The singularity is the point where known physics fails to provide a meaningful description; what it really means is unknown at present. But classical physics is fundamentally time-reversible; on a macro scale, where behaviour is largely classical, we can 'rewind' our cosmological model to the earliest time it gives meaningful results for, and find a very hot & very dense universe - the visible universe would have been very small (one respected astrophysicist puts it at ~17 cm at 10^-35 seconds).I disagree.
In science one needs to know the initial state of the entity to start the calculations. The singularity is beyond space time, hence, the singularity cannot be measured.
Since the singularity is beyond the realm of science, one cannot then mathematically connect the singularity with the observable universe.
As I said before, it is mathematically impossible to support the Big Bang.
Predictions can be made, using the same model, about what we should expect to see today given those early conditions, and those predictions have been, and continue to be, confirmed. This makes it a good model within its known bounds of applicability (it's incomplete).
It's a fully mathematical model.
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