Cosmology: Lets Take A Step Back Flashcards
Evidence for the Big Bang
Sky is dark at night
CMB
More distant galaxies appear redder
Sky is dark at night
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
More distant galaxies appear redder
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
CMB
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
What are the possible geometries of space?
Open (saddle)
Closed (sphere)
Flat
What geometry are we in?
Flat
Or like a super super flat like patch of smth else
Inflation
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
What problems does inflation solve
No longer matters what geometry space is
Uniform temp - everything could’ve cooled to equilibrium before inflation
Quantum fluctuations become normal fluctuations become us
Why matter over antimatter (???)
Quantum - spontaneous creation (smth from nothing briefly)
Negative gravity energy + positive matter energy = 0?
NEED QUANTUM GRAVITY!
Hubble’s law
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
How to find to
To = d/v = d/Hod = 1/Ho
Expansion of universe
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
Newtonian Friedman equation
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
Cosmic acceleration
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
Dark energy - P = -density c^2
1) epsilon = roc^2
2) E = epsilonV, E’ = epsilon (V + dV)
3) dE = -W = -PdV
4) dE = E’ - E
Dark energy - a(t) = ?
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
Hubble’s law - 3 scenarios for t0
t0 < 1/H0 - expansion slowing down
t0 = 1/H0 - constant expansion
t0 > 1/H0 - accelerating expansion
How was the CMB creates
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
Newtonian Friedman equation - 3 cases for da
da > 0 - universe expanding
da < 0 - universe contracting
da = 0 - universe is static
What does the Friedman equation do?
Relates expansion of universe to matter density and shape of space
U < 0
ro > roc
Big Crunch
Closed positive curvature
Sphere
U > 0
ro < roc Matter not dense enough to stop expansion Big freeze Infinite, negative curvature, open Saddle
U = 0
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
What do measurements of matter and measurements of CMB suggest?
Matter - big freeze (even with dark matter)
CMB - flat (smth is stopping expansion)
