Cat. This is the normal white font on black background, which no doubt, you were trying to achieve given the weird prior colors.We have a very adequate Big Bang Theory (more correctly, as you point out, Inflationary Model/Theory) which, however, is based on an insubstantial base where the division by zero (r) invalidates using the laws of physics.
I believe that the layman, looking at the suggested beginning – an infinitely small concept at infinite density and temperature, might find ‘bursting out of nothing rather less palatable than an honest admission that we do not know, and probably have no means of knowing, the ultimate precedent of inflation. On this occasion, might he not be correct?
To answer your question that seems directed to others.... Yes, Dr. Joe, not surprisingly, has nailed it. The limits of science are not all that fuzzy. When your equations normally produce a clean result but, say close to t=0 events, they shoot to infinity, you know your wagon no longer has wheels. It's hard to push a wagon up a mountain that has no top.