Non-singular Bounce from a Phase transition

The single field Ekpyrosis of Khoury and Steinhardt \cite{khoury}-\cite{khoury1} admits a Jordan frame scalar field with a double well potential. After the end of the ekpyrotic phase, as energy density increases we find a phase transition scenario to a symmetric phase at the conformal coupling fixed point leads to a non-singular bounce in Einstein frame. This scenario could admit a simple prescription for the small value of dark energy.
Comment: 14 pages