Einstein flow with matter sources: stability and convergence

Two recent articles (Moncrief V. 2015 In General relativity and gravitation-A centennial perspective (eds A Asthekar, B Berger, J Isenberg, M MacCallum), pp. 480–498. Cambridge, UK: Cambridge University Press; Moncrief V, Mondal P. 2019 Pure Appl. Math. Q. 15, 921–965. (doi:10.4310/PAMQ.2019.v15.n3.a7)) suggested an interesting dynamical mechanism within the framework of the vacuum Einstein flow (or Einstein-Λ flow if a positive cosmological constant Λ is included) which suggests that many closed (compact without boundary) manifolds that do not support homogeneous and isotropic metrics at all will nevertheless evolve to be asymptotically compatible with the observed approximate homogeneity and isotropy of the physical universe. These studies however did not include matter sources. Therefore, the aim of the present study is to include suitable matter sources and investigate whether one is able to draw a similar conclusion. This article is part of the theme issue ‘The future of mathematical cosmology, Volume 1’.