The "Expansion of Space" is an epistemological (teaching) device which makes no sense in language except as a local effect in descriptions of the movement of objects (as in, "they expanded the space in the living room by moving the couch into the dining room, thereby decreasing the space available there"), and is, consequently, even less likely to make sense in mathematics, which is generally much more rigorous. Attempts to make the "EoS" expression meaningful often involve elaborations of it as "an expansion of the metric", but neither the metric (an abstraction) nor space itself are physical objects, as physicality only characterizes objects observably comprised of, or bounded by, matter and / or energy (which are interchangeable as mass, in relativistic physics).
Cosmological models that explain a locally-apparent expansion of space using 1915's General Relativity alone tend to rely on "dark energy" or "repulsive gravity" for driving the astronomical objects apart and thereby explaining the redshift. The model which takes the most advantage of Einsteinian relativity is Nikodem Poplawski's "cosmology with torsion" (described in numerous papers, written between 2010 and 2021, whose preprints can be found by his name in Cornell University's "Arxiv" website). However, Poplawski's model uses Einstein-Cartan Theory, developed by Einstein and the French mathematician Elie Cartan in 1929, a few years after the discovery of particulate spin. His model applies it in the context of the gravitational collapse of large stars into black holes after their exhaustion of their nuclear fuel has left them with insufficient radiation pressure to prevent it. (As most stars are in binary pairs, there's astronomical evidence of such collapses having occurred at least 90 times within our observable region, as the surviving star in such pairs continues to follow their elliptical orbits.)
ECT, sometimes known as ECSK or ECKS after modifications to it by Sciama and Kibble in the 1960's, differs from GR primarily in an assumption that fermions (matter particles) are not absolutely "point-like" but, instead, have a tiny spatial extent. In Poplawski's model, the trajectories of fermions newly-materialized by the gravitational field (thru their separation from partners in virtual particle / antiparticle pairs by the outward-propagating event horizon of the collapsing star) are reversed and greatly accelerated thru interaction with the (vastly larger) stellar fermions, and form a new "local universe" whose shape Poplawski has compared to the skin of a basketball.
The genesis of the local universes (including our own, whose "observable region" might form a very small part of it) within a black hole has some other advantages, since its causal separation would eliminate such inconveniences as the eventual arrival of photons (light and heat) from a multiverse possibly infinite in size. That infinity in size can be consistently accompanied by a past- and future-eternality in the relativistic "block universe" view of time, which has brought Poplawski's model into some conflict with state and private universities in a number of jurisdictions, where lack of a "creation event" (other than the local one, like our own Big Bounce) remains contrary to locally-prevalent philosophical views.
Another problem for his model may be the sequential decreases in scale which it implies, in a world where (we're hoping!) "size matters".