Comment on ''Szekeres universes with homogeneous scalar fields''

Abstract

In two recently published articles, Barrow and Paliathanasis (2018, 2019) [1, 2] claim to have found exact solutions of Einstein’s field equations belonging to the class of non-trivial (i.e., spatially inhomogeneous) Szekeres models, whose source is a mixture of dust and a homogeneous time-dependent scalar field, where the energy-momentum tensors (EMTs) of both mixture components are independently conserved. We prove in the present comment that these solutions are inconsistent with the authors’ assumptions, as independent conservation of these two mixture components necessarily leads to their solutions belonging to the set of spatially homogeneous subcases of the Szekeres family: Friedmann–Lemaître–Robertson–Walker (FLRW) for class I, and Kantowski–Sachs (KS), Bianchi (or Bianchi–Behr–Schücking) I or Bianchi VI−1 for class II.