An effective Friedmann equation for a bouncing anisotropic universe

Abstract

We derive generalized effective Friedmann and Raychaudhuri equations for a bouncing polymer quantized Bianchi-I spacetime. We further prove that the relation numerically derived in the literature between the matter energy density and the anisotropic shear at the bounce holds exactly for any type of matter content, and derive explicit expressions for the constants that appear in that relation.