The accelerating Universe and a limiting curvature proposal

We consider the hypothesis of a limiting minimal curvature in gravity as a way to construct a class of theories exhibiting late-time cosmic acceleration. Guided by the minimal curvature conjecture we are naturally led to a set of scalar-tensor theories in which the scalar is non-minimally coupled both to gravity and to the matter Lagrangian. The model is compared to the Lambda cold dark matter concordance model and to observational data using the 'gold' SNeIa sample of Riess et al ((Supernova Search Team Collaboration), 2004 Astrophys. J. 607 665 [astro-ph/0402512]). An excellent fit to the data is achieved. We present a toy model designed to demonstrate that such a new, possibly fundamental, principle may be responsible for the recent period of cosmological acceleration. Observational constraints remain to be imposed on these models.