Lecture 24
Early Universe -Testing Models
ASTR 340
Fall 2006
Dennis Papadopoulos
Chapters 12- 13
The Big Bang-Brief Introduction
• What were conditions like in the early
universe?
• What is the history of the universe
according to the Big Bang theory?
BACKGROUND:
THE STRUCTURE OF MATTER
• Atom is made up of…
– Nucleus (very tiny but contains most off
mass)
– Electrons (orbit around the nucleus)
– Atom held together by attraction between
positively-charged nucleus and negativelycharged electrons.
– Binding Energy eV~ 3000-8000 K
• Electron mass .5 MeV ~ 5x109 K
Atomic nuclei
• The nucleus is itself made up of:
– Protons, p (positively charged)
– Neutrons, n (neutral; no charge)
– Collectively, these particles are known as
baryons
– p is slightly less massive than n (0.1%
difference)
– Protons and neutrons bound together by the
strong nuclear force (exchange of “gluons”)
– Binding Energy per nucleon few Mev~1010 K
Elements & isotopes
• Number of protons determines element:
–
–
–
–
–
–
–
Hydrogen – 1 proton
Helium – 2 protons
Lithium – 3 protons
Beryllium – 4 protons
Boron – 5 protons
Carbon – 6 proton
…
• Number of neutrons determines the isotope
• e.g., for hydrogen (1 proton), there are
three isotopes
– Normal Hydrogen (H or p) – no neutrons
– Deuterium (d) – 1 neutron
– Tritium (t) – 2 neutrons
Quarks
• There’s one more level below this,
consisting of quarks…
– Protons & Neutrons are made up of trios of
quarks
– Up quarks & Down quarks
– Proton = 2 up quarks + 1 down quark
– Neutron = 1 up quark + 2 down quarks
– There are other kinds of quarks (strange,
charm, top, bottom quarks) that make up
more exotic types of particles…
Quarks
•
•
•
•
In particle physics, quarks are one of the two basic constituents of matter (the other
Standard Model fermions are the leptons).
Antiparticles of quarks are called antiquarks. Quarks are the only fundamental
particles that interact through all four of the fundamental forces. The word was
borrowed by Murray Gell-Mann from the book Finnegans Wake by James Joyce,
where seabirds give "three quarks", akin to three cheers (probably onomatopoetically
imitating a seabird call, like "quack" for ducks).
The names of quark flavours (up, down, strange, charm, bottom, and top) were also
chosen arbitrarily based on the need to name them something that could be easily
remembered and used.
An important property of quarks is called confinement, which states that individual
quarks are not seen because they are always confined inside subatomic particles
called hadrons (e.g., protons and neutrons); an exception is the top quark, which
decays so quickly that it does not hadronize, and can therefore be observed more
directly via its decay products. Confinement began as an experimental observation,
and is expected to follow from the modern theory of strong interactions, called
quantum chromodynamics (QCD). Although there is no mathematical derivation of
confinement in QCD, it is easy to show using lattice gauge theory.
Nuclear fusion
• Heavier nuclei can be built up from lighter
nuclei (or free n, p) by fusion
• Need conditions of very high temperature and
density to overcome repulsion of protons
• These conditions are present only in cores of
stars and… in the early Universe!
• The original motivation of Gamow, Alpher, &
Herman in advocating big bang was that it
could provide conditions conducive to nuclear
reactions
The early
universe must
have been
extremely hot
and dense
Wien's displacement law
3 minutes
T about 109 K
T  const
~R
T~
1

~
1
R
History of
Universe
according to
BIG BANG
Theory
Planck Era
Before Planck
time (~10-43
sec)
No theory of
quantum
gravity
Photons converted into
particle-antiparticle pairs
and vice-versa
E = mc2
Early universe was full of
particles and radiation
because of its high
temperature
GUT Era
Lasts from
Planck time
(~10-43 sec) to
end of GUT
force (~10-38
sec)
Electroweak
Era
Lasts from end
of GUT force
(~10-38 sec) to
end of
electroweak
force (~10-10
sec)
Particle Era
Amounts of
matter and
antimatter
nearly equal
(Roughly 1
extra proton
for every 109
protonantiproton
pairs!)
Era of Nucleosynthesis
Begins when
matter
annihilates
remaining
antimatter at
~ 0.001 sec
Nuclei begin to
fuse
Era of Nuclei
Helium nuclei
form at age
~ 3 minutes
Universe has
become too
cool to blast
helium apart
Era of Atoms
Atoms form at
age ~ 380,000
years
Background
radiation
released
Era of
Galaxies
Galaxies form
at age ~ 1
billion years
Primary Evidence
1) We have detected the leftover radiation
from the Big Bang.
2) The Big Bang theory correctly predicts the
abundance of helium and other light
elements.
What have we learned?
• What were conditions like in the early
universe?
– The early universe was so hot and so
dense that radiation was constantly
producing particle-antiparticle pairs and
vice versa
• What is the history of the universe
according to the Big Bang theory?
– As the universe cooled, particle
production stopped, leaving matter
instead of antimatter
– Fusion turned remaining neutrons into
helium
Evidence for the Big Bang
• How do we observe the radiation left over
from the Big Bang?
• How do the abundances of elements
support the Big Bang theory?
How do we observe the
radiation left over from the Big
Bang?
The cosmic
microwave
background –
the radiation left
over from the
Big Bang – was
detected by
Penzias &
Wilson in 1965
Background radiation from Big Bang has been freely
streaming across universe since atoms formed at
temperature ~ 3,000 K: visible/IR
Background has perfect
thermal radiation
spectrum at temperature
2.73 K
Expansion of universe has redshifted thermal
radiation from that time to ~1000 times longer
wavelength: microwaves
WMAP gives us detailed baby pictures of structure in
the universe
In early Universe…
• At t=1s, neutrinos began free-streaming
• At t=14s, e stopped being created and destroyed
• Temperature continued to drop until protons and neutrons, if
they combined, were not necessarily broken apart
NUCLEOSYNTHESIS IN THE
EARLY UNIVERSE
• Nucleosynthesis: the production of different
elements via nuclear reactions
• Consider universe at t=180s
– i.e. 3 minutes after big bang
– Universe has cooled down to 1 billion (109) K
– Filled with
•
•
•
•
•
Photons (i.e. parcels of electromagnetic radiation)
Protons (p)
Neutrons (n)
Electrons (e)
[also Neutrinos, but these were freely streaming]

The first three minutes…
• Protons and Neutrons can fuse together to
form deuterium (d)
n  p  D 
• But, deuterium is quite fragile…
• Before t=180s, Universe is hotter than 1
billion degrees.
– High-T means that photons carry a lot of energy
– Deuterium is destroyed by energetic photons as
soon as it forms
D   n  p
After the first 3 minutes…
• But, after t=180s, Universe has cooled to the
point where deuterium can survive
• Deuterium formation is the first step in a
whole sequence of nuclear reactions:
– e.g. Helium-4 (4He) formation:
D D T  p
T  D He  n
4
Protons and neutrons combined to make long-lasting helium
nuclei when universe was ~ 3 minutes old
Big Bang theory prediction: 75% H, 25% He (by mass)
Matches observations of nearly primordial gases

– Further reactions can give Lithium (Li)
4
He  T Li  
7
– Reactions cannot easily proceed beyond
Lithium due to the “stability gap”… more
about that later
• If this were all there was to it, then the final
mixture of hydrogen & helium would be
determined by initial number of p and n.
– If equal number of p and n, everything would basically
turn to 4He… Pairs of protons and pairs of neutrons
would team up into stable Helium nuclei.
– Would have small traces of other species
– But we know that most of the universe is hydrogen…
why are there fewer n than p? What else is going on?
Neutron decay
• Free neutrons (i.e., neutrons that are not
bound to anything else) are unstable!
– Neutrons spontaneously and randomly decay into
protons, emitting electron and neutrino
n  p  e 
– Half life for this occurrence is 15 mins (i.e., take a
bunch of free neutrons… half of them will have
decayed after 15 mins).
• While the nuclear reactions are proceeding,
supply of “free” neutrons is decaying away.
• So, speed at which nuclear reactions occur is
crucial to final mix of elements
• What factors determine the speed of nuclear
reactions?
– Density (affects chance of p/n hitting each other)
– Temperature (affects how hard they hit)
– Expansion rate of early universe (affects how quickly
everything is cooling off and spreading apart).
• Full calculations are complex. Need to:
– Work through all relevant nuclear reactions
– Take account of decreasing density and
decreasing temperature as Universe expands
– Take account of neutron decay
• Feed this into a computer…
– Turns out that relative elemental abundances
depend upon the quantity BH2
– Here, B is the density of the baryons (everything
made of protons+neutrons) relative to the critical
density.
B
B
B 

crit 3H02 /(8G)
• Full calculations are complex. Need to:
– Work through all relevant nuclear reactions
– Take account of decreasing density and
decreasing temperature as Universe expands
– Take account of neutron decay
• Feed this into a computer…
– Turns out that relative elemental abundances
depend upon the quantity BH2
– Here, B is the density of the baryons (everything
made of protons+neutrons) relative to the critical
density.
B
B
B 

crit 3H02 /(8G)
• We can use the spectra of stars and nebulae to
measure abundances of elements
– These need to be corrected for reactions in stars
• By measuring the abundance of H, D, 3He, 4He,
and 7Li, we can
– Test the consistency of the big bang model -- are
relative abundances all consistent?
– Use the results to measure the quantity Bh2
How do the abundances of
elements support the Big Bang
theory?
Dependence of abundances on BH2
B
h2
From M.White’s
webpage, UC
Berkeley
h
H0
100km / s / Mpc
Results
• All things considered, we
have Bh20.019.
• If H0=72km/s/Mpc,
– h=0.72
– B0.04
• This is far below =1!
• Baryons alone would give
open universe
B h2
What have we learned?
• How do we observe the radiation left
over from the Big Bang?
– Radiation left over from the Big Bang is
now in the form of microwaves—the
cosmic microwave background—which
we can observe with a radio telescope.
• How do the abundances of elements
support the Big Bang theory?
– Observations of helium and other light
elements agree with the predictions for
fusion in the Big Bang theory
B  0.037
RECAP
• The density parameter for matter is defined as
matter
matter
M 

crit 3H02 /(8G)
• Value of M very important for determining the
geometry and dynamics (and ultimate fate) of the
Universe
• Constraints from nucleosynthesis
– To get observed mixture of light elements, we need the
baryon density parameter to be B0.037
– If there were only baryonic matter (“normal” stuff made of
protons, neutrons, & electrons) in the Universe, then this
would imply that M0.037.
– In that case, and if  were =0, the Universe would be open
(hyperbolic) and would expand forever
Standard model evolution
diagrams
Preview…
• But life is more complicated than that…
– Much evidence shows that M may be 5 or 10 times larger than
B , yet still M <1
– Additional evidence suggests that nevertheless, the Universe is
flat, with k=0 so k =0 (i.e. neither hyperbolic nor spherical
geometrically)
– This implies the cosmological constant  must be nonzero…and
in fact, there is observational evidence for accelerating
expansion!
• We’ll start with the accounting of all forms of mass in the
Universe…
THE MASS OF STARS IN THE
UNIVERSE
• Stars are the easiest things to see and study in
our Universe…
– Can study nearby stars in detail
– Can see the light from stars using “normal” optical
telescopes in even distant galaxies.
• But…what we see is the light, and what we’re
interested in is the mass…
• Need to convert between the two using the
mass-to-light ratio M/L.
The Sun
• Msun=21030 kg
• Lsun=41026 W
• Actual numbers not
very instructive…
• From now on, we will
reference mass-tolight ratios to the Sun
(Msun/Lsun).
Other stars
• Different types of stars have different
mass-to-light ratios
– Massive stars have small M/L (they shine
brightly compared with their mass).
– Low-mass stars have large M/L (they are
very dim compared with their mass).
– We’re interested in an average M/L
• Averaging regular stars near to the Sun,
we get M/L3 Msun/Lsun
• But, we also need to include effect of “dead”
stellar remnants…
– white dwarfs, neutron stars, black holes.
• …and also sub-stellar mass objects
– Called “brown dwarfs”
– Interior gravity is too low to compress gas and initiate
fusion at very low luminosity
• All of these have mass M, but very little light L.
– They add to the numerator of the average M/L, but not
to the denominator
– Including the remnants and (smaller) brown dwarf
contribution, this would increase the mass-to-light ratio
for spiral galaxies to about
M/L10 Msun/Lsun
• So, can add up the visible star light that we
see in the Universe, and convert to a mass in
stars (luminous and non-luminous).
– We get L0.005-0.01
– Comparing with B=0.037 from nucleosynthesis,
we see that most baryons cannot be in stars…
Where’s the rest of the baryonic
matter if its not in stars?
• Galaxy clusters contain a lot of
hot gas outside of individual
galaxies
– Gas temperature of 10-100
million K.
– Can see it using X-ray
telescopes.
– Such gas contains a lot of the
baryons
• The rest is believed to be in
“warm/hot” (1 million K) gas in
intergalactic space.
X-ray emission from the hot
gas trapped in the Cygnus-A
cluster
Real measurements
In outer parts of galaxies, V and R are based
on measurements of hydrogen gas atoms
orbiting galaxy, rather than stars
Called a dark matter “halo”
• Orbital velocity stays almost constant as far out
as we can track it
– Means that enclosed mass increases linearly with
distance
– Mass continues to increase, even beyond the radius
where the starlight stops
– While there is enough diffuse gas out there to track V,
it adds only a tiny amount of mass
– So, in these outer regions of galaxies, the mass isn’t
luminous…
– This is DARK MATTER.
• How big are galaxy halos?
– We don’t know!
– But they might be huge… maybe 10 times
bigger than luminous part of the galaxy!
• Add up all the galaxy halos… how much
mass would there be?
– Uncertain - we don’t know how far out
galaxy halos go.
– Somewhere in range halos=0.1-0.3
Non-baryonic dark matter
• This is our first evidence for non-baryonic dark
matter…
– B=0.04 (nucleosynthesis)
– halos=0.1-0.3 (galaxy rotation curves)
• So, there is substantially more mass in the
galaxy halos than could possibly be due to
baryons!
• Suggests a non-baryonic form of matter may
exist… something not based on protons and
neutrons.
MASS OF GALAXY CLUSTERS
• Galaxy clusters
– Large groups of galaxies
– Bound together by mutual gravitational
attraction
– Let’s use same arguments for velocities
and radii of galaxies in cluster as for V and
R of stars in galaxies (i.e., based on
Newton’s laws) to measure mass…
M cluster( R)  V R /G
2
gal
The Virgo cluster
Dark matter in clusters
• Find that here is a giant halo of
dark matter enveloping the
galaxy cluster
• Includes the individual halos
“attached” to each galaxy in
cluster
• Also includes dark matter ripped
from individual galaxies’ halos, or
never attached to them
• Add up the mass in these cluster
halos…
• cluster=0.3
• Some of this mass is in hot gas
in the cluster (contributing to
B=0.04 from nucleosynthesis),
but most is non-baryonic dark
matter
Gravitational lensing…
• In some cases, can also measure cluster
mass using gravitational lensing.
• Get good agreement with dynamical
measurements
NON-BARYONIC DARK MATTER:
SUMMARY
• Recap again…
– Nucleosynthesis arguments constrain the density of
baryons (B0.037)
– But there seems to be much more mass in galaxy and
cluster halos (total Matter=0.3)
– So, most of the matter in the Universe is not baryonic!
• what is it????
The cosmic concordance
• What is our universe like?
– Matter content?
– Geometry (flat, spherical, hyperbolic)?
– Anything else strange?
• Remarkable agreement between different
experimental techniques:
“Cosmic concordance” parameters
Measurements of the matter content of
the Universe (recap)
• Primordial nucleosynthesis
– Theory predicts how present light element
abundances (4He, 3He, D, 7Li) depend on mean
baryon density
– Observed abundances  B0.04
• Galaxy/galaxy-cluster dynamics
– Look at motions of stars in galaxies, or galaxies in
galaxy clusters…
– Infer presence of large quantities of “dark matter”
which gravitationally affects observed objects but
cannot be seen with any telescope
• Analysis of galaxy
motions suggests a total
matter density of
Matter0.3
• Same conclusion from
gravitational lensing by
clusters (light from
background objects is
bent due to GR effects)
• First stunning conclusion:
– Compare B0.04 and Matter0.3
– Normal matter only accounts for about 1/8 of
the total matter that’s out there!
– Dark matter provides DM0.26
– We’re made of the minority stuff!
• Can be confirmed by taking
an inventory of a cluster,
where diffuse gas is hot and
emits X-rays…
– Find that about 1/8 of a
cluster’s mass is in baryons
– We believe that clusters
should be representative
samples of the universe…
– Confirms DM0.26
MEASURING THE GEOMETRY OF
THE UNIVERSE
• Recall that universe with different curvature has
different geometric properties
• Adding up the angles in a triangle,
– Flat universe(k=0): angles sum to 180
– Spherical universe (k=+1): angles sum to >180
– Hyperbolic universe (k=-1): angles sum to <180
• Similarly, for a known length L at a given distance D,
the angular size on the sky varies depending on the
curvature of space
– Flat universe (k=0): angular size =L/D
– Spherical universe (k=+1): angular size >L/D
– Hyperbolic universe (k=-1): angular size <L/D
L
L
k=0
k=+1
L
D
k=-1
Angular size of fluctuations in the CBR
• Remember the cosmic microwave
background…
• It has fluctuations, with average separations
corresponding to a known scale L at the
distance where light last interacted with
matter (matter/radiation decoupling)
• Distance D to this “surface of last scattering”
is also known
• Can use apparent angular separations of
fluctuations compared to L/D to infer
geometry of Universe
us
D
L
Flat universe!
• Result:
– The universe is flat
– In terms of omega curvature parameter,
k=0, i.e k=0
– Recall that the sum of all three omega parameters
as measured at present time must be 1:
1 M    k
– How do we reconcile k=0 with our measurement
of the matter density, which indicates M=0.3?
– There must be a nonzero cosmological constant,
=0.7!


0
M  0 
crit (3H0 2 /8G)

 
3H 0 2
kc 2
k   2 2
R0 H 0