Has the universe expanded over time? It depends on what ruler you use to measure it.

An 'atomic' ruler using the size of an atom as the standard of length would measure an expanding universe.

A 'photonic' ruler using the wavelength of a 'cosmological' photon (e.g. sampled from the CMB) as the standard of length would measure the universe to be static. Photons 'expand' with the universe even in GR.

But how do you explain cosmological redshift without expansion? The measurement of gravitational and cosmological redshift is a comparison of the energy of the photon with the mass of the atom it interacts with. If the wavelength of a photon is defined to be the standard of length then its energy is conserved. (Why should photons on null-geodesics crossing curved space-time with no other interactions lose energy?) If so then the mass of the atom it interacts with must have increased. Now we are no longer in GR but some other gravitational theory, such as the Jordan conformal frame of

Self Creation Cosmology.

Garth