Lecture 1

Question 1

The cosmological principle

Answer 1

The universe is homogeneous and isotropic on scales larger than ~ 100 Mpc

Question 2

Homogeneous

Answer 2

looks the same

Question 3

Isotropy

Answer 3

Wherever you look

Question 4

The time evolution of the particle separation r

Answer 4

U = T + V
U = 1/2 m r(dot)^2 - 4/3πGρr^2m

Question 5

co-moving coordinates

Answer 5

r→(t) = a(t) x→

Question 6

Friedmann Equation

Answer 6

U = 1/2mȧ^2x^2 - 4/3πGρa^2x^2m

giving

(ȧ/a)^2 = 8πGρ/3 - kc^2/a^2

Question 7

k tells us about

Answer 7

the geometry or the curvature of space

Question 8

Fluid Equation

Answer 8

1st law of thermodynamics

dE + ρdV = TdS

Differentiating E and V and setting dS = 0

giving

ρ(dot) + 3ȧ/a (ρ + P/c^2) = 0

Question 9

The fluid equation shows that

Answer 9

an increase in volume causes a decrease in density and that the internal energy of the fluid changes as the universe expands

Question 10

the only source of pressure from the fluid equation is

Answer 10

associated with the change in internal energy

Question 11

if P = 0

Answer 11

non-relativistic matter - dust with no change in the internal energy

Question 12

for relativistic matter

Answer 12

radiation - we can have p ≠ 0