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It is not required by every cosmological theory which is under current serious consideration, that the universe should be expanding at the same rate in every region that is within it.
(I am not talking here about relatively small regions of space , such as clusters of galaxies, where the expansion of the universe is (of necessity) slower due to a Strong local gravitational field)
Another untested assumption of most cosmologies is that the universe is isotropic (that is, it looks the same in every direction) and homogeneous (with matter on the largest scales being evenly distributed), but even the assumption of homogeneity is becoming dubious due to the Vast structures that have been revealed in redshift surveys......
there are known supergalactic structures up to a billion light years across!
Other assumptions which are not intrinsic to Big Bang and Expanding Universe models include:
- the idea that the universe had a beginning in time
- the idea that the universe began from an actual mathematical point.
I am not the biggest fan of the Big Bang concept, as its truth seems to rest on only a small number of observed facts.
BUT it would have to be regarded as an Observational Fact that::
(1) the universe is expanding
(2) the mean density of matter in the universe was much greater in its early years than it is now, and the density of the universe has got systematically smaller with the passage of time.
If we consider, for example, a Nearby low-surface-brightness Dwarf Irregular galaxy which is surrounded by little else but a cube of empty space that is 1 million light years on a side (as dIrr galaxies so often are, as they preferentially occupy lower-density regions of space), we can easily see that the current Matter Density of the universe must be exceedingly low......only one tiny patch of stars existing within a truly vast volume! (Note: an admixture of lots of "dark matter" is also necessary to account for the gravitational mass of one of these tiny galaxies)
So really, it Must be the case that the density of the early universe had - of necessity - to be very high; without this necessary Very High density, structures such as stars and galaxies could never have formed in our universe. In fact, it is very-well-known now that the time-rate at which stars formed was exceedingly high in the early universe;
naively, one may regard this very very rapid formation of stars as being due simply to the fact that much higher gas densities and gas pressures and gas masses existed then.
I am not a cosmologist or a physicist, but these facts seem to me be be evident even to the intelligent layperson.
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