Cosmology: Lets Take A Step Back

Question 1

Evidence for the Big Bang

Answer 1

Sky is dark at night
CMB
More distant galaxies appear redder

Question 2

Sky is dark at night

Answer 2

If the universe was static and infinite, everywhere was as bright as the sun
So the universe must’ve had a beginning and be dynamic

Question 3

More distant galaxies appear redder

Answer 3

Suggests galaxies are flying away from us
Hubble’s law came from this (old and new)
Really space itself is expanding, prediction of GR
Galaxies don’t really move much
Beginning of universe was dense

Question 4

CMB

Answer 4

All of space has been uniformly filled with matter/radiation
Since early universe there’s been much clumping but it’s still uniform
Beginning of universe was hot

Question 5

What are the possible geometries of space?

Answer 5

Open (saddle)
Closed (sphere)
Flat

Question 6

What geometry are we in?

Answer 6

Flat

Or like a super super flat like patch of smth else

Question 7

Inflation

Answer 7

Extremely extreme physics
The univer goes from less than an atom to like a basket ball in hardly any time at all
Solves problems though

Question 8

What problems does inflation solve

Answer 8

No longer matters what geometry space is
Uniform temp - everything could’ve cooled to equilibrium before inflation
Quantum fluctuations become normal fluctuations become us

Question 9

Why matter over antimatter (???)

Answer 9

Quantum - spontaneous creation (smth from nothing briefly)
Negative gravity energy + positive matter energy = 0?
NEED QUANTUM GRAVITY!

Question 10

Hubble’s law

Answer 10

1) v = Hod
2) d(t) = a(t)do
3) H(t) = v/d
4) a(t) = e^Ht+C
5) e^C = a0 = 1

Question 11

How to find to

Answer 11

To = d/v = d/Hod = 1/Ho

Question 12

Expansion of universe

Answer 12

1) T1 less T0, d1 > d0
2) dE = -PdV
3) P = u/3, u = sigma(T^4)
4) dE = -PdV, d(uV) = -udV/3
5) equate dE = d(uV)
6) product rule
7) V = d^3, get in terms of dV/V
8) u - get in terms of du/u
9) equate them

Question 13

Newtonian Friedman equation

Answer 13

1) E = PE + KE
2) solve for v^2
3) M = density(V)
4) find v^2/r^2
5) v=Hr, r=ar0, H=da/a
6) U = 0, find ro(0)
7) sub back in

Question 14

Cosmic acceleration

Answer 14

1) a = second r derivative (Newtonian)
2) m = Dv
3) v = d/dt(Hr) = d/dt (da/a x ar0)
4) d2r/r = -4piGp/3
5) p = p+3P/c^2

Question 15

Dark energy - P = -density c^2

Answer 15

1) epsilon = roc^2
2) E = epsilonV, E’ = epsilon (V + dV)
3) dE = -W = -PdV
4) dE = E’ - E

Question 16

Dark energy - a(t) = ?

Answer 16

1) P + roc^2 = 0
2) da/a = -4piG/3(Ro + 3P/c^2)
3) matter and dark energy terms, matter is negligible
4) in terms of epsilon
5) plug back in for ro

Question 17

Hubble’s law - 3 scenarios for t0

Answer 17

t0 < 1/H0 - expansion slowing down
t0 = 1/H0 - constant expansion
t0 > 1/H0 - accelerating expansion

Question 18

How was the CMB creates

Answer 18

Early universe was a hot plasma in thermal equilibrium - Compton scattering so it was opaque
As space expanded, KE of particles lowered so can’t ionize H atoms - universe became transparent

Question 19

Newtonian Friedman equation - 3 cases for da

Answer 19

da > 0 - universe expanding
da < 0 - universe contracting
da = 0 - universe is static

Question 20

What does the Friedman equation do?

Answer 20

Relates expansion of universe to matter density and shape of space

Question 21

U < 0

Answer 21

ro > roc
Big Crunch
Closed positive curvature
Sphere

Question 22

U > 0

Answer 22

ro < roc
Matter not dense enough to stop expansion
Big freeze
Infinite, negative curvature, open
Saddle

Question 23

U = 0

Answer 23

ro = roc
Matter dense enough to stop expansion but only when universe is infinite
Infinite, open, zero curvature, like flat plane
Total E = 0 - nothing from nothing

Question 24

What do measurements of matter and measurements of CMB suggest?

Answer 24

Matter - big freeze (even with dark matter)

CMB - flat (smth is stopping expansion)

Question 25

How does energy density of dark energy change with expansion of space?

Answer 25

It’s constant

Question 26

Is negative pressure weird?

Answer 26

No, it’s just matter under tension (stretching a balloon)