The Big Bang
Olbers’s Paradox
If the universe is infinite, then
every line of sight should end
on a star
Why is the sky dark at night?
Finite, and no edge
The Expanding Universe
the galaxies are NOT moving through space.
Space is expanding, carrying the galaxies along!
Things that are smaller than galaxy clusters
are not expanding!
Hubble’s data (1929)
Riess et al (1996)
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George Gamow
Georges LeMaitre
Ralph
Alpher
Predictions of Big Bang Theory
• The Universe is homogeneous and isotropic (very
smooth)
• But not too smooth…
• The ratio of H/He (about 75% H, 25% He)
• Trace abundances of D, 3He, Li, Be
• The cosmic microwave background radiation
The Universe is Homogeneous and Isotropic
Homogeneous: looks the
same at all locations
Not isotropic
Isotropic: looks the same in all
directions
Not homogeneous
On the largest scales, Univese is
homogeneous and isotropic!
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Interactions among elementary particles of the Standard Model
Matter particles
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Carriers of forces
The very early Universe:
< 10-43 seconds after Big Bang singularity: The Planck Epoch
All for fundamental forces unified into one force
realm of GR, string theory, and ???
10-43 to 10-36 seconds: Grand Unification epoch
gravitation separates from unified electroweak and strong force
10-36 to 10-32 seconds (???): Inflationary epoch
universe expands faster than speed of light
large-scale structure is established
10-36 to 10-12 seconds: electroweak epoch
Universe cools off to 1028 K
strong and electroweak forces separate
triggers inflationary epoch (?)
10-12 to 10-6 seconds: quark epoch
quark-gluon plasma
10-6 to 1 second: hadron epoch
quark-gluon plasma cools until hadrons (protons, neutrons) form
T = 1 GeV
hadrons and antihadrons annihilate each other (mostly)
1 to 10 seconds: lepton epoch
leptons and antileptons annihilate each other
T = 1 MeV
10 seconds to 380,000 years: the photon epoch
Photons and electrons exist, continually recombining
Universe still sufficiently hot to ionize H atoms
3-20 minutes: Nucleosynthesis
380,000 years: Recombination
380,000 to 150 million years: Dark ages
150 million years: Reionization
Big Bang Theory
The First Day
Temperature (K)
q
q
3q 2q
p,n,π….
free
¯
qq
↔E
bound
¯
pp
↔E
e+, e−, photons
Photons dominate
e+e− ↔ E
Matter: 109 + 1 (p)
Anti-matter: 109 (p)
¯
pp¯ → 2γ
±
±
(e ,μ ,γ….)
10-6
RADIATION ERA
10-4
p, n : 1
e±, γ : 109
H fusion
n decay
q
108
LEPTON ERA
ν decouple
q
HADRON
proton freeze-out
QUARK
10-8
1010
1012
electron freezout
1014
p, e−
1:1
p, He4 12:1 (3:1)
p, γ
1:109
e+e− → 2γ
p:n → 1:1 7:1
10-2
1
Time (s)
Expansion & Cooling
102
104
1 day
The First Three Minutes: The Nucleus-building Era
At t=3 minutes, T=1 billion K:
Fusion of protons and the remaining free neutrons:
* Formation of 2H (Deuterium) & 4He
* End up with ~92% 1H, 8% 4He
* Also end up with traces of 2H, 3He, Li, Be, B
This is what the oldest stars are
observed to be made of!
Free neutrons decay into protons +
electrons in about 10 minutes => p + e-
379,000 years old: First light escapes; Universe
already has structure (light still arriving today)
Early fluctuations become denser
condensations of matter
First stars form after ~150 million years
(“reionization”)
Galaxies and galaxy clusters form, according to
the floorplan laid out at 379,000 years
The Universe today: lots of stars and galaxies!
Observations of the Universe
• 4He is extremely common: ~25% everywhere
• even oldest stars have ~24% He
• far too much to come from stars alone
 It was made in the Big Bang, before stars
existed!
Expanding, cooling
High temp & density  lower temp & density
Like the core of
a star

Radiated light
like a star
The Universe cooled down to the temperature
at which nuclei exist & nuclear fusion occurs!
Up to 1 second, thermal equilibrium:
After 1 sec, expansion is faster than
reaction: freeze-out of p/n = 6/1
1-600 seconds: n decay:
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At about 100 seconds:
Neutrons are safe in a nucleus:
D formation, p/n = 7/1
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3-20 minutes: nucleosynthesis
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Net result leaves very little D (part in ~105)
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Calculations based on binding energies
10-6 sec < t < 1 sec
Pair-production of   e+ + e-,
high energies (kT) maintain equilibrium:
n + e+  p + ~e
p + e-  n + e
As T drops:
(Average) photon below 2me = 1.02 MeV @ 1.1x1010 K
e+-e- annihilate, too few left to drive n-p conversion
 n,p can’t be maintained in equilibrium for T  1010 K
Using 1010 K as “characteristic” T when equilibrium ends…
Nn / Np = e-1.3 MeV / kT = e-1.5  0.22
So:
Nn = .22/(1 + .22) = 0.18 and Np = 1/(1 + .22) = 0.82
i.e.,
18 n’s for every 82 p’s when p-n ratio “set” (@ t = 1 sec)
1 sec < t < 250 sec
Enough high E photons (E > 2.2 MeV) to disintegrate
deuterons
 baryons only between t  3-20 minutes
4 min < t < 10-20 min
n + p  2H + 
Then:
2H
+ (n,p)  3H,
(“stabilizes” n’s)
3He
 4He
BUT: 4He wont accept more n, p as n , p = 0
Won’t work anyway: No stable nuclei with A = 5
Can we build on 4He nuclei with larger nuclei than n, p?
How about …
+ 4He  6Li + 
6Li + n  7Li + 
2H
and
and
but
7Li
3H
+ 4He  7Li + 
~
+ n  8Li +   8Be + - + 
e
8Be
 2 4He in 10-15 sec!
Or …
3He
+ 4He  7Be + 
but
7Be
+ n  8Be
and then
8Be
 2 4He
or
7Be
+ p  8B +   8Be + + + e
but then
or
but then
4He
8Be
 2 4He
(in 10-15 sec!)
(in 0.5 sec)
(in 10-15 sec!)
+ 4He  8Be + 
8Be
 2 4He (in 10-15 sec!)
BB nucleosynthesis “stops” at 4He
(& tiny amounts of others)
Problems: Must somehow “jump over” A = 5 and 8
(Thank you, stars!)
What is the composition of the universe at t = 20min?
Complication:
free n’s aren’t stable
n  p + - + ~e
with T½ = 10.3 min
As nucleosynthesis didn’t start until 4m, some of the n’s “set”
at t = 1 sec didn’t survive to be fused into 4He
Nn(at 4m) = Nn(at 1s) e- t ln2 / T½ = 18 e- 4(.693)/10.3 = 13.75
Synthesis starts with 13.75 n’s for every 82 + 4.25 = 86.25 p’s
So:
110 n’s & 690 p’s  55 4He’s + 580 p’s
% 4He by mass = (4 x 55)/(4x55 + 1x580) = .275
i.e., the BB made universe 73% H and 27% He (by mass)
379,000 years later…
• Universe cooled enough to have H atoms =
recombination of protons and electrons
• Atoms DO NOT absorb photons: light
escapes!
• Space is expanding: optical wavelength
photons redshifted to microwave
• Predicted by Gamow and Alpher
• Discovered by Penzias and Wilson (1968)
• Nobel went to P & W
Looking Back in Time: the Early Universe
The more distant the objects we
observe, the further back into the
past we are looking.
Prediction: The universe once glowed like a star.
The early glow of the Universe should still be visible!
Big
Bang
dense
hot
expansion
thin
cool
cooling
Ionized,
foggy
Now
atomic
transparent
hot glowing fog
Photons keep getting absorbed
we see a glowing
wall of bright fog
us
orange
light
redshift
z = 1000
microwaves
The Cosmic Background Radiation
The radiation from the very
early phase of the universe is
still detectable today
R. Wilson & A. Penzias
discovered in mid-1960s
Blackbody radiation with a temperature of T = 2.73 K
The Cosmic Background Radiation (2)
After recombination, photons can
travel freely through space.
Their wavelength is only stretched
(red shifted) by cosmic expansion.
Recombination:
z = 1000; T = 3000 K
This is what we can observe today as the cosmic
background radiation!
Extremely uniform!!!
Sloan Digital Sky Survey: Univese is clumpy!
Our galaxy is here
1990: Anisotropy discovered
1990
2003
The Universe’s Baby Picture: WMAP
(Wilkinson Microwave Anisotropy Probe)
Photons that were emitted when Universe was 379,000 years old.
Fluctuations in the temperature (= structure) of the
Universe appeared when it was very young
Sound waves :
red/blue = high/low
gas & light pressure
Many waves of
different sizes,
Directions & phases,
all “superposed”
Water waves :
high/low level of
water surface
Temperature and density
fluctuations are minimal:
BUT IMPORTANT!
Very uniform and smooth: no stars or galaxies yet! (379,000 years)
Smooth to 1/100,000
Patchiness due to not perfectly smooth distribution of matter (“sound waves”)
Light
can
escape!
P+e=atoms
Universe cools down as time passes
The History of the Universe
Universe expands as time passes
transparent
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Universe is ionized
(still today) but
transparent because it
is very diffuse
Reionization
After less than ~ 1 billion years, the first
stars form.
Ultraviolet radiation from the first stars reionizes gas in the early universe
Formation of the
first stars
Reionization
Lyman-alpha and cosmology
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Quasars all have similar power spectra
HI cloud near quasar - safely
assume that the light being
absorbed is 1216A
Many clouds between us and
the quasar leads to a “forest” of
Ly-alpha lines
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Lyman-alpha Forest
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But what if there is so much HI that it blocks it completely?
Extremely dense HI is only present in very early universe.
This can only happen at very high redshift!
Gunn-Peterson Trough
• One of the few examples of a real
prediction in astrophysics!! (1965,2001)
• Many clouds of HI between us and quasar
at z = 6 or so
• Ly-alpha absorption causes a “forest” of
lines
• “trough” predicted for when H is very
dense (at very high redshift)
Gunn-Peterson Trough
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The discovery of the
trough in a z = 6.28
quasar, and the
absence of the trough in
quasars detected at
redshifts just below z =
6 presented strong
evidence for the
hydrogen in the
universe having
undergone a transition
from neutral to ionized
around z = 6.
From SDSS: Quasar spectra. Note the height of the spectral lines on the left side
of the spectrum. The bottom image shows the first Gunn-Peterson trough ever
discovered.
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Further away
Why is this cool?
• How much HI is out there, and how is it
distributed?
• Ly-alpha regions trace out dark matter,
because the H atoms are concentrated by
DM’s gravity
The Cosmological Principle
1) Homogeneous: On the largest scales, the universe should
have the same physical properties throughout
Every region has the same density,
expansion rate, luminous vs. dark matter
2) Isotropic: On the largest scales, the universe looks the same in
any direction that one observes.
You should see the same largescale structure in any direction.
3) Universality: The laws of physics are the same everywhere
in the universe.