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

TL;DR

This paper investigates the inherent redundancy in the cosmological evolution equations within Friedmann-Lemaitre-Robertson-Walker models, highlighting its impact on initial conditions and the special role of certain equations.

Contribution

It demonstrates that redundancy in Einstein's equations is unavoidable and elucidates its connection to the initial value constraints in cosmology.

Findings

Redundancy is inevitable in general relativity cosmology equations.

This redundancy explains the special role of one Friedmann equation.

The method used can be generalized to other dynamical theories.

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.