Then again, epicycles were mathematically rigorous.

The main logical fallacy in Big Bang Theory is that it still treats the speed of light as the base metric.

When redshift was first detected, it was assumed to be basic doppler shift, but as it became apparent this effect is proportional to distance in all directions, it either meant we are at the exact center of the universe, or it is an optical effect.

Given there didn't seem to be a medium to "tire" the light and that was the main possibility for an optical effect, it was decided that space itself expands, based on an interpretation of Relativity, known as the Friedmann LeMaitre equation.

The problem with this is it guts the main premise of Relativity, that the speed of light is alway measured as a constant, given it assumes space expands faster than light crosses it, creating the redshift.

Logically, if space were to expand, the speed of light would have to increase, in order to remain constant.

With normal doppler effect, when the train moves away, down the tracks, it doesn't stretch the tracks, merely increases the distance. So the tracks are the denominator and the distance is the numerator.

With this theory, the basis of the redshift is still assumed to be the light taking longer to cross, so that makes the speed of light the denominator and the expansion the numerator. If it was the other way around, it would be a "tired light" theory.

As Einstein said, space is what you measure with a ruler and the ruler in this theory is still the speed of light.

There are ways light does redshift over distance alone, one of which is that multi spectrum "packets" will redshift, as the higher frequencies dissipate faster, but that would mean we are sampling a wave front, not observing photons that traveled billions of lightyears, which creates problem with the idea of quantization as fundamental and not an artifact of measurement. So we will continue with the various forms of epicycles for awhile.