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

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 motion in such spacetimes with dimension 4, 5, 6, 7, 9 or 10 of the maximal algebra of Lie point symmetries of dimension 13. Second, we give a physical interpretation of new cosmological solutions which satisfy the positive energy condition and yield critical bounds on the expansion coefficient α, in which the underlying nonflat spacetimes have 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 → ∞. 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.

Physical Significance of Noether Symmetries

“…The Lie and Noether symmetries of geodesic equations have been studied for the Friedmann metrics by Tsamparlis and Paliathanasis [48]. These symmetries have also been obtained for some of the Bianchi-type spacetimes in [49][50][51][52]. The complete analysis of Noether symmetries for Gödel-type and pp-wave spacetimes studied by Camci et al [53][54][55].…”

Scalar field cosmology via Noether symmetries in energy–momentum squared gravity

“…Capozziello and Laurentis [23] examined the NS technique in the framework of quantum cosmology. Ali and Hussain [24] investigated positive energy bounds via NS technique in Bianchi type-V universe model, whereas this work for Bianchi type-I spacetime has been studied in [25].…”

Energy Conditions and Conservation Laws in LRS Bianchi Type I Spacetimes via Noether Symmetries

“…Conversely, if the vector field X + 2ψs∂ s is an NS, then X is an HV provided that X does not depend on s. [11] In literature, NS, their relation will Killing and homothetic vectors and the corresponding conservation laws have been studied by many researchers, for details we refer to Refs. [11][12][13][14][15][16][17][18][19].…”