Cosmological evidence and the dark sector

The COBE-FIRAS spectrum fits a Planck curve at T₀ = 2.7255 ± 0.0006 K with residuals below one part in 10⁴ of the peak — the most exact blackbody ever measured, and nothing in the present universe can make one. Scattered starlight, warm dust and free-free emission all leave a spectrum with a shape, and a shape is what is absent here. So the spectrum by itself establishes a past that was optically thick and in thermal equilibrium, and dates the release of these photons to recombination near T = 3000 K, which the present 2.7255 K places at redshift 3000/2.7255 − 1 ≈ 1100. Notice what it does not do. It fixes a temperature and a thermal history, and the photon energy density that follows, Ω_γ ≈ 5.4 × 10⁻⁵, is negligible in today's budget. Every density parameter in this lesson comes from something else.

The largest departure from uniformity on the sky is a pure dipole of amplitude 3.362 mK — one part in 810 of T₀, so about 10⁻³. It is kinematic: a moving observer sees ΔT/T₀ = (v/c) cos θ, so the amplitude is v/c and nothing more, and it would appear in a perfectly smooth universe. It gives 370 km s⁻¹ for the solar-system barycentre, and about 620 km s⁻¹ for the Local Group once the Sun's galactic orbit is removed. Fit that dipole, subtract it, and the residual sky has an rms near 30 μK, or 1.1 × 10⁻⁵. Two orders of magnitude separate the observer's velocity from the physics, which is why every published anisotropy map is a map of what is left after the dipole has been taken out.

Before recombination the photons and baryons are one fluid: gravity compresses an overdensity, radiation pressure pushes back, and the modes that have completed exactly half an oscillation when the photons decouple show maximum contrast. That sets a physical length — the sound horizon, about 147 Mpc comoving — of known size at a known distance, so its angular size is a measurement of geometry, ℓ₁ ≈ 220/√Ωₜₒₜ. The observed ℓ₁ ≈ 220 gives Ωₜₒₜ ≈ 1, and the full spectrum combined with baryon acoustic oscillations in the galaxy distribution sharpens this to Ωₖ = 0.001 ± 0.002. A second number falls out of the same spectrum: baryons weigh the fluid down, deepening odd compression peaks against even rarefaction peaks, and the ratio returns Ω_b h² = 0.0224 independently of any nuclear physics. Flatness is the assumption that later lets Ω_Λ be obtained by subtraction.

Above about 0.8 MeV, weak interactions hold n/p at its equilibrium value exp(−Δmc²/kT) with Δmc² = 1.293 MeV. Freeze-out at 0.8 MeV leaves n/p = exp(−1.616) = 0.199, near 1/5; free neutrons then decay for the few minutes it takes deuterium to survive photodissociation, dropping the ratio to about 1/7, and essentially every surviving neutron is swept into ⁴He. So Yₚ = 2(1/7)/(1 + 1/7) = 0.25, a number governed by the expansion rate and the neutron lifetime and only logarithmically by the baryon density — a test of the framework, not a scale. Deuterium is its opposite: a fragile intermediate burned away faster the denser the baryons, with D/H ∝ (Ω_b h²)^−1.6. Measure it where no star has processed it, in metal-poor absorbers along quasar sightlines, D/H = 2.53 × 10⁻⁵, and Ω_b h² = 0.0224 follows — Ω_b = 0.049 at h = 0.674.

Rotation curves come first: v stays near 220 km s⁻¹ far beyond the optical disc, so M(<r) = v²r/G keeps rising linearly while the light has stopped, giving 2.3 × 10¹¹ M☉ inside 20 kpc. Cluster galaxies move far too fast for the mass their light implies, which is what Zwicky found in Coma in 1933. Weak lensing then maps the potential with no equilibrium assumption at all, and in the Bullet Cluster the lensing mass travels with the galaxies while the X-ray gas — which carries most of the baryonic mass — is left behind in the collision, separating a collisionless component from the baryons in a single image. The three methods converge on Ωₘ ≈ 0.315, while nucleosynthesis caps baryons at 0.049. About 84 per cent of the matter therefore takes part in neither nuclear nor electromagnetic processes.

Type Ia supernovae, standardised through the width–luminosity relation, work as distance indicators to z ≈ 1. Near z = 0.5 they arrive roughly 0.4 magnitudes fainter than a decelerating Ωₘ = 1 model predicts — a flux ratio 10^(−0.4/2.5) = 0.69, so about 20 per cent farther away than that model puts them — and about 0.1 magnitudes fainter than even an empty universe, which merely coasts. Combine flat geometry from the CMB with Ωₘ = 0.315 from dynamics and Ω_Λ = 0.685 follows by subtraction; the supernovae then confirm the same value along an independent route. What does not agree is H₀. The CMB read through ΛCDM gives 67.4 ± 0.5 km s⁻¹ Mpc⁻¹ and the Cepheid-calibrated distance ladder gives 73.0 ± 1.0, five standard deviations apart. Because the CMB constrains Ω h² rather than Ω, that disagreement moves the whole budget: at h = 0.730 the same measured densities give Ωₘ = 0.268.