Cosmology MOC

Core map for cosmology notes: expansion history, distance measures, and age calculations.

Core notes

• Age of Universe — derivation of the age integral from the Friedmann equation.
• Age of universe derivation — duplicate/alternate derivation of the same age result; keep until consolidated.
• Angular diameter distance — how physical size maps to observed angular size.
• Cosmology distance methods — quick comparison of comoving, angular-diameter, and luminosity distances.

Key quantities

• Scale factor: $a=1/(1+z)$.
• Hubble function: $H(a)=H_{0}E(a)$.
• Comoving distance: line-of-sight distance in coordinates expanding with the universe.
• Angular-diameter distance: $d_A=D_M/(1+z)$.
• Luminosity distance: $d_L=(1+z)D_M$.
• Etherington relation: $d_L=(1+z{)}^2{d}_A$.

Mental model

Cosmological distance is annoying because “distance” can mean several observationally different things. The same object has:

• a coordinate distance used in the metric/comoving grid;
• an angular-size distance used for rulers;
• a luminosity distance used for standard candles.

Do not mix them casually — this is where cosmology algebra goes to die lol.

Nearby

• Salpeter Initial Mass Function
• ASTRO MOC
• NF2 solar extrapolation MOC