Bouncing cosmology without anisotropy

Abstract: Using non-linear equation of state for pressure and density energy, we show that the universe is began with a smooth and isotropic bounce. We use a non-linear equation of state which is a binary mixture of perfect fluid and dark energy. We show that in order to preserve a smooth and isotropic bounce, the source for contraction before the bounce, must have an equation of state with $\omega>1$ (Ekpyrotic matter) and a dark energy with positive pressure.