Cosmology

The Expanding Universe

1929 - Redshift and Luminosity used to measure distance and velocity of galaxies. The velocity-distance relation of galaxies.
- $V = H_{0} R$
- The expansion of space $R (t) = a (t) R_{0}$
- The hubble parameter is the derivative of $R$
- Hubble fitted a straight line to this relationship, so the further a galaxy is away, the faster it is moving
- This was really revolutionary at the time.
Friedman equation
- F1
  - So how do we find $a (t)$ ? What is the time evolution of the scale factor?
  - We can build an intuition for this just using gravity.
  - Constant U in Friedman equation, energy conservation (kinetic - potential)
    - U > 0 ⇒ expands forever
    - U < 0 ⇒ collapse
    - U = 0 ⇒ constant rate
- F2 - consider the universe as a homogenous gas or fluid and use thermodynamics to understand how different quantities are related
  - continuity equation
Epochs of Cosmological history → Assume U=0
- $ω = P / g$ equation of state
- Plugging this into the continuity equation F2, we can solve the equation
- ⇒ we get the energy density as a function of omega