A common question in cosmology is “why are all the galaxies receding from each other?” In other words, the cosmological principle requires that we not be at a special place in the Universe. Since all the galaxies are moving away from us, then they must all be moving away from each other. This is explained if the Universe, as a whole, is expanding.
In a real sense, Hubble’s law, the recession velocity of galaxies, is an illusion. The galaxies are not moving, the space between them is literally expanding. To see how this produces a Doppler effect, consider a simple Universe that is a circle. To the observers in this type of Universe, they believe they live in a 1D structure. But, in fact, they live in a 2D structure, a circle. The position of the galaxies can be measured by the distance between them (S, see diagram) or what are called the co-moving coordinates, an angle ‘q’ between the galaxies.
The radius of the Universe is given by ‘R’, notice that ‘R’ is a quantity only seen in 2D space, not measured directly by the inhabitants of the 1D circle unless they measure ‘2pR’ by walking around the Universe. Now, we let the Universe expand by a factor of 2, ‘R’ becomes 2R. The distance between the galaxies becomes 2S, but the co-moving coordinate, angle ‘q’ remains unchanged. Since the distance between the galaxies has increased, then the galaxies will appear to have moved apart by S/time of expansion. When, in fact, the galaxies have not moved at all, the space between them has increased.
Expanding spacetime also explains the redshift of galaxies, which is interpreted as Doppler motion. Since space expands, any photons traveling through that space (from distant galaxies to us) must also expand, i.e. the photons are ‘stretched’ as they travel across the Universe.
So the redshift we see for distant galaxies is really an effect of spacetime expanding, not real motion. This is good because some of the redshifts for the most distant galaxies have recessional velocities in excess to the speed of light. But this is not a contradiction for special relativity since the space is expanding, not true motion. We will also see that photons created as gamma rays in the early Universe are now redshifted to the microwave region of the spectrum to make up what is called the cosmic microwave background (CMB).