What do you think of this argument? Lets suppose an infinite and eternal universe that is homogenous on a large scale. Since there is no privileged inertial reference frame, regardless of the chosen inertial reference frame, the observed statistical velocity distribution of matter is nearly the same. But that also implies that the maximum observed 4-momentum is unbound, and the only way to avoid collisions liberating an infinite amount of energy is for particles whose observed 4-momentum is infinite to be infinitely far away, and that requires a statistical correlation between position and four-velocity that can also be understood as cosmological expansion. Thus an infinite universe is necessarily in expansion.