← Mathematical compendium

Published equation contexts

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

Why this formula appears here

The European Space Agency’s Planck satellite, launched in 2009 and operating until 2013, extended this to still finer angular resolution and a wider frequency range, cooling its bolometer detectors to a fraction of a degree above absolute zero to suppress instrumental noise. Planck’s 2018 final cosmological parameter release fit the standard six-parameter flat Lambda-CDM model to its temperature and polarization data, reporting the acoustic scale — the characteristic angular size of the sound-wave pattern imprinted on the CMB — to 0.03 percent precision, a cold dark matter density of 0.120 ± 0.001 (in units of the density parameter times the reduced Hubble parameter squared), and a Hubble…

Read the full article-specific guide →

Read the representative guide

θ∗\theta_*

Symbol theta_*

theta∗a_* is part of the quantity the equation computes from the expression on the right.

Read this term in its guide →
r∗r_*

Symbol r_*

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 —.

Read this term in its guide →
z∗z_*

Symbol z_*

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

Read this term in its guide →
DA(z∗)D_A(z_*)

Denominator: D_A(z_*)

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

Read this term in its guide →

How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

Research cited beside this formula

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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

Equation 1 · Astronomy & Cosmology

From Origins to Frontier: A History of Precision Cosmology

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

The European Space Agency’s Planck satellite, launched in 2009 and operating until 2013, extended this to still finer angular resolution and a wider frequency range, cooling its bolometer detectors to a fraction of a degree above absolute zero to suppress instrumental noise. Planck’s 2018 final cosmological parameter release fit the standard six-parameter flat Lambda-CDM model to its temperature and polarization data, reporting the acoustic scale — the characteristic angular size of the sound-wave pattern imprinted on the CMB — to 0.03 percent precision, a cold dark matter density of 0.120 ± 0.001 (in units of the density parameter times the reduced Hubble parameter squared), and a Hubble…

Meanings in this article

  • r∗r_*: 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 —.
  • DAD_A: the angular diameter distance to that same epoch.
Equation guide → · Article →