Cosmology

CMB Anisotropy

Tiny ΔT/T ~ 10⁻⁵ temperature fluctuations encode acoustic oscillations of pre-recombination plasma

The cosmic microwave background (CMB) is the relic radiation from when the universe became transparent to photons at z ≈ 1100 (cosmic age 380,000 years), now seen as a near-perfect 2.725 K blackbody. Anisotropies — tiny temperature variations of order ΔT/T ~ 10⁻⁵ across the sky — encode the state of the universe at recombination. Discovered by COBE 1992 (Smoot, Mather; Nobel 2006). The angular power spectrum C_ℓ has a series of acoustic peaks at angular scales corresponding to sound waves in the photon-baryon plasma. Position of first peak (ℓ ≈ 220) → flatness, Ω_total ≈ 1; height ratio of first to second peak → baryon density Ω_b ≈ 0.049; third peak → cold dark matter density Ω_cdm ≈ 0.262; damping tail → number of relativistic species. Planck 2018: H₀ = 67.4 km/s/Mpc, Ω_Λ = 0.685, Ω_m = 0.315, age 13.8 Gyr. Polarization: E-mode detected (acoustic), B-mode unconfirmed (would prove inflation).

  • Temperature2.725 K blackbody
  • AnisotropyΔT/T ~ 10⁻⁵
  • Recombinationz ≈ 1100 (380,000 yr)
  • First peakℓ ≈ 220 (flatness)
  • Planck 2018H₀ = 67.4, Ω_m = 0.315
  • E-modePolarization detected

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Why CMB anisotropy matters

  • Cosmological parameters. The CMB is the most precise single source for parameters like H₀, Ω_m, Ω_b, Ω_Λ, age, optical depth, and spectral index — Planck 2018 measured most to sub-percent precision.
  • Dark matter constraint. The relative heights of acoustic peaks (especially the third) require non-baryonic dark matter at exactly the abundance independently inferred from galaxy dynamics — strong corroborating evidence.
  • Inflation tests. The shape of the primordial power spectrum (n_s, running, non-Gaussianity) directly tests inflationary models. Future B-mode detection would essentially confirm inflation.
  • Reionization signal. Late-time reionization at z ≈ 7 imprints a low-ℓ polarization bump, measuring the optical depth τ ≈ 0.054 and constraining when stars first lit up.
  • Lensing potential. Gravitational lensing of CMB photons by intervening structure reconstructs the matter distribution back to z ~ 2, complementing galaxy surveys.
  • Number of neutrino species. The damping tail of the spectrum is sensitive to the relativistic-energy budget at recombination, giving N_eff ≈ 3.04 — consistent with three Standard Model neutrinos.
  • SZ cluster surveys. CMB experiments doubling as cluster catalogs through SZ effect measure thousands of high-z clusters.

Common misconceptions

  • "Uniform = no info." The CMB looks uniform, but the 10⁻⁵ anisotropies contain virtually all our quantitative knowledge of cosmological parameters — gold dust, not noise.
  • "B-mode = inflation." Only large-scale primordial B-modes signal inflation; small-scale B-modes are produced by gravitational lensing of E-modes and have already been detected.
  • "1992 was the first detection." Penzias and Wilson detected the CMB itself in 1965 (uniform 3 K signal). COBE in 1992 first measured the anisotropies — different discovery.
  • "CMB photons come from the Big Bang." They come from recombination at z ≈ 1100, 380,000 years after the Big Bang. Earlier the universe was opaque to photons; the CMB is the surface of last scattering, not the Big Bang itself.
  • "COBE proved everything." COBE's resolution was ~7°, missing the acoustic peaks. WMAP (2003) and Planck (2013, 2018) had the angular resolution and sensitivity needed to extract precision parameters.
  • "Anomalies disprove the model." Some hemispherical asymmetries and the Cold Spot have intriguing low-significance anomalies, but none rise to a level that overturns ΛCDM.

Anatomy of the power spectrum

  • First peak (ℓ ≈ 220). The largest sound-horizon mode caught at maximum compression — its angular position calibrates the geometry, requiring Ω_total ≈ 1.
  • Second peak (ℓ ≈ 540). Maximum rarefaction. Its height relative to the first peak measures baryon density Ω_b — baryons drag the oscillations, lowering odd-numbered peak heights.
  • Third peak (ℓ ≈ 810). Sensitive to the dark-matter to baryon ratio; its boost relative to expectations from baryons alone confirmed cold dark matter.
  • Damping tail (ℓ > 1000). Photon diffusion (Silk damping) erases small-scale anisotropies; the slope measures the number of relativistic species N_eff and the helium fraction.
  • Sachs-Wolfe plateau (ℓ < 30). Large-scale anisotropies from gravitational redshift of photons climbing out of/falling into potential wells at recombination, plus the integrated SW effect from late-time dark-energy domination.

Frequently asked questions

What is the CMB temperature and why 2.725 K?

The CMB has a near-perfect blackbody spectrum at T = 2.725 K, measured by COBE/FIRAS to extraordinary precision. The temperature reflects the universe's cooling since recombination at z ≈ 1100, when photons last scattered and the plasma temperature was ~3000 K. Subsequent expansion redshifted those photons by a factor of about 1100, dropping their effective blackbody temperature to today's 2.725 K. The blackbody form is preserved because adiabatic expansion shifts every photon by the same factor.

Why are there acoustic peaks in the spectrum?

Before recombination, photons and baryons were tightly coupled into a single fluid. Pressure from photons resisted gravitational compression by dark matter, producing oscillations — sound waves in the plasma. Different wavelength modes were caught at different phases when recombination froze the pattern: modes at maximum compression contribute to the first peak, modes at maximum rarefaction to the second, and so on. The result is a series of harmonic peaks at angular scales corresponding to the sound horizon at recombination.

What does the first peak tell us about geometry?

The first acoustic peak's angular position depends on the physical sound horizon (~150 Mpc, well-known from physics) and the angular-diameter distance to the surface of last scattering. If the universe is flat, the peak appears at multipole ℓ ≈ 220; in a closed universe, it shifts to lower ℓ; in an open universe, to higher ℓ. Observed peak position pins down spatial curvature: Ω_total = 1.000 ± 0.005, the universe is flat to better than half a percent.

What is E vs B-mode polarization?

CMB photons are partially polarized by Thomson scattering at recombination. Polarization patterns decompose into two components: E-modes (gradient-like, parity-even) and B-modes (curl-like, parity-odd). E-modes are sourced by density perturbations and have been detected since 2002 (DASI). B-modes have two sources: gravitational lensing converts E to B at small scales (detected); primordial gravitational waves generate B-modes at large scales (not yet detected — would confirm inflation).

What is the SZ effect (galaxy cluster CMB distortion)?

Sunyaev-Zel'dovich effect: hot electrons in galaxy clusters inverse-Compton scatter CMB photons to higher energies, producing a frequency-dependent shift — the CMB looks colder at frequencies below ~217 GHz and hotter above. The thermal SZ amplitude is independent of cluster redshift (great for cluster surveys at high z), and the kinetic SZ tracks cluster bulk motion along the line of sight. Surveys like ACT, SPT, and Planck use SZ to find and characterize thousands of clusters.

What's the cosmic variance limit on small ℓ?

We can only see one universe, so for each multipole ℓ there are only 2ℓ+1 statistically independent modes on the sky. At low ℓ (large angular scales), this means small samples and large statistical uncertainties — the cosmic variance limit. For instance, the quadrupole has only 5 modes, giving an irreducible ~45% statistical scatter even with perfect measurements. This fundamental limit caps how precisely we can ever measure the largest-scale features of the early universe.