Cosmology - Models and theory

Andrew Conway

General Relativity and Space-time

(See the section on black holes for an introduction to relativity.)

Mass tells space-time how to curve, and space-time tells mass how to move.

John Wheeler

Isotropic and homogenous

The Cosmological Principle

Pythagoras in flat 2D

Pythagoras's theorem Source: Andrew Conway CC-BY SA 3.0


Distance on a sphere

Great circle distance

Source: Andrew Conway, adapted from this by Cffk

CC-BY SA 3.0

Great circle distance

The Metric for a flat 3D space

The distance squared ds2 between two points is given by

ds2 = dx2 + dy2 + dz2

Flat space-time metric

ds2 = dx2 + dy2 + dz2 - c2dt2

Cosmology space-time metric

ds2 = R2(dx2 + dy2 + dz2) - c2dt2

Scale factor and redshift

Recall from before, that if λ0 is the stationary wavelength and λ is the observed (shifted) wavelength, then the redshift is given by

z = (λ - λ0) / λ0

The correct explanation for this is not the Doppler effect due to the source's motion, but because the scale factor has changed, which tells us that:

z = (R - R0) / R0

where R is the scale factor at observation and R is the scale factor as the light was emitted.

Solutions to Einstein's equations

ρcrit = 3 H2 / 8 π G

The critical density

ρ < ρcrit

ρ > ρcrit

ρ = ρcrit

The Cosmological Constant

A cosmic surprise.