Under what conditions will space-time be flat?

Question

Quizplus · Accepted Answer

The condition for space-time to be flat is that the average density of the universe is equal to the critical density. If the density is lower than the critical density, space-time will be curved inwards (like in a saddle shape) and if it is higher than the critical density, space-time will be curved outwards (like in a sphere). A flat universe also requires the absence of any large-scale curvature caused by gravitational fields, which is achieved if the universe is homogeneous and isotropic. However, this condition alone is not sufficient for a flat space-time. In fact, a universe with any density can be homogeneous and isotropic, but only one with a specific density (i.e., the critical density) will be flat. Therefore, choices A, B, and D are not by themselves sufficient conditions for space-time to be flat.

Under What Conditions Will Space-Time Be Flat