The two original explanations of the observed distance-redshift relation are:
- Doppler effect (universe is expanding)
- Tired light theory (light traveling from distance sources getting absorbed and re-emitted by dust)
My new explanation — several years old — the universe is static with fixed curvature. My preferred model is a membrane in a four-sphere but the explanation is equally good in the original Einstein static three-sphere. This is that spherical waves do not have an inverse relation between frequency and wavelength. It is easiest to see this by considering a circle of radius versus a three sphere of the same radius. The frequencies of standing waves on the circle have eigenvalues of Laplacian $C n^2$ while on a three-sphere they are . For light traveling on a sphere of a large distance, the resulting wavelength will seem to grow linearly with distance while there has been no actual physical feature of the universe that has changed. Thus my explanation of the redshift is that it is a MATHEMATICAL ARTIFACT of expecting an inverse wavelength-redshift relationship while in fact it is just an effect of curvature.
One could then bring up the evidence for acceleration on measurements of supernovae. Well this is actually a real redshift but this is actually graviational redshift. Heavier objects have a higher redshift due to time dilation according to Einstein, and in fact there is work addressing this issue: gravitationalredshift. So once you correct for this there is no acceleration of any expansion.
DARK ENERGY does not exist. It is simply the curvature of a static spherical eternal universe. And the Big Bang singularity does not exist either. By the way, the cosmic background radiation was predicted by steady state theorists as the temperature more accurately before Gamow which is well known: