BBT is not proved and it can not be proved, and I point in this answer to a new model that will knock it down.
While a physical law was never broken, and is expected to be unbreakable; a theory come and go as time goes by.
In the begining of BBT (Big Bang Theory) it was expected that gravity will, in due time, make the universe to collapse. A few years ago, against the expectations, it was measured an acceleration of the expansion.
Because the matter content of Universe is not working to bring an end to the expansion we can deduce that Bariogenesis can not be an argument in favor of BBT (matter plays a minor role).
The cosmological constant and the Dark Energy appeared magically to explain the feature, without explaining. Its only a parameter inserted in the equations, and proceed as usual.
To explain the observed, i.e. measured, expansion of the space we have to consider what stands behind 'making a measure', what referential can we chose, etc,... and one have to search for more than the naive explanation that you know of.
ΛCDM model (BBT) has 6 parameters: H0 , w, ΩΛ , ΩM , ΩR and ΩK
You can find here a killing theory with only one parameter (H0); this paper was dated July 1, 2011 and submitted to PRX; it is easy reading and any undergrad student can understand it. It is my hope that the teachers will follow. I'm very proud to see my name in this foundational paper, and I will stand up to argue in favor of it.
A self-similar model of the Universe unveils the nature of dark energy
This work presents a critical yet
previously unnoticed property of the
units of some constants, able of
supporting a new, self-similar, model
of the universe. This model displays a
variation of scale with invariance of
dimensionless parameters, a
characteristic of self-similar
phenomena displayed by cosmic data.
The model is deducted from two
observational results (expansion of
space and invariance of constants) and
has just one parameter, the Hubble
parameter. Somewhat surprisingly,
classic physical laws hold both in
standard and comoving units, except
for a small new term in the angular
momentum law that is beyond present
possibilities of direct measurement.
In spite of having just one parameter,
the model is as successful as the ΛCDM
model in the classic cosmic tests, and
a value of H0 = 64 km s−1 Mpc−1 is
obtained from the fitting with
supernovae Ia data from Union
compilation. It is shown that in
standard units the model corresponds
to Big Bang cosmologies, namely to the
ΛCDM model, unveiling what dark energy
stands for. This scaling (dilation)
model is a one-parameter model that
seems able of fitting cosmic data,
that does not conflict with
fundamental physical laws and that is
not dependent on hypotheses, being
straightforwardly deducted from the
two observational results above
I will try to explain this novel theory in a few words:
All system of units we use are 'atomic units' because are based in the properties of the atoms around us. And we only knew how to apply the laws of nature if we use those units.
We are 'anthropocentric' and we can only imagine that the atom is absolute, invariant in time. Yes, we are using an 'absolute reference' and also denying that an 'absolute reference' can exist.
A measure is an adimensional quantity, a ratio of two quantities: e.g. if we are measuring a distance in the numerator is the amount of length and in the divisor is the amount corresponding to the unit of measure.
As we are measuring an expansion we have to consider : the space expands, the unit of measure is decreasing (our atom) or a mix of both.
In the paper it is shown that the laws of nature can support a scaling property of the universe, where the atom is no more invariant. It is shown that by choosing a proper referential, a comoving one, the dark energy and the cosmological constant are artifacts of BBT. The BB is no more needed; the Inflation era is no more needed, etc.
The unexpected: (quote)
Atomic measures are number counts
We will now see that the measures of
bodies’ properties using atomic units
are independent of the base quantities
and dependent on the number of
particles or atoms.