Meanwhile, what do you think of #156?

I have the same misgivings about extrapolating the BBT back to extreme densities and temperatures, and especially to extremely fast expansions.

As an aside, on the mathematics. division by zero at a point on a graph is not necessarily going to give a "blow-up" result. Yes, it is "undefined", but there are mathematical methods for defining the result, and some come out as reasonable and realistic numbers.

To explain a bit, if you have a theory that give a functional relationship as f(x)/g(x), and g(x) = 0 at x = 0, we really need to think about what f(x) is doing as it approaches zero. In some cases, the limiting value of f(0)/g(0) is a finite number. The easy way to think about that is if the two functions are simply multiples of one another. If f(x)= 2 x g(x), then the relationship can be algebraically simplified to 2g(x)/g(x) =2 for all of x, including x=0.

For more complicated functions, think about their Taylor's Expansions as they approach zero. For instance tan(x)/x approaches 1 as x approaches zero, and the expansion terms divided by x are 1 + terms with x in the numerator, not the denominator.

There are more complicated limit calculations for more complex functions.

And, there are also cases where the limiting result is "infinity". A distinction is made for functions that go to positive or negative infinity on both sides of the zero point, compared to those that go from negative infinity to positive infinity across the zero point.