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Lecture 25: The Big Bang
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Penzias & Wilson
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describe brightness distribution on sphere
superpositions of terms
what scales have power?
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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!)
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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)
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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!)
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Cosmographydifferent “distances”
comoving distance (proper distance today)
angular diameter distance
luminosity distance
proper motion distance
light travel distance (lookback time)
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Inflation
flatness problem
horizon problem
magnetic monopole problem
early, tremendous growth phase solves these problems...and generates fluctuations that can grow
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Perturbation Theory
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