Caption: 2-dimensional space analog of possible 3-dimensional space geometries in simple GR models of the universe: i.e., the FLRW models and the FLRW-Λ models.
Features:
Ω is a sort of dimensionless density for the universe.
where ρ is density and ρ_{c} is the critical density ρ_c = 3H_0**2/(8πG) = (9.20387*10**(-27))*h_70**2 kg/m**3 = (1.35983*10**11)*h_70**2 M_☉/Mpc**3, where H_0 is the Hubble constant, the gravitational constant G = 6.67408(31)*10**(-11) (MKS units), and h_70 = H/[(70 km/s)/Mpc] (see Hubble Units). Modern determinations of the Hubble constant consistent with 70 (km/s)/Mpc to within about 5 % (see Wikipedia: Hubble's law: Observed values) and so 70 (km/s)/Mpc is a fiducial value for the Hubble constant.
But Omega if greater than 1, stays greater than 1 for all time, if less than 1, stays less than 1 for all time, if exactly 1, stays exactly 1 for all time, in pure FLRW models with Λ=0.
These people believe the models can only be extended to our pocket universe.
So the universe geometry is important somehow.