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| critical density (cosmology) | |
|---|---|
| Name | Critical density (cosmology) |
| Field | Cosmology |
| Introduced | 20th century |
| Key people | Albert Einstein, Alexander Friedmann, Georges Lemaître, Edwin Hubble, George Gamow |
| Related | Hubble parameter, Friedmann equations, Cosmological constant, Lambda-CDM model |
critical density (cosmology) The critical density is the energy density value that separates different global geometries and expansion behaviors of the Universe in relativistic cosmology. It is central to models developed by Alexander Friedmann and Georges Lemaître and appears in the Friedmann equations alongside the Hubble parameter and the cosmological constant. Observational programs led by teams using the Hubble Space Telescope, the Planck mission, and the Sloan Digital Sky Survey constrain the present-day value.
In relativistic cosmology the critical density ρ_c is defined by inserting a spatially flat geometry into the Friedmann equations; it is given by ρ_c = 3H^2/(8πG), where H is the Hubble parameter and G is Newton's gravitational constant. The expression ties together the dynamics discovered by Alexander Friedmann and applied by Georges Lemaître with the observational scaling first quantified by Edwin Hubble. Modern formulations incorporate the cosmological constant Λ and are used in the Lambda-CDM model to normalize fractional density parameters such as Ω_m and Ω_Λ.
The critical density enters the first Friedmann equation as the normalization that delineates spatial curvature: if the total density parameter Ω_total = ρ_total/ρ_c equals unity the spatial geometry is flat, a result that traces to work by Alexander Friedmann and was emphasized in analyses by Stephen Hawking and Roger Penrose. If Ω_total > 1 the geometry is closed (positive curvature) as in models discussed by Albert Einstein when invoking a static Einstein universe before dynamical solutions were accepted; if Ω_total < 1 the geometry is open (negative curvature), possibilities explored in classical treatments and in later reviews by George Gamow and Robert Dicke.
Total density ρ_total comprises contributions from baryonic matter, cold dark matter, radiation, neutrinos, and dark energy. The fractional contributions are expressed as Ω_i = ρ_i/ρ_c, with canonical components denoted Ω_b for baryonic matter, Ω_c for cold dark matter, Ω_r for radiation including photons from the Cosmic Microwave Background, and Ω_Λ for the dark energy component associated with the cosmological constant. Measurements of Ω_b have been cross-checked between Big Bang nucleosynthesis predictions by groups associated with George Gamow and Ralph Alpher and observations from missions such as WMAP and Planck that constrain Ω_b and Ω_c within the Lambda-CDM model.
Because ρ_c ∝ H^2, the critical density evolves as the Hubble parameter changes with cosmic time; early epochs with large H had correspondingly larger ρ_c, influencing the relative importance of radiation, matter, and dark energy. The time dependence of H is governed by the Friedmann equations given specific Ω_i evolution laws (e.g., ρ_m ∝ a^−3, ρ_r ∝ a^−4, ρ_Λ = constant), where a(t) is the scale factor used in models developed by Georges Lemaître and formalized in modern cosmology. This scaling affects epochs such as matter–radiation equality and the onset of accelerated expansion associated with the discovery by teams led by Saul Perlmutter, Brian Schmidt, and Adam Riess.
Determinations of ρ_c and Ω_total rely on multiple probes: anisotropies in the Cosmic Microwave Background measured by Planck and WMAP; baryon acoustic oscillations mapped by the Sloan Digital Sky Survey and the 2dF Galaxy Redshift Survey; Type Ia supernovae campaigns by the teams of Saul Perlmutter and Brian Schmidt; weak gravitational lensing surveys such as those by the Dark Energy Survey; and direct Hubble constant measurements using the Hubble Space Telescope distance ladder anchored by the Cepheid variable calibration methods upheld by the SH0ES Team. Combined analyses yield a present critical density near 10^−26 kg m^−3 and constrain Ω_total to be close to unity in concordance models advanced by the Planck Collaboration.
Whether the total density equals, exceeds, or falls below the critical value has historically determined scenarios for the Universe’s fate: eternal expansion, eventual recollapse, or marginally bound evolution—analyses central to debates involving Albert Einstein and later Fritz Zwicky and George Gamow. In modern Lambda-CDM model cosmology, a dominant Ω_Λ leads to accelerated expansion and affects the growth rate of cosmic structure, modifying predictions of halo formation studied within the framework of Cold Dark Matter simulations by groups such as those behind the Millennium Simulation. The critical density thus sets the normalization for the amplitude of perturbations and the timing of nonlinear collapse relevant to galaxy formation investigated by teams associated with Vera C. Rubin Observatory and James Webb Space Telescope studies.
Extensions of the concept arise in models with dynamical dark energy (e.g., quintessence proposals influenced by theoretical work from researchers connected to Paul Steinhardt and Robert J. Scherrer), modified gravity theories such as f(R) gravity and MOND-inspired frameworks proposed by Mordehai Milgrom, and in inflationary paradigms developed by Alan Guth and Andrei Linde. In these extensions the notion of a single critical density can be generalized to effective densities, curvature terms, or scale-dependent measures appearing in studies by the Planck Collaboration and groups working on alternatives at institutions such as CERN and the Perimeter Institute for Theoretical Physics.