Abstract

Lie symmetries are discussed for the Wheeler-De Witt equation in Bianchi Class A cosmologies. In particular, we consider General Relativity, minimally coupled scalar field gravity and Hybrid Gravity as paradigmatic examples of the approach. Several invariant solutions are determined and classified according to the form of the scalar field potential. The approach gives rise to a suitable method to select classical solutions and it is based on the first principle of the existence of symmetries.

Highlights

  • Nowadays astronomical observations have shown that if we consider our Universe on a large scale, its visible structure is accelerating, homogeneous and isotropic, and, essentially, filled with pressureless dust

  • By applying the results in [7], we find that the Wheeler–DeWitt equation (WDW) equation (19) admits: (1) for the Bianchi I model, 11 Lie symmetries, (2) for the Bianchi II model, five Lie symmetries, (3) two Lie symmetries for the models VI0/VII0, and (4) one Lie symmetry, the linear one, for the models VIII and IX

  • In this work we studied the Lie symmetries of the WDW equation in the Bianchi Class A spacetimes for general relativity and scalar field cosmologies, considering minimally coupled scalar-tensor gravity and non-minimally coupled gravity coming from Hybrid Gravity

Read more

Summary

Introduction

Nowadays astronomical observations have shown that if we consider our Universe on a large scale, its visible structure is accelerating, homogeneous and isotropic, and, essentially, filled with pressureless dust. In this paper we will consider the Lie symmetries of the Wheeler–DeWitt equation (WDW) in general relativity and in scalar field cosmology assuming Bianchi spatially homogeneous spacetimes. The symmetries which can be used are the Noether symmetries of the Lagrangian of the field equations and they have been applied in several models such as scalar-tensor cosmology [8,9,10,11,12,13,14,15], f (R) gravity and higher-order theories of gravity [16,17,18,19,20,21], spherically symmetric spacetimes [22,23,24,25], and many others. The basic theory of Lie symmetries is briefly discussed

The Class A of Bianchi spacetimes
Symmetries of the WDW equation in general relativity
Invariant solutions of the WDW equation in general relativity
Bianchi I cosmology
Bianchi II cosmology
The WKB approximation and the classical solution
Symmetries of the WDW equation in minimally coupled scalar-tensor cosmology
Invariant solutions of the WDW equation in scalar-field cosmology
The WKB approximation and the classical solutions
Discussion and conclusions
Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call