Cosmology

Modelled[M] for a web-cell reading of the peak. The exact printed match ℓ₁=220.50 is withdrawn. Full C_ℓ stays open.

CMB Angular Scale

The placed acoustic comparison is π√18≈13.3 against ~220. An inserted 147 Mpc cell on the clothes radius gives ℓ≈227.5, which sits 3.2% from the quoted peak 220.5. The full spectrum stays open.

Last updated: 19 October 2026

Reading this entry

The CMB angular-scale page reads the first peak as a length on the clothes radius. An inserted 147 Mpc cell on R₀ = 10646.75 Mpc subtends ℓ ≈ 227.5, a web-cell reading [M] beside the quoted ℓ₁ = 220.5 ± 0.5, together with the acoustic comparison π√18 ≈ 13.3 against ~220.

What this is used for

Microwave and S³ pages share this projection when they quote a cell on the lock radius. The angle θ = 147/10646.75 = 0.013807 rad = 0.791° gives ℓ = π/θ = 227.5, and π√18 ≈ 13.3 against ~220 remains the placed acoustic reading.

Walk through

The quoted first peak is ℓ₁ = 220.5 ± 0.5. On R₀ = √6 c/H₀ = 10646.75 Mpc at H₀ = 68.973, an inserted 147 Mpc cell subtends θ = 147/10646.75 = 0.013807 rad = 0.791°, so ℓ = π/θ = 227.5, which is algebra of that length and the lock radius and is read as a cosmic-web cell [M]. Relative to 220.5 the projection lies 7.0 units away, 3.2 percent of 220.5 and about 14 times the half-width ±0.5. The acoustic comparison kept with this reading is π√18 ≈ 13.3 against ~220, and the full spectrum is named on ℓ from 2 to 2500.

Integrity note: A formula that returns 220.50 by inserting a recombination redshift is not a theorem of

. The native comparison already on the books is

against ~220.

1. What is scored

The quoted first peak is . On the clothes radius Mpc at , an inserted length of 147 Mpc — the same numeral as the standard sound horizon — subtends

[E algebra] of the inserted length and the lock radius. The lock itself stays [M].

Relative to 220.5 the projection lies 7.0 units away: 3.2% of 220.5, and about 14 times the quoted half-width. Reading that angle as a cosmic-web cell seen at distance is [M]. The full on stays open.

2. The comparison that stays

against ~220 is the placed acoustic comparison. The 227.5 projection does not replace it. A blackbody transfer that would turn a cell diameter into is not computed on this page.

STATUS: PROJECTION [M], SPECTRUM OPEN

ℓ≈227.5 is algebra of 147 Mpc on . It is not a derived peak at 220.50.

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