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