Image 1 Caption: The expansion of the universe is a literal growth of space between gravitationally unbound systems according to general relativity. All the cosmological physical distances between the gravitationally unbound systems undergo a general, uniform scaling up with cosmic time.
Gravitationally bound systems and bound systems in general do NOT expand. So you and yours truly don't expand. Moons, planets and stars don't expand. Galaxies and galaxy clusters (if they are gravitationally bound systems which they mostly are) don't expand. Galaxy superclusters, though gravitationally interacting, seem to be mostly gravitationally unbound systems, and so will probably be mostly torn apart eventually by the expansion of the universe if it continues long enough.
In Image 1, we see the ideal scaling up in cosmological physical distances between 3 spiral galaxies 6 dwarf galaxies.
The expansion of the universe is really the expansion of the observable universe. Beyond the observable universe, there is probably expansion for a long way, but we do NOT know how far it extends.
There is NO center of expansion and nothing is being expanded into as far as we can see in the observable universe. There is just a scaling up. But maybe there is a center of expansion and a realm to expand into beyond the observable universe.
Note the animation gives the impression that there is a center of expansion. But everyone in the observable universe can take the perspective that they are at the center of expansion. We and they actually just see the scaling up of the observable universe.
The comoving frames, in fact, form a continuum of fundamental free-fall frames throughout the observable universe.
For cosmologically remote astronomical objects, recession velocities do exceed the vacuum light speed c = 2.99792458*10**8 m/s ≅ 3*10**8 m/s =3*10**5 km/s ≅ 1 ft/ns. But this is NOT a violation of special relativity since recession velocities are NOT with respect to inertial frames
Typically peculiar velocities are relatively small for cosmological physical distances >∼ 10 Mpc and typically become relatively large and even dominating for cosmological physical distances <∼ 1 Mpc.
Actually, several observers had partially anticipated Hubble, but he observationally discovered Hubble's law which gave the expansion behavior, and thus made the expansion of the universe a definite result. Hubble's law (which holds between points participating in the mean expansion of the universe) is
where v is recession velocity, r is cosmological physical distance, and we have Hubble constant H = 70 (km/s)/Mpc fiducial value accurate to within ∼ 10 %.
Willem de Sitter (1872--1934) had predicted expansion of the universe in 1917 with his de Sitter universe which was based on general relativity plus the assumptions of the cosmological principle and the cosmological constant with NO matter.
The Friedmann equation implies Hubble's law, but it seems that the first to present Hubble's law as mathematical result explicitly was Lemaitre in 1927 in a scientific article in French in the pretty obscure Annals of the Scientific Society of Brussels. No one seems to have noticed at this mathematical result in 1927 and Lemaitre did NOT draw much attention to it.
All the cosmologicalphysical distances r(t) separating points participating in the expansion of the universe scale with a(t):
Note we define a_0 = a(t_0) = 1 by convention. Thus, the cosmological physical distances at cosmic present t_0 are also referred to as the comoving distances since they are the same for all cosmic time.
Of course, for Friedmann equation (FE) models other than the Λ-CDM model cosmic present t_0 may have other values. In fact, for those Friedmann equation (FE) models like the de Sitter universe and the Steady State Universe which are eternal in both cosmic time directions, t_0 is usually set to 0.
The Λ-CDM model is the standard model of cosmology (SMC, Λ-CDM model) circa 1998--2025?.
The Einstein-de Sitter universe (which is neither the Einstein universe (1917) nor the de Sitter universe) was probably the most standard model of cosmology (SMC) for circa 1965--circa 1998).
The positive-curvature universe is formally a closed universe: i.e., finite, but unbounded. It is a hyperspherical space: i.e., the curved 3-sphere space which is the surface of a 4-dimensional Euclidean geometry (AKA flat geometry) sphere. In fact, it is NOT clear that FE models can be extrapolated endlessly beyond the observable universe. If the observable universe is embedded in a pocket universe of a eternal inflation universe, then the FE models CANNOT be extrapolated endlessly beyond the observable universe. There must be point at which the behavior of the pocket universe changes in a way we do NOT know.