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The Big Bang
Necessary?
– Expansion of the Universe
– Origin of CMBR
• 400 photons/cc
• Black body temperature profile
– Helium content
• Universal nucleosynthesis (like a star)
Basics
– Universe was hotter, denser in the past
A few assumptions
– Universe is a closed system
• Physically
• Heating/cooling – adiabatic
– Treat like an adiabatic fluid (easy!)
Energy of the Universe
E=kT
Second law of Thermodynamics
DE=p DV
Change in energy depends on change in
volume
Pressure defined
p = 1/3 e
e=energy density – all radiation early on
Energy of light
ef=hf
So energy density = ef/volume
hf
hc
e

V V
D E  e DV
eDV  1 / length
So the energy of the Universe goes down as the size
goes up
Since E=kT, the temperature goes down as it expands
Energy = all energy
Photons, mass (via E=mc2), velocity, gravity, etc…
Zero-th Step
Time <0
Anything before the BB?
How could we tell?
Where could we look?
Time=0
What’s it like?
Don’t know…
Gravity + QED = Quantum Gravity = ?
Haven’t figured it out yet
Time=10-43 sec
Time=Planck time
Based on quantum physics principles
Temperature = 1032 K
Density = 1093 gm/cc
Scale = very small
Interactions between energy/matter
Quantum physics (QED), gravity – separate
Can use them to describe characteristics of the
Universe
How?
Some boring math…
hG
 43

10
s
5
2c
h
DE D t 
2
h
2
mc Dt 
2
h
5
mp 

2
.
5

10
gm
2
2c t p
tp 
l p  ct p  1.7  1033 cm
Planck lengths, time, masses…
Okay what does that mean?
Have to define some more stuff….
Compton time – time for a
mass to violate
conservation of energy law
This activity is known as
“quantum fluctuations”
Formation of particles
(matter/anti-matter) out of
energy, quick destruction
Happens over a quantum
length (Compton length)
h
tc 
2
2mc
lc  ctc
Schwarzschild Radius –
“size” of a black hole
Schwarzschild Time – time
for a photon to travel
across a black hole
This defines the realm of
“gravity”
2Gm
ls  2
c
ls
ts 
c
2 types of ways to describe the Universe
– Planck length, time = QED
– Compton length, time = QED
– Schwarzschild length, time = gravity
The way these are related defines who is in charge – gravity or
QED
Funny feature: a Planck mass into the formula for Compton,
Schwarzschild lengths = Planck length
Also, all times are equal.
Meaning?
Planck mass = black hole that exists for Planck time!
If mass>Planck mass
Enter the realm of gravity (relativity),
QED not important
If mass<Planck mass
QED important, gravity loses.
This time, this mass, this realm is when
there are two separate forces – gravity,
GUT
GUT = grand unified theory (QED laws)
So what is REALLY happening?
Mini-black holes can come into/out of
existence
Gravity brings them into being
Hawking radiation destroys them
Particles (non-black holes) come into/out of
existence (Compton stuff)
Have energy, some particles, strange
things going on – still not easy to define
(or understand).
Time=10-35 sec
During GUT – quarks, leptons identical
Now the GUT breaks down into
Strong nuclear force (quarks force)
Electoweak force (lepton/photon force)
Breaks “symmetry” of the Universe
“Freezing out” of forces – loss of freedom
Release of energy (vacuum energy)
Inflation starts
Quarks form (along with anti-quarks)
Time=10-32 sec
End of Inflation
After inflation, size of Universe increased by
factor of 1050
Really?
Expains uniformity of Universe
Flatness of Universe
Time=10-12 sec
Another symmetry breaking
Electroweak force breaks down into
electromagnetic force
weak nuclear force
Leptons/anti-leptons form
Universe full of energy (photons), quarks,
leptons
Time=10-10 sec
Quarks win over anti-quarks
Another symmetry breaking!
Protons/neutrons can form
Interactions between all sorts
of things
Not what happens today
Neutrinos forced into
interactions
e  p  e  n

e  p  e  n

Time=10-5 sec
End of neutrino interactions
Universe too cool (10 billion K)
Neutrinos still out there!
Where are they?
Time=1-3 Minutes
Nucleosynthesis
Universe Temperature = Stellar interior
Protons, Neutrons combine to make
– H2, H3 (Deuterium, Tritium)
– He3, He4
– Li6, Li7, Be7
End composition: 75% p+ (H), 25% He4
(~0.01% - the rest)
Gravity starts to become noticeable
Time = 1 year
Energy and Matter starting to diverge
Cooling down at their own rates
Energy (photons) – cooled by the expansion
Matter – temperature determined by
photons, fewer interactions
Time=380,000 years
Era of Decoupling
Energy + Matter intertwined before now
After this, they go their separate ways
Energy of photons too low to interact
effectively
Universe becomes “transparent” to radiation
Matter (gravity) controls Universe
Time <1 billion years
Galaxy Formation/Cluster formation?
Proto-galaxy formation?
Something is starting to happen….
This would be the epoch of the largest
observable redshifts
Might have missed a previous step (or two)
Time = Now
You’re looking at this.
End of story (for now)