The Big Bang
 Lemaitre was the first to point out that if
the Universe is expanding, it must have
been much hotter and denser in the past
 This was first called the big bang by
steady-state cosmologist Fred Hoyle as a
term of ridicule
 Now all cosmological models with an
evolving Universe are called “big bang
cosmologies”
Three fundamental questions in cosmology are:
• Can we explain the observed structures in the universe in
a self-consistent cosmological model?
• Can we explain the observed cosmic background
radiation?
• Can we explain the abundances of light elements within
the same model?
Yes, for a hot big bang model (adiabatically expanding,
monotonically cooling undergoing a series of phase
transitions with structure defined by RW metric and
Friedmann equations).
Timeline for the evolution of the Universe
(109 K)
• Direct observations limited to t > 372 kyrs (recombination or decoupling)
• Nucleosynthesis constraints extend to timescales of ~1 s
• Contains several categories of events (force unification, evolution of
particle species, radiation-matter equality, formation and evolution of large
scale structure)
Temperature Evolution
Before exploring the thermal history of the universe in the big bang model, we
first need to know how the temperature scales with redshift (or scale factor).
Consider matter and radiation temperatures when the two are thermally
decoupled and evolving independently. Also, assume both are approximated by
adiabatically expanding ideal fluid in local thermodynamic equilibrium.
Non-relativistic matter
E
Relativistic matter and Radiation
photon density decreases with a3
but photons loose energy due to
cosmological redshifting (extra
factor of 1+z), so
Before recombination, both go as T = To(1+z)
Radiation-Matter Equality and
a Matter Dominated Universe
Similarly, the thermal history of the Universe
reveals a change from radiation to matter
dominated.
Energy density (matter) ~ ρmc2
ρm ~ 1/a3
9400 K
# density (photons) ~ 1/a3
But, the redshifting means that energy per
photon ~ 1/a. Thus, energy density (radiation)
~ 1/a4
Energy density of radiation drops more
quickly than matter as scale factor
increases.
The time when radiation
and matter contributed
equally in the Universe
occurred at:
zeq = 3454 (~50,000 yrs
after BB) when temp was
about 9400 K
Consensus (or Concordance) Model
Friedmann equation (now including
radiation density term and assuming
flat curvature)
Since the three components have different
dependences on scale factor, there are
long stretches of history when one
component dominates. First radiation,
then matter, then Λ…
•matter and radiation energy densities
equal  arm = 0.00029 (z=3454)
•Λ and matter energy densities equal 
amΛ = 0.75 (z=0.33)
Photon - Baryon Number Density Ratio
Present number density of baryons is
Photon’s obey Bose-Einstein statistics and integrating over the applicable
distribution function give their number density:
mostly CMB (only 10% from starlight)
(see discussion on page 57 - 59 in Cosmology Notes for derivation)
The photon-baryon ratio (using
noϒ
nob
= 0.022 (Planck CMB values))
= 1.7 x 109
 There are far more photons than baryons in the present Universe
Recombination
Epoch when charged electrons and protons first became bound to form neutral
hydrogen atoms - a snapshot of the universe when temp was around 3000K
At recombination, the mean free
path of a photon rapidly goes from
being very short to essentially
infinite as the probability for
scattering off an electron becomes
negligible. Thus, this epoch is
often called the surface of last
scattering or the time of
decoupling – when radiation and
matter became decoupled.
Cosmic Microwave Background: Gamow, Alpher and Herman(1948)
suggested that the Universe should have been filled with radiation shortly after
the Big Bang. A remnant of this radiation should still be detectable today as low
intensity background microwaves.
•About one second after the Big Bang,
the Universe had temperatures of a
few MeV – emitting gamma-rays
•This radiation would redshift due to
the expansion of the Universe so that
the peak today is at microwave
wavelengths with T = 2.7 K.
Free-free emission, Compton
scattering and other processes
occur frequently enough for
photons to have Planck distribution
Radiation density
decreases as (1+z)4
The initial black body spectrum retains its
shape as the temperature cools.
Observations of the CMB
• First observed (inadvertently) in 1965 by
Arno Penzias and Robert Wilson at the Bell
Telephone Laboratories in Murray Hill, NJ.
• Detected excess noise in a radio receiver
peak emission at BB temp = 3 degrees
• In parallel, researchers at Princeton were
preparing an experiment to find the CMB.
• When they heard about the Bell Labs result
they immediately realized that the CMB had
been detected.
•The result was a pair of papers in the Physical Review: one by Penzias and Wilson
detailing the observations, and one by Dicke, Peebles, Roll, and Wilkinson giving the
cosmological interpretation.
•Penzias and Wilson shared the 1978 Nobel prize in physics.
•Almost immediately after its detection, the Steady State theory was dead.
Observations of the CMB
CMB formed when Universe was ~370,000 yrs old
at a temperature of ~3000 degrees K
Cosmic Background Explorer Satellite (COBE)
launched in 1989 and revealed precise spectrum of
CMB – best fit BB peaks at 2.725K. At what z would
CMB have formed then?
CMB should be generally isotropic but high
sensitivity observations with COBE revealed small
anisotropies
Major source of anisotropy is Earth’s (Sun, galaxy,
cluster) motion wrt Hubble flow – Dipole Anisotropy
Galactic Plane
All sky plot of CMB radiation with bright regions (yellow)
being hotter and dark regions being cooler than Tavg
Measurements of CMB have become more precise over time
Small scale fluctuations in
the CMB map are ~10-5 the
strength of the radiation
itself.
Fluctuations reveal:
•geometry of universe – indicates flatness
•seeds of various scales of structure that we see
•measure of several cosmological parameters
Power spectrum reveals relative intensities of
fluctuations on different angular scales
The dominant angular scale fluctuation is the angle
subtended by the sonic horizon at CMB. In a flat universe,
where light will move in a straight line, this scale is roughly
one degree. The relative amplitude of the second peak
constrains the baryon density, while the third peak can be
used to measure the total matter density. Meanwhile, the
damping tail provides a cross-check on the above
measurements.
Open Universe: photons move on
diverging paths in a negatively curved
space. Our ruler would appear to
have a smaller angular size - location
of the first peak would appear at
smaller angular scales (grey line)
Closed Universe: Angle would appear
larger (first peak shifted to the left)
Flat Universe: A flat universe –
undistorted (red line)
http://map.gsfc.nasa.gov/mission/sgoals_parameters_geom.html for movie!
CMB Isotropy and Causality (the horizon problem)
Is the background radiation too isotropic?
Conditions should only be identical at different locations if they have
some way of communicating with each other. Two objects separated
by a distance greater than that which light can traverse cannot affect
each other – Causality problem
θo = (1/a)*(t/to) is the maximum current
separation between 2 points that could
have been causally connected before
decoupling.
What is the maximum angular separation for
causality if the Universe is 13.7 Gyr old and
was 372,000 years old at decoupling?
(recall relationship between scale factor and
temperature for radiation)
Big Bang Nucleosynthesis
In the first three minutes, the
Universe was hot enough for
nuclear reactions to take place.
Protons and neutrons formed 2H
(deuterium), 3He and 4He.
4He
is most stable and, within 3
minutes, made up 25% of the
Universe.
What determined the abundance of 4He?  need to know Universal conditions
(density, relative number of neutrons and protons) at T=109 K (about t ~ 200s).
In a hot universe, equilibrium between protons and neutrons maintained by
weak interactions:
Decay of free neutron
(half-life 10.6 min)
Ratio of neutrons to protons is set
when T < 1010K (less than 1s after BB
when neutrinos decouple). Protons
favored over neutrons because they
are slightly lighter. Weak interactions
stop and nn/np fixed at about 1/7.
Because 2H is so reactive, most
neutrons in 2H will end up in 4He
Mass fraction in 4He is
Y = 2nn/(np+nn) = 2(nn/np)(1+nn/np)-1
Proton to neutron ratio set at 1/7
which yields Y ~ 0.25.
Actual value lower because D forming
reaction is suppressed by the high
photon to baryon ratio.
In these terms, mass fraction of 4He is
NL is number of light particles, like
neutrinos. Best model fit for a relativistic
gas (dominated by neutrino motions) is
3.
Final mixture of elements from BB depends
on density at t = 1s when reactions started
•4He is stable and depends more on
the p/n ratio than the baryon density
•Deuterium drops sharply with
density because greater density
yields more particles to react with
•3He has slightly less density
dependence
Best density
estimate from
abundance data
•7Li is heavier – higher density 
more reactions for building heavier
elements. Low density  more
abundant as well because it relies
on reactions involving D and there is
more of that at the lowest densities.
•C, N and O increase for ρ > ρcrit
(but still well below current observed
values – most produced via stars )
Density of baryons
Ratio of D/H constrains the density of baryons in the Universe.
D created in BBN but destroyed during stellar.
From abundance data, best estimate of baryonic density ~5% of ρcrit.
Unification of Forces – are all forces a manifestation of one larger force?
Maxwell unified
electricity and
magnetic forces
Energies must
be even greater
to unite the
electroweak and
strong forces
Nobel prize in
physics in 1979
Predictions of
GUTs:
Decay of proton
and magnetic
monopole (not
observed yet)
For the electroweak force to exist, the photon (massless) and W (or Z) particle
(massive) must be indistinguishable. This can only happen when particle energy
is greater than the difference in mass (nature is symmetric as long as there is
enough energy). This occurred briefly in the early Universe....
Re-examining the Universe timeline…
•Begin at Planck Time (light travel time across a Planck length where Rs is
equivalent to particle wavelength), GR breaks down – cannot probe history further
•High temps allow for GUT. Particles, anti-particles and photons are created and
annihilated. Baryon number was not conserved.
•Symmetry breaking as the Universe cools produces slight excess of matter over
antimatter - one excess particle for every 1010 particle-antiparticle pairs produced
(explains ~1010 photons for every baryon in the Universe).
•Universe cools (at 10-36 s after BB) to temp where color (strong) and electroweak
forces separate (end of GUT). Baryon number now conserved.
Inflation
During time of GUTs, the vacuum of the Universe was not really a vacuum
It is theorized that the nature of vacuum changed during this time (like a
phase transition from liquid to gas state of water)
Resulted in extremely rapid expansion of vacuum. Scale factor underwent
exponential growth (1026 growth in 10-32 s)
Solves flatness problem - inflation drives the
universe towards critical density - stretches
any initial curvature of the universe to near
flatness.
Solves causality/horizon problem – everything
within horizon was closer together in the past
and in causal contact.
Re-examining the Universe timeline…
•By 10-12 s, Universe cools to temp allowing for separation of EM and weak forces
(average energy is comparable to mass of W particle ~ 100 GeV).
•Hot Universe allows quarks to move as in a fluid until 10-5 s. Then quarks are
confined to hadrons.
•Lepton Era – when Universe is dominated by leptons (electrons, neutrinos)
•Weak force continues to weaken w.r.t. EM force. At 1s it is weak enough that
neutrinos are rarely absorbed by matter (matter-neutrino decoupling – sets
proton/neutron ratio). This occurs during BB nucleosynthesis.
Why do we believe the Big Bang model?
1. provides a natural explanation for the observed expansion of the universe
2. explains the observed abundance of helium via cosmological production of
light elements. Indeed, the high helium abundance cannot be explained via
stellar nucleosynthesis, but explained well if one assumes that it was produced
at early times when the universe was hot enough for fusion.
3. explains the cosmic microwave background. The CMB is a natural
consequence of the cooling expansion.
4. provides a framework for understanding structure formation. Initial
fluctuations (from whatever origin) remain small until recombination, after which
they grow via gravity to produce stars, galaxies, and other observed structure.
Numerical simulations show that this works remarkably well given (a) a
prescription for the power spectrum of the initial fluctuations, and (b) inclusion
of non-baryonic dark matter.
End..
Sunyaev-Zeldovich Effect
Another source of small scale anisotropy in
the CMB that is not cosmological
- Compton scattering - gamma-ray strikes
a low energy electron and becomes a
lower frequency photon with excess
energy going to the electron.
- Inverse Compton scattering - low energy
photon scatters off a high energy
electron, with the photon gaining energy
and the electron losing it.
- SZ effect occurs when low energy CMB
photons strike the hot gas within a
cluster of galaxies and inverse Compton
scattering takes some of the photons
from the low energy side of the CMB
blackbody and transfers them to the high
energy side.
Fundamental
Particles and
Forces Primer
Leptons – do not interact by strong force – no internal structure
Hadrons – strongly interacting – made of quarks
Baryons – massive (n and p); composite fermions; made of 3 quarks
Mesons – less massive; composite bosons; made of 2 quarks (don’t obey PE)
Other CMB results
•dark matter and atoms become less dense as
the universe expands
• photon and neutrino particles lose energy as
the universe expands, so their energy density
decreases faster than the matter.
• dark energy density does not appear to
decrease
• it now dominates the universe even though it
was a tiny contributor 13.7 billion years ago
•4 fundamental forces in nature by which particles interact
•Short range forces felt on scales of nuclei
•Long range forces fall as 1/r2
•Particles (bosons) carry the forces
•QED theory - photons carry EM force (can be real or virtual photons)
•Massless graviton thought to carry gravity (so far undetected)
•Strong force (color force; QCD) carried by pion (gluons) and its mass is
determined by the force range
•Weak force carried by massive W and Z particles (80 and 90 x proton mass))