Overclosure

Overclosure is a concept in cosmology describing a universe whose total energy density exceeds the critical density. The critical density is defined by rho_c = 3 H^2 / (8 pi G), where H is the Hubble parameter and G is Newton's gravitational constant. The density parameter Omega = rho / rho_c gauges how the actual density compares to this threshold. If Omega > 1, the universe is said to be overclosed; Omega = 1 corresponds to a flat geometry, and Omega < 1 to an open geometry.

In simple, matter- and radiation-dominated models without a cosmological constant, an overclosed universe would have positive spatial curvature and would eventually stop expanding and recollapse in a finite time, potentially ending in a Big Crunch. The fate hinges on the balance of density, pressure, and gravity.

In contemporary cosmology, the situation is more nuanced due to the presence of dark energy, typically modeled as a cosmological constant. Dark energy can drive accelerated expansion and alter the ultimate fate of the universe, so an Omega > 1 condition does not automatically imply recollapse. Current observations indicate that the total density parameter is very close to unity and that dark energy dominates the current energy budget, making the universe effectively flat with no imminent overclosure.

The term overclosure is largely historical and arises from simplified early-universe models. Modern usage emphasizes the total energy budget through the separate components Omega_m, Omega_r, and Omega_lambda, rather than a single overclosure criterion.