What exactly is the big bang model today?
It's known as the LCDM. L=Lambda=cosmological constant, CDM= Cold Dark Matter.
The core Big Bang model is based on general relativity and is known as the Friedman-Walker (or, more inclusively, the Friedman-LeMaitre-Robertson-Walker) model. It is a collection of solutions to the equations for general relativity that describe an expanding (or contracting) universe and how the rate of expansion correlates to the energy density.
The next level up, which is also considered core these days, adds in thermodynamics, so describes the way temeprature changes with the expansion. This also is connected to nucleosynthesis and thereby the abundances of light elements (Hydrogen, Helium, Lithium) and their isotopes. It also includes the formation of the Cosmic Microwave background Radiation (CMBR).
This much is not going to change when the details change. It is similar to saying that the planets orbit the sun--the previous description didn't have that, but it was simply wrong. Any new theory will certainly include that basic fact. In the same way, any new desription of cosmology will certainly include an expanding universe, the period of nucleosynthesis, and the formation of the CMBR.
The next level includes dark matter. This is more uncertain (given that we don't know what dark matter is composed of) and may be overturned if our description of gravity changes (so, general relativity is replaced by something else...like MOND). At present, we don't have any descriptions that do not include dark matter, but until we get actual detection in our particle accelerators, it is *possible* we may need to modify our theory of gravity.
The next level is dark energy (cosmological constant) and its properties. This is MUCH more subject to change as we generally don't have many of the details concerning dark energy, including precisely what happens to its density upon expansion (is it actually constant, or does it change in some way?).
Both dark matter and dark energy affect the size and distribution of density fluctuations in the early universe. And it is these fluctuations that determine the size and distribution of early galaxies and stars. At present, there are some significant constraints baed on what we know of the CMBR: any fluctuations in the very early universe should show up as fluctuations in temperature of the CMBR and those are now known pretty well.
So, the core BB model: FW model plus thermo, is very secure. It isn't going to go away unless there is a HUGE revolution (tantamount to saying that planets don't actually orbit the sun). The detials of dark matter and dark energy, and thereby the distribution of energy in the early universe and the size of the fuctuations is very much subject to change at this point.
I should also point out that the sizes and masses of these galaxies are based on computational models that may or may not be accurate in the very early universe. They are calibrated by data from later time periods, but we know that early stars were much hotter and larger because they didn't have the heavier elements in them (those elements were formed when the early stars exploded). This relates to the IMF (a mass function) that determines the size and nature of early stars and galaxies. Leja notes that the models may need to be modified to account for exactly this effect.