asymptotic splitting methods. In the broader context, our findings reveal the existence of initially expanding closed models that undergo subsequent recollapse towards a future singularity, and open universes exhibiting perpetual expansion into the future. The specific characteristics of these singularities are also expounded upon.