Comment on "Szekeres universes with homogeneous scalar fields"

TL;DR

This paper critiques recent claims of exact solutions in Szekeres models with scalar fields, demonstrating that such solutions are necessarily spatially homogeneous, thus limiting their generality.

Contribution

It proves that the supposed inhomogeneous solutions with scalar fields are actually homogeneous, clarifying the structure of Szekeres models with scalar fields.

Findings

Independent conservation implies spatial homogeneity.

Solutions reduce to known homogeneous cosmologies.

Claims of inhomogeneous solutions are invalid.

Abstract

Two recently published papers (J.D. Barrow and A. Paliathanasis, Eur. Phys. J. C. (2018, 2019)) claim to have found exact solutions of Einstein's field equations belonging to the class of non-trivial Szekeres models, whose source is a mixture of dust and a homogeneous time-dependent scalar field, where the energy-momentum tensors of both mixture components are independently conserved. We prove that the independent conservation of these two mixture components necessarily leads to solutions belonging to the set of spatially homogeneous subcases of the Szekeres family: Friedmann-Lema\^itre-Robertson-Walker for class I, and Kantowski-Sachs, Bianchi-Behr I or Bianchi-Behr $\mbox{VI}_{\tiny{\mbox{-1}}}$ for class II.