The flatness problem is a cosmological problem with the Big Bang theory, which is solved by hypothesising an inflationary universe.

In an expanding universe, the gravity field created by the matter within the universe will tend to slow down its expansion. If there is enough matter, the expansion will eventually stop, and the universe will contract, returning to a singularity at a hypthetical big crunch. If there is not enough matter, the universe will simply expand forever. The critical density at which the expansion rate of the universe will tend asymptotically towards zero is about

1×10^-29

grammes per cubic centimeter, and the ratio of the actual density of the universe to this value is known as Ω.

Currently, observations indicate that Ω is between 0.98 and 1.06 - in other words, that the universe's density is very close to or exactly the critical value. In its very early history, an Ω only very slightly above 1 would have resulted in a very rapid big crunch, while with an Ω only very slightly below 1, the universe would have expanded so fast that stars and galaxies could not have formed. The fact that approximately 15 billion years after its formation, the universe still has an Ω so close to unity indicates that Ω must have been within one part in 10¹⁵ of unity when the universe formed.

The problem is that a simple big bang theory cannot explain how an Ω so close to unity could arise. The problem is solved by the hypothesis of an inflationary universe, in which very shortly after the Big Bang, the universe increased in size by an enormous factor. Such an inflation would have smoothed out any non-flatness originally present and resulted in a universe with a density extremely close to the critical density.