Review for Test #4 on December 15
Topics:
• Gamma Ray Bursts (GRB) and Black Holes
• Our Milky Way Galaxy
• Galaxies
• Clusters of Galaxies and Large Scale Structure of the Universe
• Cosmology, a past and future history of the Universe
Methods
• Conceptual Review and Practice Problems Chapters 9 - 13
• Review lectures (on-line) and know answers to clicker questions
• Try practice quizzes on-line
• Review (time Sunday, Nov 15 starting at 3pm) mainly Q&A format
Bring:
• Two Number 2 pencils
• Simple calculator (no electronic notes)
• UNM Student ID
Test #3 Review
How to take a multiple choice test
1) Before the Test:
• Study hard (~2 hours/day Friday through Tuesday)
• Get plenty of rest the night before
• Bring at least 2 pencils, UNM student ID, and a calculator
2) During the Test:
• Write out and bubble your last name, space, first name and Exam
color in the name space of the scantron form. Write out and
bubble your Banner ID in the ID space.
• Draw simple sketches to help visualize problems
• Solve numerical problems in the margin
• Come up with your answer first, then look for it in the choices
• If you can’t find the answer, try process of elimination
• If you don’t know the answer, Go on to the next problem and
come back to this one later
• TAKE YOUR TIME, don’t hurry
• If you don’t understand something, ask me.
Test #4 Possibly Useful Equations
Schwarschild Radius:
2 GM
R=
c2
Lifetimes of stars (on the main sequence):
L = 1010/M2 years where M is the Mass in solar masses
and L is the Lifetime
Equivalence of Matter and Energy:
E = mc2
Gamma-Ray Bursts
Gamma-ray bursts also occur, and were first
spotted by satellites looking for violations of
nuclear test-ban treaties. This map of where the
bursts have been observed shows no “clumping”
of bursts anywhere, particularly not within the
Milky Way. Therefore, the bursts must originate
from outside our Galaxy.
Gamma-Ray Bursts
Distance measurements of some gamma bursts show
them to be very far away – 2 billion parsecs for the first
one measured.
Occasionally the spectrum of a burst can be measured,
allowing distance determination.
Gamma-Ray Bursts
Two models – merging neutron stars or a
hypernova – have been proposed as the
source of gamma-ray bursts.
Black Holes and General Relativity
General Relativity: Einstein's (1915) description of
gravity (extension of Newton's). It begins with:
The Equivalence Principle
Here’s a series of thought experiments and arguments:
1) Imagine you are far from any source of gravity, in free space,
weightless. If you shine a light or throw a ball, it will move in a
straight line.
2. If you are in freefall, you are also
weightless. Einstein says these are
equivalent. So in freefall, light and ball
also travel in straight lines.
3. Now imagine two people in freefall on
Earth, passing a ball back and forth.
From their perspective, they pass it in a
straight line. From a stationary
perspective, it follows a curved path. So
will a flashlight beam, but curvature of
light path small because light is fast (but
not infinitely so).
The different perspectives are called
frames of reference.
4. Gravity and acceleration are equivalent. An apple falling in
Earth's gravity is the same as one falling in an elevator accelerating
upwards, in free space.
5. All effects you would observe by being in an accelerated frame
of reference you would also observe when under the influence of
gravity.
Examples:
1) Bending of light. If light travels in straight lines in free space, then
gravity causes light to follow curved paths.
Observed! In 1919 eclipse.
Gravitational lensing. The gravity of a foreground cluster of
galaxies distorts the images of background galaxies into arc shapes.
2. Gravitational Redshift
later, speed > 0
light received when
elevator receding at
some speed.
Consider accelerating elevator in
free space (no gravity).
time zero, speed=0
light emitted when
elevator at rest.
Received light has longer wavelength (or shorter frequency) because
of Doppler Shift ("redshift"). Gravity must have same effect! Verified
in Pound-Rebka experiment.
3. Gravitational Time Dilation
A photon moving upwards in gravity is redshifted.
Since
 1
T
the photon's period gets longer. Observer 1
will measure a longer period than Observer 2.
So they disagree on time intervals. Observer 1
would say that Observer 2's clock runs slow!
All these effects are unnoticeable in our daily experience!
They are tiny in Earth’s gravity, but large in a black hole’s.
1
2
Escape Velocity
Velocity needed to escape the gravitational pull of an object.
vesc =
2GM
R
Escape velocity from Earth's surface is 11 km/sec.
If Earth were crushed down to 1 cm size, escape velocity
would be speed of light. Then nothing, including light, could
escape Earth.
This special radius, for a particular object, is called the
Schwarzschild Radius, RS.
RS  M.
Black Holes
If core with about 3 MSun or more collapses, not even neutron
pressure can stop it (total mass of star about 25 MSun ?).
Core collapses to a point, a "singularity".
Gravity is so strong that nothing can escape, not even light => black hole.
Schwarzschild radius for Earth is 1 cm. For a 3 MSun object, it’s 9 km.
Event horizon: imaginary sphere around object with radius equal to
Schwarzschild radius.
Event horizon
Schwarzschild Radius
Anything crossing over to inside the event horizon, including light,
is trapped. We can know nothing more about it after it does so.
Black hole achieves this by severely curving space. According to Einstein's
General Relativity, all masses curve space. Gravity and space curvature are
equivalent.
Like a rubber sheet, but in three dimensions, curvature dictates how all
objects, including light, move when close to a mass.
Curvature at event horizon is so great that space "folds in on itself", i.e. anything
crossing it is trapped.
Space Travel Near Black Holes
Matter encountering a black hole will experience
enormous tidal
forces that will
both heat it
enough to radiate,
and tear it apart.
Space Travel Near Black Holes
A probe nearing the event horizon of a black hole
will be seen by observers as experiencing a
dramatic redshift as it gets closer, so that time
appears to be going more and more slowly as it
approaches the event horizon.
This is called a gravitational redshift – it is not
due to motion, but to the large gravitational
fields present.
The probe itself, however, does not experience
any such shifts; time would appear normal to
anyone inside.
What’s inside a black hole?
No one knows, of course; present theory
predicts that the mass collapses until its radius
is zero and its density infinite; this is unlikely to
be what actually happens.
Until we learn more about what happens in such
extreme conditions, the interiors of black holes
will remain a mystery.
Effects around Black Holes
1) Enormous tidal forces.
2) Gravitational redshift. Example, blue
light emitted just outside event horizon
may appear red to distant observer.
3) Time dilation. Clock just outside
event horizon appears to run slow to a
distant observer. At event horizon, clock
appears to stop.
Do Black Holes Exist?
Observational Evidence for Black Holes
The existence of black
hole binary partners
for ordinary stars can
be inferred by the
effect the holes have
on the star’s orbit, or
by radiation from
infalling matter.
Do Black Holes Really Exist?
Good Candidate: Cygnus X-1
- Binary system: 30 MSun star with unseen companion.
- Binary orbit => companion > 7 MSun.
- X-rays => million degree gas falling into black hole.
Final States of a Star
1. White Dwarf (WD)
If initial star mass < 8 MSun or so
(Max WD mass is 1.4 MSun ,
radius is about that of the Earth)
No Explosive Event +
Planetary Nebula
(Possible Nova from
Carbon Flash)
2. Neutron Star (NS)
8 MSun < initial star mass < 25 Msun
(1.4 MSun < NS mass < 3? Msun
radius is ~ 10 km - city sized)
Supernova + ejecta
3. Black Hole (BH)
If initial mass > 25 MSun
(For BH with mass = 3 Msun
radius ~ 9 km)
GRB + Hypernova +
ejecta
Take a Giant Step Outside the Milky Way
Artist's Conception
Example
(not to
scale)
Perseus arm
from above ("face-on")
see disk and bulge
Orion arm
Sun
Cygnus arm
Carina arm
from the side
("edge-on")
The Three Main Structural Components of the Milky Way
1. Disk
- 30,000 pc diameter (or 30 kpc)
- contains young and old stars, gas, dust. Has spiral structure
- vertical thickness roughly 100 pc - 2 kpc (depending on component.
Most gas and dust in thinner layer, most stars in thicker layer)
2. Halo
- at least 30 kpc across
- contains globular clusters, old stars, little gas and dust,
much "dark matter"
- roughly spherical
3. Bulge
- About 4 kpc across
- old stars, some gas, dust
- central black hole of 3 x 106 solar masses
- spherical
Shapley (1917) found that Sun was not at center of Milky Way
Shapley used distances to variable “RR Lyrae” stars (a kind of Horizontal
Branch star) in Globular Clusters to determine that Sun was 16 kpc from
center of Milky Way. Modern value 8 kpc.
Stellar Orbits
Halo: stars and globular clusters swarm around center of Milky Way. Very
elliptical orbits with random orientations. They also cross the disk.
Bulge: similar to halo.
Disk: rotates.
Rotation of the Disk
Sun moves at 225 km/sec around center. An orbit takes 240 million years.
Stars closer to center take less time to orbit. Stars further from center take
longer.
=> rotation not rigid like a phonograph record or a merry-go-round. Rather,
"differential rotation".
Over most of disk, rotation velocity is roughly constant.
The "rotation
curve" of the
Milky Way
Spiral Structure of Disk
Spiral arms best traced by:
Young stars and clusters
Emission Nebulae
HI
Molecular Clouds
(old stars to a lesser extent)
Disk not empty between arms,
just less material there.
Problem: How do spiral arms survive?
Given differential rotation, arms should be stretched and smeared out after
a few revolutions (Sun has made 20 already):
The Winding Dilemma
The spiral should end up like this:
Real structure of Milky
Way (and other spiral
galaxies) is more loosely
wrapped.
Proposed solution:
Arms are not material moving together, but mark peak of a
compressional wave circling the disk:
A Spiral Density Wave
Traffic-jam analogy:
Traffic jam on a loop caused by merging
Now replace cars by stars
and gas clouds. The traffic
jams are actually due to the
stars' collective gravity.
The higher gravity of the
jams keeps stars in them
for longer. Calculations
and computer simulations
show this situation can be
maintained for a long time.
Molecular gas clouds pushed together in arms too => high density of
clouds => high concentration of dust => dust lanes.
Also, squeezing of clouds initiates collapse within them => star formation.
Bright young massive stars live and die in spiral arms. Emission nebulae
mostly in spiral arms.
So arms always contain same types of objects, but individual objects come and go.
90% of Matter in Milky Way is Dark Matter
Gives off no detectable radiation. Evidence is from rotation curve:
10
Rotation
Velocity
(AU/yr) 5
Solar System Rotation Curve: when
almost all mass at center, velocity
decreases with radius ("Keplerian")
1
1
10
20
30
R (AU)
observed curve
Milky Way
Rotation
Curve
Curve if Milky
Way ended
where visible
matter pretty
much runs out.
Not enough radiating matter at large R to explain rotation
curve => "dark" matter!
Dark matter must be about 90% of the mass!
Composition unknown. Probably mostly exotic particles that
don't interact with ordinary matter at all (except gravity).
Some may be brown dwarfs, dead white dwarfs …
Most likely it's a dark halo surrounding the Milky Way.
Mass of Milky Way
6 x 1011 solar masses within 40 kpc of center.
Galaxy Classification
Spirals
Ellipticals
barred unbarred
SBa-SBc Sa-Sc
E0 - E7
Irregulars
Irr I
"misshapen
spirals"
Irr II
truly
irregular
First classified by Hubble in 1924 => "tuning fork diagram"
bulge less prominent,
arms more loosely wrapped
Irr
increasing apparent flatness
disk and large
bulge, but no spiral
bulge less prominent,
arms more loosely wrapped
Irr
increasing apparent flatness
disk and large
bulge, but no spiral
Still used today. We talk of a galaxy's "Hubble type"
Milky Way is an SBbc, between SBb and SBc.
Later shown to be related to other galaxy structural properties and
galaxy evolution.
Ignores some notable features, e.g. viewing angle for ellipticals,
number of spiral arms for spirals.
Irr I vs. Irr II
Irr I (“misshapen spirals”)
Irr II (truly irregular)
bar
poor beginnings
of spiral arms
Large Magellanic Cloud
Small Magellanic Cloud
These are both companion galaxies of the Milky Way.
Ellipticals are similar to halos of spirals, but generally larger, with
many more stars. Stellar orbits are like halo star orbits in spirals.
Stars in ellipticals also very old, like halo stars.
An elliptical
Orbits in a spiral
A further distinction for ellipticals and irregulars:
Giant
1010 - 1013 stars
10's of kpc across
Dwarf Elliptical NGC 205
Spiral M31
Dwarf Elliptical M32
vs.
Dwarf
106 - 108 stars
few kpc across
In giant galaxies, the average elliptical has more stars than the
average spiral, which has more than the average irregular.
What kind of giant galaxy is most common?
Spirals - about 77%
Ellipticals 20%
Irregulars 3%
But dwarfs are much more common than giants.
"Star formation history" also related to Hubble type:
Ellipticals formed all their stars early on,
no gas left. Stars are old, red, dim.
amount of star
formation
1
time (billions of years)
14 (now)
Spirals still have star formation, and gas.
Luminous, massive, short-lived stars make
spirals bluer than ellipticals
amount of star
formation
1
time (billions of years)
Irregulars have a variety of star formation histories.
14 (now)
Distances to Galaxies
For "nearby" (out to 20 Mpc or so) galaxies, use a very bright class of
variable star called a "Cepheid".
luminosity
time
Cepheid star in
galaxy M100
with Hubble.
Brightness
varies over a
few weeks.
From Cepheids in Milky Way star clusters (with known
distances), it was found that period (days to weeks) is
related to luminosity (averaged over period).
So measure period of Cepheid in nearby galaxy, this gives
star's luminosity. Measure apparent brightness. Now can
determine distance to star and galaxy.
Has been used to find distances to galaxies up to 25 Mpc.
Spectra of galaxies
in clusters of
increasing distance
prominent
pair of absorption
lines
In 1920's, Hubble used Cepheids to find distances to
some of these receding galaxies. Showed that redshift
or recessional velocity is proportional to distance:
V = H0 x D
velocity (km / sec)
(Hubble's Law)
Distance (Mpc)
Hubble's Constant (km / sec / Mpc)
Or graphically. . .
Current estimate:
H0 = 73 +/- 2 km/sec/Mpc
If H0 = 75 km/sec/Mpc, a
galaxy at 1 Mpc moves
away from us at 75 km/sec,
etc.
Get used to these huge distances!
Milky Way
30 kpc
Milky Way to Andromeda
700 kpc
Milky Way to Virgo Cluster
17 Mpc
Clusters
Larger structures typically containing thousands of galaxies.
The Virgo Cluster of about 2500 galaxies
(central part shown).
The center of the Hercules Cluster
Galaxies orbit in groups or clusters just like stars in a stellar cluster.
Most galaxies are in groups or clusters.
Galaxy Interactions and Mergers
Galaxies sometimes come near each other,
especially in groups and clusters.
Large tidal force can draw stars and gas out
of them => tidal tails.
Galaxy shapes can become badly distorted.
Galaxies may merge.
Some ellipticals may be mergers of two or more spirals. Since
they have old stars, most mergers must have occurred long ago.
Interactions and mergers also lead to "starbursts": unusually
high rates of star formation. Cause is the disruption of orbits of
star forming clouds in the galaxies. They often sink to the
center of each galaxy or the merged pair. Resulting high
density of clouds => squeezed together, many start to collapse
and form stars.
M82
Interactions and mergers can be simulated by computers.
Yellow = stars
Blue = gas
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Mihos et al.
How do Galaxies Form?
Old idea: they form from a single large collapsing cloud of gas, like a star
but on a much larger scale.
New idea: observations indicate that "sub-galactic" fragments of size
several hundred parsecs were the first things to form. Hundreds might
merge to form a galaxy.
Deep Hubble image of a region 600 kpc across. Small fragments are
each a few hundred pc across, contain several billion stars each. May
merge to form one large galaxy. This is 10 billion years ago.
Galaxy Formation and Evolution
This simulation shows how interaction with a
smaller galaxy could turn a larger one into a
spiral.
Active Galaxies
Seyfert Galaxies
Between normal galaxies and most active
galaxies
Radio Galaxies
Gives off energy in radio part of spectrum
not from nucleus but from lobes
Quasars (Quasi-stellar object)
Brightest objects in the universe
Black Holes and Active Galaxies
This galaxy is viewed
in the radio spectrum,
mostly from 21-cm
radiation. Doppler
shifts of emissions
from the core show
enormous speeds
very close to a
massive object – a
SUPER massive black
hole.
Black Holes and Active Galaxies
Careful measurements show that the mass of
the central black hole is correlated with the size
of the galactic core.
Quasars - Quasi-stellar objects
The quasars we see are very distant, meaning
they existed a long time ago. Therefore, they may
represent an early stage in galaxy development.
The quasars in this image are shown with their
host galaxies.
Quasars - Quasi-stellar objects
The end of the quasar epoch seems to have
been about 10 billion years ago; all the
quasars we have seen are older than that.
The black holes powering the quasars do not
go away; it is believed that many, if not most,
galaxies have a supermassive black hole at
their centers.
Evolution of Galaxies?
This figure shows how galaxies may have
evolved, from early irregulars through active
galaxies, to the normal ellipticals and spirals we
see today.
Structures of Galaxies
Groups
A few to a few dozen galaxies
bound together by their
combined gravity.
No regular structure to them.
The Milky Way is part of the Local Group of
about 30 galaxies, including Andromeda.
The Universe on Very Large Scales
Galaxy clusters join
in larger groupings,
called superclusters.
This is a 3-D map of
the superclusters
nearest us; we are
part of the Virgo
Supercluster.
Classifying clusters:
1) “rich” clusters vs. “poor” clusters
Poor clusters include galaxy groups (few to a few dozen members) and
clusters with 100’s of members. Masses are 1012 to 1014 solar masses.
Rich clusters have 1000’s of members. Masses are 1015 to 1016 solar masses.
Higher density of galaxies.
2) “regular” vs. “irregular” clusters
Regular clusters have spherical shapes. Tend to be the rich clusters.
Irregular clusters have irregular shapes. Tend to be the poor clusters.
Fraction of giant galaxies
Spirals dominate isolated galaxies, groups, poor clusters.
Ellipticals and SO’s dominate rich clusters, especially dense central parts.
Why?
One explanation: denser environment => more mergers => more
ellipticals made as bulges grew. Most mergers happened long ago when
galaxies were closer together.
At cluster centers lie the largest ellipticals: “cD” galaxies. They
have digested many companions. Masses up to 1014 solar masses
(remember: Milky Way about 6 x 1011 solar masses)!
Are these cores of
swallowed companions
or galaxies seen in
projection? Opinion
differs.
There is more mass between galaxies in clusters than within them
Abell 2029: galaxies (blue), hot intracluster gas (red)
X-ray satellites (e.g. ROSAT, Chandra) have revealed massive amounts of
hot (107-108 K!) gas in between galaxies in clusters (“intracluster gas”). A
few times more than in stars!
What is the origin of intracluster gas? Possibilities:
1) “Leftover” gas from the galaxy formation process
2) Gas lost from galaxies in tidal interactions, ram pressure stripping,
supernova explosions, and jets from active galactic nuclei
High density of galaxies in clusters means
that tidal interactions are common
How could you tell between 1) and 2) ?
X-ray brightness
Take a spectrum! Many lines of elements produced by nucleosynthesis in stars. Can’t be mostly “leftover” gas.
X-ray frequency
Most mass in clusters is in Dark Matter
Recall Escape Velocity: needed to completely escape the
gravity of a massive object.
vescape =
√
2 G Mobject
R
Example: Coma Cluster
Mass in visible matter (galaxies and intracluster gas) 2 x 1014 solar masses.
Size 3 Mpc. Escape speed then 775 km/s.
But typical velocity of galaxy within cluster observed to be 1000 km/s, and
many have 1000-2000 km/s! Must be more mass than is visible (85% dark
matter inferred).
Clusters of galaxies also bend the light of more distant galaxies
seen through them
All the blue images are
of the same galaxy!
From the lensed galaxy images, you can figure out the total mass
of the cluster. Results: much greater than mass of stars and gas => further
evidence for dark matter!
The Bullet Cluster
Dark matter predicted not to interact with ordinary matter, or itself,
except through gravity. Gas clouds, by contrast, can run into each other.
A collision of two clusters provides dramatic evidence for dark matter:
cluster
trajectory
red shows hot gas
from two clusters,
seen with Chandra Xray observatory.
The gas clouds have
run into each other,
slowing each one
down
cluster
trajectory
blue shows inferred
distribution of cluster
mass from gravitational
lensing of background
galaxies. The dark matter
has gone straight through
with no interaction, like
the galaxies have.
In 1920's, Hubble used Cepheids to find distances to
some of these receding galaxies. Showed that redshift
or recessional velocity is proportional to distance:
V = H0 x D
velocity (km / sec)
(Hubble's Law)
Distance (Mpc)
Hubble's Constant (km / sec / Mpc)
Or graphically. . .
Current estimate:
H0 = ~75 km/sec/Mpc
If H0 = 75 km/sec/Mpc, a
galaxy at 1 Mpc moves
away from us at 75 km/sec,
etc.
So by getting the spectrum of a galaxy, can measure its redshift,
convert it to a velocity, and determine distance.
Results from a
mid 1980's
survey.
Assumes H0 = 65
km/sec/Mpc. Note
how scale of
structure depends on
this.
Hubble's Law now used to unveil Large Scale Structure of the
universe. Result: empty voids surrounded by shells or filaments,
each containing many galaxies and clusters. Like a froth.
Cosmology
The Study of the Universe as a Whole
What is the largest kind of structure in the universe? The ~100-Mpc
filaments, shells and voids? On larger scales, things look more uniform.
600 Mpc
Given no evidence of further structure, assume:
The Cosmological Principle
On the largest scales, the universe is roughly homogeneous (same at all
places) and isotropic (same in all directions). Laws of physics same.
Hubble's Law might suggest that everything is expanding away
from us, putting us at center of expansion. Is this necessarily true?
(assumes
H0 = 65
km/sec/Mpc)
If there is a center, there must be a boundary to define it => a finite
universe. If we were at center, universe would be isotropic (but only
from our location) but not homogeneous:
Finite volume of galaxies
expanding away from us
into...what, empty space?
Us
But if we were not at center, universe would be neither isotropic nor
homogeneous:
Us
So if the CP is correct, there is no center, and no edge to the Universe!
Best evidence for CP comes from Cosmic Microwave Background
Radiation (later).
The Big Bang
All galaxies moving away from each other. If twice as far away from
us, moving twice as fast (Hubble's Law). So, reversing the Hubble
expansion, everything must have been together once. How long ago?
H0 gives rate of expansion. Assume H0 = 75 km / sec / Mpc. So
galaxy at 100 Mpc from us moves away at 7500 km/sec. How long
did it take to move 100 Mpc from us?
distance
time =
velocity
100 Mpc
=
7500 km/sec
=
13 billion years
(Experts note that this time is just
1
).
H0
The faster the expansion (the greater H0), the shorter the time to get to
the present separation.
Big Bang: we assume that at time zero, all separations were infinitely
small. Universe then expanded in all directions. Galaxies formed as
expansion continued.
But this is not galaxies expanding through a pre-existing, static space.
That would be an explosion with a center and an expanding edge.
If CP is correct, space itself is expanding, and galaxies are taken
along for the ride. There is no center or edge, but the distance
between any two points is increasing.
A raisin bread analogy provides some insight:
But the cake has a center and edge. Easier to imagine having no center or
edge by analogy of universe as a 2-d expanding balloon surface:
Now take this analogy "up one dimension". The Big Bang occurred
everywhere at once, but "everywhere" was a small place.
(To understand what it would be like in a 2-d universe, read Flatland by
Edwin Abbott: www.ofcn.org/cyber.serv/resource/bookshelf/flat10 )
If all distances increase, so do wavelengths of photons as they travel and
time goes on.
When we record a photon from a distant source, its wavelength will be
longer. This is like the Doppler Shift, but it is not due to relative motion of
source and receiver. This is correct way to think of redshifts of galaxies.
The Cosmic Microwave Background Radiation (CMBR)
A prediction of Big Bang theory in 1940's. "Leftover" radiation from
early, hot universe, uniformly filling space (i.e. isotropic,
homogeneous). Predicted to have perfect black-body spectrum.
Photons stretched as they travel and universe expands, but spectrum
always black-body. Wien's Law: temperature decreases as wavelength
of brightest emission increases => was predicted to be ~ 3 K now.
All-sky map of the CMBR temperature, constant everywhere to one part in
105 ! For blackbody radiation, this means intensity is very constant too
(Stefan’s law).
(WMAP satellite)
Deviations are -0.25 milliKelvin (blue) to +0.25 milliKelvin
(red) from the average of 2.735 Kelvin.
That the CMBR comes to us from every direction is best evidence
that Big Bang happened everywhere in the universe. That the
temperature is so constant in every direction is best evidence for
homogeneity on large scales.
IF the Big Bang happened at one point in 3-d space:
Later, galaxies form and fly apart.
But radiation from Big Bang
streams freely at speed of light!
Wouldn't see it now.
The Expansion of the Universe Seems to be Accelerating
The gravity of matter should retard the expansion. But a new distance
indicator shows that the expansion rate was slower in the past!
Redshift (fractional shift in
wavelength of spectral lines)
Type I supernovae: from ones in nearby
galaxies, know luminosity. In distant galaxies,
determine apparent brightness. Thus
determine distance. Works for more
than 3000 Mpc. From redshifts, they are
not expanding as quickly from each
other as galaxies are now.
Taking this into account, best age estimate of
Universe is 13.8 Gyrs.
H0 was
smaller in
past (i.e.
for distant
galaxies)
The Cosmological Constant, 
Introduced by Einstein in 1917 to balance gravitational attraction and
create static Universe (turned out to be wrong!). Can think of  as
repulsive force that exists even in a vacuum. But accelerating universe
indicates there is a .Also often called "dark energy". We have little idea
of its physical nature.
The measured acceleration implies that there is more “dark energy” than
the energy contained in matter.
The Early Universe
The First Matter
At the earliest moments, the universe is thought to have been
dominated by high-energy, high-temperature radiation. Photons had
enough energy to form particle-antiparticle pairs. Why? E=mc2.
pair
production
annihilation
At time < 0.0001 sec, and T > 1013 K, gamma rays could form protonantiproton pairs.
At time < 15 sec, and T > 6 x 109 K, electron-positron pairs could form.
Annihilation occurred at same rate as formation, so particles coming in
and out of existence all the time.
As T dropped, pair production ceased, only annihilation. A tiny
imbalance (1 in 109) of matter over antimatter led to a matter universe
(cause of imbalance not clear, but other such imbalances are known to
occur).
Primordial Nucleosynthesis
Hot and dense universe => fusion reactions.
At time 100-1000 sec (T = 109 - 3 x 108 K), helium formed.
Stopped when universe too cool. Predicted end result: 75% hydrogen,
25% helium.
Oldest stars' atmospheres (unaffected by stellar nucleosynthesis)
confirm Big Bang prediction of 25% helium.
Successes of the Big Bang Theory
1) It explains the expansion of the universe.
2) It predicted the cosmic microwave background radiation, its
uniformity, its current temperature, and its black-body spectrum.
3) It predicted the correct helium abundance (and lack of other
primordial elements).
Misconceptions about the Big Bang
1. “The universe was once small.” The observable universe, which is
finite, was once small. The nature of the entire universe at early times
is not yet understood. It is consistent with being infinite now.
2. “The Big Bang happened at some point in space.” The microwave
background showed that it happened everywhere in the universe.
3. “The universe must be expanding into something.” It is not expanding
into “empty space”. That would imply the Big Bang happened at some
location in space. It is a stretching of space itself.
4. “There must have been something before the Big Bang.”
The Big Bang was a singularity in space and time (like the center
of a black hole). Our laws of physics say the observable universe
had infinitesimally small size, and infinite temperature and
density.
In these conditions, we don’t have a physics theory to describe
the nature of space and time. At the Big Bang, time took on the
meaning that we know it to have.
"Before" is only a relevant concept given our everyday
understanding of time. We must await a better understanding of
the nature of space and time. Such theories are in their infancy.
Shouldn’t be surprising that these concepts are hard to grasp.
So was the heliocentric Solar System 400 years ago.
Plot of how the black-body temperature of the background radiation
varies over the sky (the Galactic disk runs across the middle).
Our motion relative to this background causes a Doppler shift, so that
the temperature varies by a few milliKelvin (blue-pink difference).
The Early Universe
Inflation
A problem with microwave background:
Microwave background
reaches us from all
directions.
Temperature of background in opposite directions nearly identical. Yet
even light hasn't had time to travel from A to B (only A to Earth), so A
can know nothing about conditions at B, and vice versa. So why are A
and B almost identical? This is “horizon problem”.
Solution: Inflation. Theories of the early universe
predict that it went through a phase of rapid expansion.
Separation
between two
points (m)
If true, would imply that points that are too far apart now were
once much closer, and had time to communicate with each other
and equalize their temperatures.
Inflation also predicts universe has flat geometry:
Microwave background observations seem to suggest that this is true.
What drove Inflation?
-
State change of the Vacuum
Vacuum has energy fluctuations, Heisenberg uncertainty
principle states:
-
E t > h/2

-
The End of the Universe
How will the Universe end? Is this the only Universe? What, if anything,
will exist after the Universe ends?
The Five Ages of the Universe
1) The Primordial Era
2) The Stelliferous Era
3) The Degenerate Era
4) The Black Hole Era
5) The Dark Era
The Geometry of the Universe determines its fate