Linear density perturbations

Question 1

delta_c redshift relation

Answer 1

delta_c*(1+z)

Question 2

Comoving hubble radius

Answer 2

R_H = c/a dot

Question 3

R_H functions

Answer 3

a^-1 if w=-1
a if w=1/3
a^(1/2) if w=0

Question 4

Superhorizon

Answer 4

delta ~t (a^2) , t^(2/3) (a) for rad, matter

Question 5

Subhorizon static background not pressureless

Answer 5

Solve the wave equation, if rho_0 term negligible then w^2=k^2 c_s^2

Question 6

Jeans length

Answer 6

if w^2<0, exponential unstable growth. Happens if lambda =2pi/k > c_s*(pi/(G rho_0))^(1/2) = Lj

Question 7

Jeans mass

Answer 7

Mj = 4/(3pi (Lj/2)^3 rho_0), will collapse if the mass is larger

Question 8

subhorizon expanding, pressureless

Answer 8

Matter dominated: delta ~t^x, x=-1 or 2/3. So 1 growing mode

radiation dominated: delta ~a^2

Question 9

subhorizon expanding, not pressureless

Answer 9

delta ~ exp(-Ht) sin(c_s k t/a)

Question 10

Dark matter is collisionless

Answer 10

So c_s=0

Question 11

For DM, superhorizon is the same as subhorizon

Answer 11

I hope

Question 12

Largest scales, enter after decoupling

Answer 12

Both DM and bayons behave the same, delta ~ a^2 before Teq, a after. Decoupling has no effect because the perturbation enters after

Question 13

Perturbation enters between teq and tdec

Answer 13

Dm acts the same, a^2 before eq and a after. The baryons oscillate between entering and decoupling. Ohter than that, they follow DM

Question 14

Perturbation enters before teq

Answer 14

Dm will acts as superhorizon, except that it will pause before teq because it cannot grow in the horizon. So it is frozen between tenter and teq. Baryons will oscillate until tdec

Question 15

Structure can be erased by:

Answer 15

• free streaming
• silk damping = diffusion of baryons due to radiation
• Radiation dominated expansion