On the (1 + 3) threading of an almost FLRW universe

Abstract

Based on the Riemannian spatial connection and the kinematic quantities, we develop a new approach on the [Formula: see text] threading of an almost FLRW universe, with respect to a non-normalized vector field. By this method, we obtain simple expressions for geometric objects and equations involved in the theory of cosmological perturbations. We state three forms of Raychaudhuri equation, which lead us to more accurate intervals for the conformal time with respect to the existence of caustics in the congruence of geodesics.