What you seem to be wondering about is the

Friedmann-Lemaître-Robertson-Walker (FLRW) model. That model assumes that the universes shape will depend on the density, where 'Omega is the average density of the universe divided by the critical energy density, i.e. that required for the universe to be flat (zero curvature).

I saw someone write that

"The gravitational energy of the universe is precisely equal to its kinetic energy (the energy an object possesses by virtue of its motion) for a particular value of the mass density in the universe. This value, which separates eternal expansion from eventual contraction, is called the critical density"

discussing it but that definition seems quite shaky to me as any motion in this universe has to be related to some other 'frame of reference' to make sense. And we don't have a 'gold standard' anywhere, as far as I know. so to define a objects kinetic energy is a relation to another frame of reference. there is no way to define a uniformly moving objects speed without involving subjective parameters, that is, defining a 'system'.

But I'm not entirely sure if this definition is what they went out from? It seem to build on the universes isotropic apparition, that everything looks much the same, no matter from where, and on what you look on in space. "it describes a homogeneous, isotropic expanding or contracting universe that may be simply connected or multiply connected."

The assumption that 'the kinetic energy is exactly equal to the gravitational energy' seem to make a certain sense though, if we look at it as a symmetric solution, and ignore the idea of 'gravity' as an 'energy'. In Einsteins universe gravity is not an energy as far as I know, it's a geometry. But the universe seems to have a symmetry, like an equilibrium that keeps it in balance, so from that point of view I agree. Maybe we have some guys that have looked closer on this?