overdensity

Overdensity refers to a region of space where the local matter density exceeds the average density of the universe. In cosmology, the degree of overdensity is quantified by the density contrast δ, defined as δ ≡ (ρ − ρ̄)/ρ̄, where ρ is the local density and ρ̄ is the cosmic mean density. Overdensities, like underdensities, are fundamental in the growth of cosmic structure.

In the early universe fluctuations are small (δ << 1) and evolve under gravity according to linear perturbation theory, with δ growing as the linear growth factor D(t). Overdense regions decouple from the Hubble expansion, stop expanding, and eventually undergo gravitational collapse. In the nonlinear regime, virialization leads to stable bound halos that host galaxies and clusters. The spherical collapse model yields a critical overdensity δc ≈ 1.686 for a matter-dominated cosmos; in a ΛCDM universe the value is similar but slightly model dependent.

Overdensities also define structures within the cosmic web. Large overdense regions form galaxy clusters and superclusters, while lower-density regions form filaments and walls. In observational surveys, regions with higher-than-average galaxy counts are identified as overdense, and their statistics are used to study cosmology, structure formation, and the distribution of dark matter.