The situation became worse with the cosmological discoveries of the 1980’s. The two key cosmological parameters are the cosmic expansion rate (Hubble’s constant, which determines the age of the Universe) and the cosmic density parameter, which determines the acceleration of the Universe and its geometry.
The cosmic density parameter determines the three possible shapes to the Universe; a flat Universe (Euclidean or zero curvature), a spherical or closed Universe (positive curvature) or a hyperbolic or open Universe (negative curvature). Note that this curvature is similar to spacetime curvature due to stellar masses except that the entire mass of the Universe determines the curvature.
The description of the various geometries of the Universe (open, closed, flat) also relate to their futures. There are two possible futures for our Universe, continual expansion (open and flat) or turn-around and collapse (closed). Note that flat is the specific case of expansion to zero velocity.
Current values for the critical density range from 0.1 to 1, which produces a new dilemma from modern cosmology, the flatness problem.
The flatness problem relates to the density parameter of the Universe. Values for can take on any number, but it has to be between 0.01 and 5. If is more than 0.01 the Universe is expanding so fast that the Solar System flys apart. And has to be less than 5 or the Universe is younger than the oldest rocks. The measured value is near 0.2. This is close to 1, which is strange since 1 is an unstable critical point for the geometry of the Universe.
Values slightly below or above 1 in the early Universe rapidly grow to much less than 1 or much larger than 1 (like a ball at the top of a hill). So the fact that the measured value of 0.2 is so close to 1 that we expect to find in the future that our measured value is too low and that the Universe has a value of exactly equal to 1 for stability.
And therefore, the flatness problem is that some mechanism is needed to get a value for to be very, very close to one (within one part in a billion billion).