Reversed the direction of time in Penrose’s theorem

At first sight, Penrose’s result didn’t have anything to say about the question
of whether there was a big bang singularity in the past. However, at the time
that Penrose produced his theorem, I was a research student desperately looking for a problem with
which to complete my Ph.D. thesis. I realized that if one
reversed the direction of time in Penrose’s theorem so that the collapse became
an expansion, the conditions of his theorem would still hold, provided the
universe were roughly like a Friedmann model on large scales at the present
time. Penrose’s theorem had shown that any collapsing star must end in a
singularity; the time-reversed argument showed that any Friedmann-like
expanding universe must have begun with a singularity. For technical reasons,
Penrose’s theorem required that the universe be infinite in space. So I could
use it to prove that there should be a singularity only if the universe was
expanding fast enough to avoid collapsing again, because only that Friedmann
model was infinite in space.
During the next few years I developed new mathematical techniques to
remove this and other technical conditions from the theorems that proved
that singularities must occur. The final result was a joint paper by Penrose
and myself in 1970, which proved that there must have been a big bang singularity provided only that general relativity is correct and that the universe
contains as much matter as we observe.
There was a lot of opposition to our work, partly from the Russians, who
followed the party line laid down by Lifshitz and Khalatnikov, and partly from
people who felt that the whole idea of singularities was repugnant and spoiled
the beauty of Einstein’s theory. However, one cannot really argue with the
mathematical theorem. So it is now generally accepted that the universe must
have a beginning.