Arguments against the flatness problem in classical cosmology: a review

Several authors (including myself) have made claims, none of which has been convincingly rebutted, that the flatness problem, as formulated by Dicke and Peebles, is not really a problem but rather a misunderstanding. In particular, we all agree that no fine-tuning in the early Universe is needed in order to explain the fact that there is no strong departure from flatness, neither in the early Universe nor now. Nevertheless, the flatness problem is still widely perceived to be real, since it is still routinely mentioned as an outstanding (in both senses) problem in cosmology in papers and books. Most of the arguments against the idea of a flatness problem are based on the change with time of the density parameter Ω and normalized cosmological constant λ (often assumed to be zero before there was strong evidence that it has a non-negligible positive value) and, since the Hubble constant H is not considered, are independent of time scale. In addition, taking the time scale into account, it is sometimes claimed that fine-tuning is required in order to produce a Universe which neither collapsed after a short time nor expanded so quickly that no structure formation could take place. None of those claims is correct, whether or not the cosmological constant is assumed to be zero. I briefly review the literature disputing the existence of the flatness problem, which is not as well known as it should be, compare it with some similar persistent misunderstandings, and wonder about the source of confusion.