Equivalence between fourth-order theories of gravity and general relativity: Possible implications for the cosmological singularity.

Abstract

A recent result has shown that the fourth-order theories of gravity with the action S=F \ensuremath{\surd}-g (2\ensuremath{\Lambda}+R+(1/2)${\mathrm{aR}}^{2}$)${d}^{4}$x are conformally equivalent to general relativity with a scalar field. This result may enlighten the validity of timelike and null convergence conditions in spatially homogeneous cosmological models with a diagonal metric. This approach points out that, under particular conditions, the timelike and null geodesics may be complete.