On The Big Bang Singularity in $k=0$ FLRW Cosmologies

Ikjyot Singh Kohli

Published 2016-02-08Version 1

In this brief paper, we consider the dynamics of a spatially flat FLRW spacetime with a positive cosmological constant and matter obeying a barotropic equation of state. By performing a change of variables on the Raychaudhuri equation, we are able to compactify the big bang singularity to a finite point. We then use Chetaev's instability theorem to prove that such a model is always past asymptotic to a big bang singularity assuming only the weak energy condition, which is more general than the strong energy condition used in the classical singularity theorems of cosmology.