The working model of cosmology. Six numbers explain almost everything we observe.
Plain ΛCDM
Flat geometry, cold dark matter, a cosmological constant Λ for dark energy. Fits cosmology with six numbers.
Looping ambient scene for Standard Cosmological Model. The Standard Cosmological Model, ΛCDM, is the working framework of modern cosmology. The universe is flat, expanding, filled with ordinary matter, cold dark matter, photons, neutrinos, and a cosmological term Λ that drives accelerating expansion. The whole framework is fixed by six numbers, plus a handful of nuisance parameters, and fits cosmic microwave background, baryon acoustic oscillations, supernova distances, light-element abundances, and large-scale structure with extraordinary precision.
§1 · The claim, in one sentence
Six numbers, set by data, describe nearly everything we observe in cosmology, from the cosmic microwave background through galaxy surveys to today's expansion rate.
§2 · Why it might be true
Plain ΛCDM is the working framework of modern cosmology. It assumes the universe is flat on large scales, filled with ordinary matter, cold dark matter, photons and neutrinos, and a cosmological term Λ with constant negative pressure that drives the observed accelerating expansion. Everything else, every measurement and every competing theory, is positioned against this baseline.
The framework is specified by six free parameters: the densities of baryons and cold dark matter, the angular size of the sound horizon at recombination, the optical depth to reionization, and the amplitude and tilt of the primordial fluctuation spectrum. Six numbers. From those, ΛCDM derives the predicted shape of the cosmic microwave background, the scale of the baryon acoustic oscillation feature in galaxy clustering, the abundance of primordial helium, and the present-day rate of expansion.
What's unusual about ΛCDM is the precision of the fit. Planck's 2018 measurement of the CMB temperature angular power spectrum is fit to fractional precision by these six numbers, with no statistically compelling residual structure. The same six numbers, fixed by Planck, also reproduce the baryon acoustic feature at ~150 megaparsecs measured in galaxy surveys, the cosmic distance-redshift relation traced by type Ia supernovae, and the abundance of deuterium produced in the first three minutes.
The family stance
Five percent ordinary baryonic matter, twenty-six percent cold dark matter, sixty-nine percent dark energy modelled as a cosmological constant Λ, with essentially zero spatial curvature. The exact percentages depend on the data combination but all serious cosmological measurements converge here.
§2.5 · Evidence
- Planck 2018 fits the CMB to ~permil precision with six parameters
- BAO scale at z ~ 0.1 to 2.5 measured by major galaxy-mapping surveys (SDSS, eBOSS, DESI) matches the prediction fixed by CMB data
- BBN-predicted light-element abundances agree with primordial abundance measurements
- DESI 2024 BAO alone gives Ωm = 0.295 ± 0.015, fully consistent with ΛCDM
- DESI 2024 BAO + Planck + CMB lensing: H0 = 67.97 ± 0.38 km/s/Mpc (within ΛCDM)
§3 · What you'd need to test it
- Cosmic microwave background temperature anisotropies have a specific acoustic peak structure, peaking at angular scales near 1 degree, with secondary peaks at well-defined harmonics
- A baryon acoustic oscillation feature at ~150 Mpc (comoving) in galaxy clustering at all redshifts where galaxies form
- Big Bang Nucleosynthesis primordial abundances of ~75% hydrogen, ~25% helium-4, and well-defined trace abundances of deuterium and lithium
- How fast cosmic structure grows and clumps, captured by the growth-rate measure fσ8(z), is predicted exactly from the matter density Ωm, the dark energy density ΩΛ, and the primordial spectrum
- H0 ≈ 67 to 68 km/s/Mpc inferred from CMB + BAO + the standard inverse-distance ladder
§4 · Where it breaks
- The Hubble tension: CMB + BAO predict H0 ≈ 67.4, the local distance ladder (SH0ES) measures H0 = 73.04 ± 1.04, a ~5σ disagreement that has resisted >100 proposed solutions
- The S8 / σ8 tension: large-scale-structure surveys (KiDS, DES) measure ~2-3σ lower clustering amplitude than CMB-fixed ΛCDM predicts
- DESI 2024 BAO combined with supernovae gives 2.5 to 3.9σ preference for an evolving equation of state (w0waCDM) over Λ, with the strongest preference using the DES-SN5YR sample
- Λ itself: no satisfactory theory explains why the vacuum energy is the observed value rather than zero or 10¹²⁰ times larger
- Dark matter has never been directly detected; all evidence is gravitational
Go deeper
The six base parameters in Planck's convention: ωb = Ωbh² (baryon density), ωc = Ωch² (cold dark matter density), 100θMC (acoustic scale at recombination), τ (optical depth to reionization), ln(10¹⁰As) (amplitude of primordial fluctuations), ns (spectral tilt). All other ΛCDM quantities are derived. Best-fit Planck 2018 values: ωb ≈ 0.02237, ωc ≈ 0.1200, 100θMC ≈ 1.04092, τ ≈ 0.0544, ln(10¹⁰As) ≈ 3.044, ns ≈ 0.9649.
ΛCDM as a model hierarchy: ΛCDM is the special case of wCDM where w = -1, which is itself the special case of w0waCDM where wa = 0. Each extension adds one free parameter. The DESI 2024 evidence for evolving dark energy lives in the w0wa plane, not in the w sub-plane.
The name 'concordance model' reflects that independent probes converge: CMB anisotropies, BAO, type Ia supernovae, weak gravitational lensing, primordial nucleosynthesis, and the integrated Sachs-Wolfe effect all point to the same parameter values within their statistical uncertainties.
Open puzzles within ΛCDM at small scales: the missing satellites problem, the too-big-to-fail problem, and the cusp-core problem all concern whether ΛCDM N-body simulations correctly predict subgalactic structure. Baryonic feedback and warm dark matter variants are proposed solutions, but no consensus has formed.
▸§5 · Who built it, and when(8 sources, 8 established)
- EstablishedEinstein (1917). 'Cosmological Considerations in the General Theory of Relativity.' Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) 1917, 142
- EstablishedLemaître (1927). 'A Homogeneous Universe of Constant Mass and Growing Radius Accounting for the Radial Velocity of Extragalactic Nebulae.' Annales Soc. Sci. Bruxelles A 47, 49
- EstablishedZwicky (1933). 'Die Rotverschiebung von extragalaktischen Nebeln.' Helv. Phys. Acta 6, 110
- EstablishedWeinberg (1989). 'The Cosmological Constant Problem.' Rev. Mod. Phys. 61, 1
- EstablishedRiess et al. (1998). 'Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant.' Astron. J. 116, 100919,223 citations
- EstablishedPerlmutter et al. (1999). 'Measurements of Omega and Lambda from 42 High-Redshift Supernovae.' Astrophys. J. 517, 56518,529 citations
- EstablishedPlanck Collaboration (2020). 'Planck 2018 Results VI: Cosmological Parameters.' Astron. Astrophys. 641, A622,331 citations
- EstablishedRiess et al. (2022). 'A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team.' Astrophys. J. Lett. 934, L72,699 citations
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