Redundancy of the cosmological evolution equations and its relationship with the initial conditions

Abstract

It is known that in Friedmann-Lemaitre-Robertson-Walker cosmology one has more number of dynamical equations, compared to the number of unknown variables. This fact makes some equations redundant. The situation becomes complicated because all the relevant differential equations in cosmology are not of the same order. In this article we study the fate of the redundant equations. We show that this redundancy is inevitable in general relativity. It is shown that this redundancy is primarily responsible for a special role of one of the Friedmann equations, which constrains the initial values of the problem. Our method of analyzing the dynamical structure of the theories relies on an operational approach and can be generalized further.