A study of positive energy condition in Bianchi V spacetimes via Noether symmetries

TL;DR

This paper uses Noether symmetries to analyze Bianchi V spacetimes, identifying symmetry subalgebras and deriving cosmological solutions that satisfy positive energy conditions with diverse energy density behaviors.

Contribution

It identifies the subalgebras of Noether symmetries in Bianchi V spacetimes and provides new physical interpretations of solutions satisfying positive energy conditions.

Findings

Energy density can be positive and constant over time.

Energy density can vary, reach a maximum, then decay to zero.

Energy density can increase indefinitely, approaching a maximum at infinity.

Abstract

In this paper we use Noether symmetries of the geodesic Lagrangian in Bianchi V spacetimes to study various cosmological solutions of Einstein's field equations. Our first result is the identification of the subalgebras of Noether symmetries of the equations of motions in such spacetimes with dimension 4, 5, 6, 7, 9 or 10 of the maximal algebra of Lie point symmetries of dimension 13. Secondly we give physical interpretation of new cosmological solutions which satisfy positive energy condition and yield critical bounds on the expansion coefficient $\alpha$, in which the underlying non-flat spacetimes carry interesting physical properties. Specifically the energy density behaves in one of the following ways. (i) It is positive and constant for all time. (ii) It varies with time and attains a global maximum after some time and then asymptotically converges to zero. (iii) It increases for all time and attains a maximum value at the asymptotic limit $t\rightarrow \infty$. In particular a non-flat spacetime is obtained that mimics the expansion in a flat FRW universe dominated by vacuum energy such that the expansion factor has the same form in both. However, the energy density is dynamical in the former.