CMB Power Spectrum Simulator: Acoustic Peaks & Cosmological Parameters

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First peak at ℓ ≈ 220 — consistent with flat geometry

With standard ΛCDM parameters (Ωb=0.05, Ωc=0.25, h=0.67), the first acoustic peak appears at multipole ℓ ≈ 220, confirming spatial flatness to within 0.4%.

Formula

C_ℓ ∝ ℓ(ℓ+1) × power spectrum amplitude
θ_s = r_s / d_A (sound horizon / angular diameter distance)
T₀ = 2.7255 ± 0.0006 K

Relic Light from the Dawn of Time

The cosmic microwave background is the oldest light in the universe, released when the cosmos cooled to ~3000 K and became transparent for the first time. Discovered accidentally by Penzias and Wilson in 1965, the CMB provides a snapshot of conditions just 380,000 years after the Big Bang. Its near-perfect blackbody spectrum confirms the hot Big Bang model, while its tiny anisotropies — temperature variations of about 30 μK — contain a wealth of cosmological information.

Acoustic Oscillations in the Primordial Plasma

Before recombination, photons and baryons were tightly coupled into a single fluid. Gravitational collapse of dark matter overdensities drove this fluid inward, while radiation pressure pushed it outward, setting up standing acoustic waves. The resulting pattern of compressions and rarefactions at the moment of recombination imprinted a characteristic series of peaks in the angular power spectrum — a cosmic barcode encoding fundamental parameters.

Decoding the Power Spectrum

Each feature of the CMB power spectrum constrains specific physics. The position of the first peak at ℓ ≈ 220 confirms the universe is spatially flat. The relative heights of odd and even peaks measure baryon density. The damping of high-ℓ power constrains photon diffusion (Silk damping) and the number of relativistic species. Together, the Planck satellite's measurements of six parameters describe the entire observable universe to percent-level precision.

Precision Cosmology

The CMB has enabled an era of precision cosmology: six numbers (Ωbh², Ωch², θs, τ, ns, As) suffice to describe the primordial fluctuations and the universe's composition. Cross-correlating CMB data with galaxy surveys, lensing maps, and baryon acoustic oscillation measurements tests the ΛCDM model at multiple redshifts and scales, searching for cracks that might reveal new fundamental physics.

FAQ

What is the cosmic microwave background?

The CMB is thermal radiation from the early universe, emitted ~380,000 years after the Big Bang when electrons and protons first combined into neutral hydrogen (recombination). It has a near-perfect blackbody spectrum at T = 2.7255 K with tiny fluctuations (~1 part in 100,000) that encode the seeds of all cosmic structure.

What do the acoustic peaks tell us?

The peaks in the CMB power spectrum arise from acoustic oscillations in the photon-baryon fluid before recombination. The first peak position constrains spatial curvature, peak height ratios constrain baryon density, and the damping tail constrains the spectral index and number of neutrino species.

How does baryon density affect the CMB?

Baryons add inertia to the photon-baryon fluid, deepening gravitational potential wells. This boosts odd-numbered peaks (compression phases) relative to even peaks (rarefaction), making the odd/even ratio a precise baryon-density probe.

Why is the first peak at ℓ ≈ 220?

The first peak corresponds to the mode that completed exactly half an oscillation by recombination. Its angular scale (~1°, or ℓ ≈ 220) depends on the sound horizon size and the angular diameter distance to the last scattering surface — both sensitive to spatial curvature.

Sources

Embed

<iframe src="https://homo-deus.com/lab/cosmology/cosmic-microwave/embed" width="100%" height="400" frameborder="0"></iframe>
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