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Equation 1 · Part 8 · From Origins to Frontier: A History of Precision Cosmology

Denominator: D_A(z_*)

θ∗=r∗DA(z∗)\theta_* = \frac{r_*}{D_A(z_*)}
DA(z∗)D_A(z_*)

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

DA(z∗)D_A(z_*) occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

…on it: θ∗=r∗DA(z∗)\theta_* = \frac{r_*}{D_A(z_*)}. where r∗r_* is the physical size of the sound horizon at recombination — how far a pressure wave in the primordial plasma could travel before the plasma became neutral and transparent — and DA(z∗)D_A(z_*) is the angular diameter distance to that same epoch. Planck measures θ∗\theta_* directly from the angular spacing of peaks in the CMB power spectrum to extraordinary precision; converting that angle into a present-day expansion rate H0H_0 requires assuming a cosmological model (matter content,…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.