On the existence of singularity-free solutions in quartic gravity

We study a general field theory of a scalar field coupled to gravitation through a quadratic Gauss-Bonnet term $\xi (\varphi )$$R_{GB}^2$. We show that, under mild assumptions about the function $\xi (\varphi )$, the classical solutions in a spatially flat FRW background include singularity - free solutions.