More Big Bang
• Big Bang Nucleosynthesis
• Problems with the Big Bang
Big Bang Nucleosynthesis
• Around 10-9 s, quarks froze out into protons and
neutrons, note neutrons are unstable, but lifetime
is long enough, 15 minutes.
• When did nuclei form? Simplest nucleus is
deuterium, D, consists of p+n. Energy to
dissociate D is 2.2 MeV, which is 160,000 that
needed to dissociate H atom, so temperature
should be 1.61053000 K = 5108 K.
• Nuclei started to form when temperature dropped
below 5108 K.
Big Bang Nucleosynthesis
• At this time, there were lots of p+n around, so it
was easy to make nuclei by adding one p or n at
time. For example:
p+n  D+, D+p  3He+, 3He+n  4He+
• No stable nuclei with atomic number 5, this
mostly stops nucleosynthesis at He.
• Can make 4He+D  6Li+  and 4He+3H  7Li+ ,
but only small amounts because there is not much
D or 3H.
Big Bang Nucleosynthesis
• Measurement of ratios H : 4He : 6Li : 7Li in
environments unaffected by any stellar nucleosynthesis
are important tests of the Big Bang theory.
Problems with the Big Bang
• The horizon problem
• The flatness problem
• How to fix the problems: inflation
Cosmic Microwave Background
The Universe glows at 2.7 K in every direction.
The temperature is the same to < 0.1%.
Observable
Universe
We can only see
the parts of the
Universe from
which light has
had time to travel
to us.
The Horizon
Horizon Problem
CMB is 0.98lhorzion away
Two antipodal points of CMB
are 1.96lhorzion away from each
other, but at same temperature
within 10-5.
Flatness Problem
• In matter and radiation dominated eras, any deviation
of  from 1 grows with time.
2
• Friedman equation
κc
2 8πG
H =
2
3c
u−
a 2 r 2c , 0
2
κc
1− Ω(t )= − 2 2 2 ⇒∣1− Ω∣∝a− 2 H − 2
a H r c ,0
• Radiation era: a 
t1/2
and H 
t-1,
• Matter era: a  t2/3 and H  t-1, so
so
∣1− Ω∣∝t ∝a
2 /3
∣1− Ω∣∝t ∝a
2
Scale factor
versus time
• Nuclei form at 3 minutes, radiation era ends at 47 kyr, flatness
grows by 8109.
• Matter dominated from 47 kyr to 9.8 Gyr. Deviation from flatness
grows by (9.8109/47,000)2/3 = 3500.
• Now universe is flat to 0.02, at 3 minutes must have been flat to
0.02/(8109  3500) = 710-16
Flatness problem
Any tiny deviation from the critical density is
amplified over time.
Inflation makes the Universe flat
Inflation is expansion driven by a
cosmological constant
In Λ era: a ∝e
Hi t
where H i =
−2
Flatness: ∣1− Ω∣∝a
H
8π Gu Λ
1/ 2
( )
−2
2
3c
− 2Hi t
∝e
If duration of inflation era is long compared to Hubble
time, 1/H, during inflation, then universe exponentially
expands and is driven exponentially towards flatness.
Inflation
Size
[cm]
Time [seconds]
Whole observable universe came from a tiny region.
Inflation in GUT
• In Grand Unified Theories (GUT) there was an
quantum mechanical field that caused inflation at
10-35 s and lasted for ~100 e-foldings.
• Starting with a strongly curved universe, this
would drive the flatness to e-2100 ~ 10-87.
• If inflation ended at 10-33 s, then size of current
CMB surface was 0.98lhora = 4 m (a = 810-27).
• At start of inflation, now visible universe had a
size of (4 m)e-100 ~ 10-43 m. Horizon distance
was 10-27 m, much larger.
Inflation and cosmology
• Inflation solves flatness problem by driving the
Universe exponentially towards flatness.
• Inflation solves the horizon problem because the
whole universe originally came from a very small area.
Thus, the different parts of the CMB were causally
connected before inflation began.
• Inflation can be tested by looking at the polarization of
the CMB.
Polarization
Electromagnetic radiation consists of propagating
electric and magnetic fields
Polarization of CMB
• Density waves produce E-mode polarization patterns.
• Gravitational waves produce B-mode polarization patterns.
BICEP2
Review questions
• Why is it surprising that the microwave
background has almost exactly the same
temperature in all directions on the sky?
• Why is it surprising that the geometry of the
universe is so close to flat?
• What is the best explanation to date of why
the Universe is uniform and flat?