Cosmology index

Local index for cosmology notes in PHYSICS/ASTRO/Cosmology.

What belongs here

Cosmology notes cover the large-scale universe: expansion, redshift, the Friedmann equation, distance measures, and age calculations.

Current notes

• Cosmology MOC — map of this folder.
• Age of Universe — age integral and special cases.
• Age of universe derivation — alternate/older copy of the age derivation.
• Angular diameter distance — ruler-distance relation and luminosity-distance relation.
• Cosmology distance methods — quick distance taxonomy.

Key equations to remember

Scale factor and redshift:

$$1+z=\frac{1}{a}.$$

Hubble function:

$$H(a)=H_0\sqrt{{\Omega }_m{a}^{-3}+{\Omega }_r{a}^{-4}+{\Omega }_{\Lambda }+{\Omega }_k{a}^{-2}}.$$

Time step from scale factor:

$$dt=\frac{da}{aH(a)}.$$

Line-of-sight comoving distance:

$$\chi (z)=c{\int }_0^z\frac{d{z}^{\prime }}{H(z^{\prime })}.$$

Common pitfalls

• Using $d_A$, $d_L$, and comoving distance interchangeably. They answer different observational questions.
• Forgetting the factor $dz=-da/a^2$ when changing variables from redshift to scale factor.
• Dropping curvature without saying the universe is assumed flat.
• Treating $H_0^{-1}$ as exactly the age of the universe; it is only a timescale unless the cosmological model makes it exact-ish.

Parent / nearby maps

• ASTRO MOC
• 00 Vault MOC