T-Duality and Penrose limits of spatially homogeneous and inhomogeneous cosmologies

TL;DR

This paper investigates the Penrose limits of inhomogeneous cosmologies with abelian symmetries and their T-duals, revealing that non-abelian T-duality and Penrose limits do not commute, and provides explicit wave profiles for specific solutions.

Contribution

It introduces a general method to find Penrose limits of inhomogeneous cosmologies with T-duality, highlighting the non-commutativity of non-abelian T-duality and Penrose limits.

Findings

Penrose limits of inhomogeneous cosmologies with abelian symmetries are derived.

Explicit wave profiles are provided for particular solutions.

Non-abelian T-duality and Penrose limits are shown to be non-commutative procedures.

Abstract

Penrose limits of inhomogeneous cosmologies admitting two abelian Killing vectors and their abelian T-duals are found in general. The wave profiles of the resulting plane waves are given for particular solutions. Abelian and non-abelian T-duality are used as solution generating techniques. Furthermore, it is found that unlike in the case of abelian T-duality, non-abelian T-duality and taking the Penrose limit are not commutative procedures.