CMB Power Spectrum (Acoustic Peaks)
This interactive simulator explores CMB Power Spectrum (Acoustic Peaks) in Astronomy & The Sky. Cosmic Microwave Background temperature D_ℓ vs ℓ with Sakharov peaks: tune Ω_b h², Ω_c h², n_s, A_s, τ, h and watch the parity flip between odd / even peaks, the Silk damping tail, and the Sachs–Wolfe plateau move. Pedagogical parametric ΛCDM model. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.
Who it's for: For learners comfortable with heavier math or second-level detail. Typical context: Astronomy & The Sky.
Key terms
- cmb
- power
- spectrum
- acoustic
- peaks
- cmb power spectrum
- astronomy
How it works
**CMB temperature power spectrum** — D_ℓ = ℓ(ℓ+1)C_ℓ/2π in μK² as a function of multipole ℓ — the cornerstone observable of precision cosmology. The simulator is a *parametric* model (no Boltzmann code), but it captures the qualitatively correct response of the spectrum to the six standard ΛCDM parameters: **Sachs–Wolfe plateau** at ℓ ≲ 30, **acoustic / Sakharov peaks** at ℓ ≈ 220, 540, 810, … set by the angular sound horizon ℓ_A; baryon-loading **parity** (raising Ω_b h² boosts odd peaks and suppresses even ones), the **Silk damping** tail at high ℓ, the **scalar tilt** n_s, and reionisation suppression e^{−2τ}. Slide Ω_b h² and watch the second peak shrink relative to the first — that's how Planck pinned the baryon density.
Key equations
More from Astronomy & The Sky
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Heliocentric geometry: full disk vs crescent at inferior conjunction; Earth-view inset.
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Bradley: telescope tilt v/c ~ 10⁻⁴ rad; annual ~20.5″ — not parallax.
Milankovitch Cycles
e, obliquity, precession → toy high-latitude insolation curve; ice-age pacing context.