1. Graduate Course: Cosmology
Zong-Kuan Guo

2. metric flat, 𝐾=0 closed, 𝐾=1 open, 𝐾=−1
𝑑 𝑠 2 =−𝑑 𝑡 2 + 𝑎 2 (𝑡) 𝑑 𝑟 2 1−𝐾 𝑟 2 + 𝑟 2 𝑑 𝜃 2 + 𝑟 2 sin 2 𝜃 𝑑 𝜙 2

3. redshift
setting 𝑎 𝑡 0 = 𝑎 0 =1
1+𝑧= 𝑎( 𝑡 0 ) 𝑎(𝑡)

4. equations
𝐻 2 = 8𝜋𝐺 3 𝜌− 𝐾 𝑎 2 + Λ 3
𝐻 =−4𝜋𝐺 𝜌+𝑃 + 𝐾 𝑎 2
𝜌 +3𝐻(𝜌+𝑃) =0

5. evolution matter dominance, 𝑤=0 radiation dominance, 𝑤=1/3
vacuum dominance, 𝑤=−1

6. observables Hubble constant, 𝐻 0 deceleration parameter, 𝑞 0
CMB temperature, 𝑇 CMB,0
spatial curvature parameter, Ω 𝐾,0
dark energy density parameter, Ω Λ,0
cold dark matter density parameter, Ω 𝑐,0

7. distances comoving distance, 𝑟(𝑧) luminosity distance, 𝑑 𝐿 (𝑧)
angular diameter distance, 𝐷 𝐴 (𝑧)

8. thermal history
𝑇= 𝑇 CMB,0 𝑎(𝑡)