Fifty Years of the Flatness Problem

The flatness problem is by and large still regarded as a problem in
classical cosmology, and inflation is the solution most commonly
mentioned. However, many arguments to the effect that it is not really
a problem have been presented, many by well known cosmologists in the
leading journals in the field, but those arguments seem to have been
mostly ignored. Also, to my knowledge none of them has been rebutted.
I discuss various aspects of the flatness problem and reasons for not
regarding each aspect as a problem. Of course, inflation either
happened or it didn't, and could have happened even in the absence of a
flatness problem in classical cosmology. However, if inflation is not
needed to solve problems in classical cosmology, then it must be
supported by independent evidence. We now know that the Universe is
very close to being flat, i.e. lambda+Omega=1 to within a per cent or
better. That is a much tighter constraint than their sum being equal to
1 to within an order of magnitude or so (which was the state of
knowledge when the flatness problem was originally formulated), which
might need an explanation even if there is no flatness problem in the
original sense. However, even the observed degree of flatness might be
explained by arguments against the original flatness problem. Even if
independent evidence proves that inflation made the Universe very flat,
it is still important to understand that the flatness problem as
originally formulated is, in fact, not a problem at all.