In the absence of a cosmological constant, there is a critical density (in the FLRW model) at which the universe expands asymptotically to zero velocity. If the density of the universe (without a cosmological constant) is above that critical density, at some point the expansion reverses and galaxies start moving towards each other. If the density of the universe is below that critical density, the universe keeps expanding forever. Then it is said that if the universe has the critical density it is infinite and flat (zero curvature), if it has a greater density it is finite and spherical (positive curvature), and if it has a lower density it is infinite and hyperbolic (negative curvature). I have some questions about the above. Why cannot a universe with positive curvature be infinite? Is that because the bigger a spherical universe the smaller its curvature, and so that the infinite flat universe is the limit of a spherical universe as its curvature tends to zero? Once again assuming no cosmological constant, why in a spherical universe the expansion reverses while in a hyperbolic universe the expansion keeps going forever? Why couldn't galaxies always keep moving away from each other in a spherical universe, and why couldn't they move towards each other at some point in a hyperbolic universe? A spherical universe is one in which light sent in one direction eventually 'circles' the universe and returns to its starting point. Why couldn't galaxies always keep moving away from each other in such a universe?