Regularizing cosmological singularities by varying physical constants
  Varying physical constant cosmologies were claimed to solve standard cosmological problems such as the horizon, the flatness and the $\Lambda$-problem. In this paper, we suggest yet another possible application of these theories: solving the singularity problem. By specifying some examples we show that various cosmological singularities may be regularized provided the physical constants evolve in time in an appropriate way. 
Mariusz P. Dabrowski and Konrad Marosek
hep-th astro-ph.CO gr-qc