In article , jacob navia
writes:

Ptolomeus rotating spheres model could ALWAYS accomodate new
observations by making a NEW sphere. But at some point people
just preferred the new model because it was simpler...

No. As Fourier pointed out, ANY periodic motion can be thought of as
consisting of a sum of sinusoidal motions of various periods, so in that
sense, yes (I bet Ptolemy didn't know he was doing Fourier synthesis).
However, this applies just to TRANSVERSE motions. Ptolemy's model
predicts completely different RADIAL motions than that of Copernicus or
Kepler so, as soon as you can measure the distance to a planet, you can
falsify Ptolemy's model.

As for the rest of the discussion, I think you need to define "big bang
theory" before going any further. A common mistake is to define "big
bang theory" to mean more than it actually does. Even if these
additional details really are falsified by some observations, it just
means that these additional details are falsified, not the "core" of the
big bang theory.