Newton-Hooke spacetimes, Hpp-waves and the cosmological constant

TL;DR

This paper explores the symmetries of non-relativistic cosmological models with a cosmological constant, linking Newton-Hooke groups to pp-wave spacetimes and their conformal extensions, with implications for harmonic oscillators and matrix models.

Contribution

It explicitly demonstrates how Newton-Hooke groups act as symmetries in non-relativistic cosmology and connects these to higher-dimensional pp-wave spacetimes, revealing new symmetry structures.

Findings

Newton-Hooke groups act as symmetries of non-relativistic cosmological equations.

Non-relativistic spacetimes can be obtained from null reduction of 5D pp-wave spacetimes.

Extended conformal groups influence equations of motion and have applications in oscillators.

Abstract

We show explicitly how the Newton-Hooke groups act as symmetries of the equations of motion of non-relativistic cosmological models with a cosmological constant. We give the action on the associated non-relativistic spacetimes and show how these may be obtained from a null reduction of 5-dimensional homogeneous pp-wave Lorentzian spacetimes. This allows us to realize the Newton-Hooke groups and their Bargmann type central extensions as subgroups of the isometry groups of the pp-wave spacetimes. The extended Schrodinger type conformal group is identified and its action on the equations of motion given. The non-relativistic conformal symmetries also have applications to time-dependent harmonic oscillators. Finally we comment on a possible application to Gao's generalization of the matrix model.