Lecture 25: The Big Bang

Penzias & Wilson

describe brightness distribution on sphere

superpositions of terms

what scales have power?

Measuring Spacetime

define a metric

for a plane

Robertson-Walker metric

homogeneous-isotropic flat universe

scale factor a(t), cosmic time t (time measured by observer in uniformly expanding universe)

are co-moving coordinates (remain constant in t)

d�2 = dx2 + dy2 + dz2

d�2 = −c2dt2 + a(t)2[dr2 + r2(dθ2 + sin2θdφ2)]

(r, θ,φ)

proper distance (can’t measure this!)

Friedmann Equation�a

a

�2

=8πG

3c2u(t)− κc2

r2c,0a(t)2+

Λ

3

from energy conservation for expanding sphere, but relativistically correct

relativistic particles like photons contribute energy density too

kappa tells us if universe positively or negatively curved

cosmological constant is new energy density term arising from vacuum energy (virtual particles, anti-particles)

often rewritten....

u_r = radiation density (energy density from relativistic particles like photons), u_m = matter density (energy density from non-relativistic particles such as protons, neutrons, electrons, WIMPs? ), u_Lambda = constant energy density from vacuum

for flat universe, kappa = 0, so

�a

a

�2

=8πG

3c2[ur(t) + um(t) + uΛ]−

κc2

r2c,0a(t)2

3H(t)2c2

8πG= ur(t) + um(t) + uΛ (at t_0, H_0, and we know this!)

Cosmographydifferent “distances”

comoving distance (proper distance today)

angular diameter distance

luminosity distance

proper motion distance

light travel distance (lookback time)

Inflation

flatness problem

horizon problem

magnetic monopole problem

early, tremendous growth phase solves these problems...and generates fluctuations that can grow

Perturbation Theory