Today in Astronomy 102: the Big Bang
 General relativistic
Universes: dynamic and
static.
 The Universe expands:
no use for static models.
 Cosmological models:
Big Bang and steady
state.
 Observational tests of the
models, and the direct
observation of the Big
Image: Bob Wilson (left) and Arno Penzias
Bang.
with the horn antenna they used to discover
the cosmic microwave background.
4 December 2001
Astronomy 102, Fall 2001
1
“Mid”-lecture break will be at the end of class.
That’s so we can issue the Student
Course Opinion Questionnaires.
Stick around.
 Note, also, that Homework #7
is available now on WeBWorK,
and due on 14 December.
This is Edwin Hubble, pretending
he’s observing at the Newtonian
focus of the Mt. Wilson 100-inch
Telescope. It would be dark if he
were really observing, of course.
(Caltech Archives)
4 December 2001
Astronomy 102, Fall 2001
2
Back to general relativity and the structure of the
Universe …
Einstein and de Sitter (late 1910s and 1920s, Germany),
Friedmann (1922, USSR), Lemaître (1927, Belgium), and
Robertson and Walker (1935, US/UK) produced the first
solutions of the field equations for an isotropic and
homogeneous Universe.
The types of solutions they found:
 Collapse, ending in a singularity.
 Expansion from a singularity, gradually slowing and
reversing under the influence of gravity, ending in a
collapse to a singularity.
This, and the previous outcome, are for universes with
total kinetic energy (energy stored in the motions of
galaxies) less than the gravitational binding energy. They
are called closed universes.
4 December 2001
Astronomy 102, Fall 2001
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General relativity and the structure of the Universe
(continued)
 Expansion from a singularity, that gradually slows, then
stops. (Total kinetic energy = gravitational binding
energy.)
This is generally called a marginal, or critical, Universe.
 Expansion from a singularity, that continues forever (total
kinetic energy greater than gravitational binding energy).
This is called an open universe.
Model 1 is of course a lot like what we now call black hole
formation, since it ends in a singularity.
Note that models 2-4 all involve expansion from a
singularity, so the creation and development of the Universe
must be rather like black hole formation running in reverse.
4 December 2001
Astronomy 102, Fall 2001
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Einstein doesn’t like it.
All the solutions have these features in common:
 singularities, and
 dynamic behavior: the structure given by the solutions is
different at different times between singularities (at which time
doesn’t exist, of course).
Einstein thought that singularities such as these indicated that
there were important physical effects not accounted for in the field
equation. He also thought that the right answer would involve
static behavior: large-scale structure should not change with time.
He also saw how he could “fix” the field equation to eliminate
singular and dynamic solutions: introduce an additional constant
term, which became known as the cosmological constant, to
represent the missing, unknown, physical effects.
4 December 2001
Astronomy 102, Fall 2001
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The field equation and the cosmological constant:
hieroglyphics (i.e. not on the exam or homework)
The field equation under a particularly simple set of
assumptions and conditions for a homogeneous and isotropic
2
Universe:
1
dR

 8 G
Spacetime
2 k




c


curvature
R
dt
3


R2
Typical distance Mass per
between galaxies unit volume
The same equation modified by Einstein (1917):
2
c2
 1 dR  8 G
2 k
    c 2

 
3
3
 R dt 
R
Cosmological constant
A certain positive value of  leads
a static solution.
4 December 2001
Astronomy 102, Fall 2001
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Edwin Hubble strikes again: the Universe expands.
Then, in 1929, Hubble made his third great contribution to
cosmology; he observed that:
 distant galaxies are always seen to have redshifted
spectra. Thus they all recede from us.
 the magnitude of this Doppler shift for any given distant
galaxy is in direct proportion to the distance to this
galaxy: with V = velocity and D = distance to galaxy,
V  H 0D
(Hubble’s Law)
where H0 = 20 km/sec/Mly according to the most recent
measurements by the Hubble Space Telescope.
This means that the Universe is expanding.
4 December 2001
Astronomy 102, Fall 2001
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Relation between
galaxy redshift and
distance
Visible-light spectra (left) of
several different galaxies
(right). The extent of the
redshift, denoted by the
horizontal yellow arrows,
and the distance to each
galaxy (in the center)
increase from top to bottom.
1 parsec = 3.26 ly.
(Figure: Chaisson and
McMillan, Astronomy Today.)
4 December 2001
Astronomy 102, Fall 2001
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Einstein gives up.
The Universe is observed to be expanding; it is not static.
 Thus the real Universe may be described by one of the
dynamic solutions to the original Einstein field equation.
Of the four types we discussed above, the last three spend
at least part of their time, if not all, expanding.
 Thus there appeared to be no point in Einstein’s
cosmological constant, so he let it drop, calling it “my
greatest blunder.”
 Thereafter he began trying to show that the singularities
in the dynamic solutions simply wouldn’t be realized. His
effort resulted in the steady-state model of the Universe,
which we’ll describe later.
This isn’t the last we’ll see of the cosmological constant,
though.
4 December 2001
Astronomy 102, Fall 2001
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Possibilities for the structure of the expanding
Universe
Unbound (open)
Typical
distance
between
galaxies
Marginal (total kinetic
energy = binding energy)
Bound (closed)
Big Bang
Big
Squeeze
Time
All three expanding solutions predict that the matter in the
universe was concentrated at earlier times, and that the expansion started as an explosion of this concentration: the Big Bang.
4 December 2001
Astronomy 102, Fall 2001
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Possibilities for the structure of the expanding
Universe (continued)
Unbound (open)
Typical
distance
between
galaxies
Marginal (total kinetic
energy = binding energy)
Bound (closed)
Time
To tell which solution describes the real Universe, we need
to measure the acceleration of the galaxies as well as their
velocities. Astronomers have been working on this for
decades.
4 December 2001
Astronomy 102, Fall 2001
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Summary of Hubble’s findings
 The Universe is isotropic: on large scales it looks the same
in all directions, from our viewpoint.
 The Universe is homogeneous: it is uniform on large
scales. In other words, the Universe looks the same from
any viewpoint.
 The Universe is expanding:
• The galaxies recede from us, faster the further away
they are.
• And since the Universe is homogeneous, we would see
the same recession no matter where we stood. That is,
there is no unique center in space, of the expansion, as
in an ordinary explosion and blast wave.
4 December 2001
Astronomy 102, Fall 2001
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Why galaxies recede from an observer in the
expanding Universe, no matter where she stands.
A
B
Universal
expansion
A’
B’
All intergalaxy distances
increase: A’ > A, B’ > B.
(The galaxies themselves do
not expand, though.)
4 December 2001
Astronomy 102, Fall 2001
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Why galaxies recede from an observer in the
expanding Universe, no matter where she stands.
A
Universal
expansion
A’
B
B’
Galaxies recede from one
another, and recede faster the
further apart they are: B’-B >
A’-A. Because the galaxies
recede, the Doppler shifts are all
redshifts.
4 December 2001
Astronomy 102, Fall 2001
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Results by Hubble and Humason, 1929
V  H 0D ,
H 0  142 km /sec /Mly
1 Mly = 106 ly
Graph from Ned Wright’s
Cosmology Tutorial.
4 December 2001
Astronomy 102, Fall 2001
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An up-to-date Hubble-constant determination
(Riess, Press and Kirschner 1996)
H0  19.6  0.9 km/sec/Mly
In AST 102 we’ll take the
Hubble constant to be H0 =
20 km/sec/Mly.
Graph from Ned Wright’s
Cosmology Tutorial.
4 December 2001
Astronomy 102, Fall 2001
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Simple use of Hubble’s Law
Example. The redshift of 3C 273 corresponds to a speed of
48,000 km/sec. How far away is 3C 273?
km
48000
V
sec  2.4  10 3 Mly
D

km
H 0 20
sec  Mly
Example. The center of the nearest cluster of galaxies, the
Virgo Cluster, is 70 Mly away. What is the recession speed we
expect for galaxies near the center of this cluster?
V  H0 D  20
4 December 2001
km
km
 70 Mly=1400
sec  Mly
sec
Astronomy 102, Fall 2001
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Cosmological models
Once Hubble’s observations made it clear that the Universe is
not static, two types of model remained for the structure of
the Universe:
The Big Bang model: based upon non-static universes with
constant total mass and energy, presently in a state of
expansion, but originating in a singularity. Major
proponents: Friedmann, Lemaitre, Robertson, Gamow, Pope
Pius XII, Sandage.
The Steady-State model: in which the singularities are not
realized, because steady creation of new matter leads to a
constant density on the average, expansion, and no
“beginning” or “end”. Major proponents: Einstein, Bondi,
Gold, Hoyle, Chairman Mao, Arp.
4 December 2001
Astronomy 102, Fall 2001
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Observational tests of cosmological models
Big Bang Universe proponents made these specific
predictions on the basis of their models:
 On very large scales - a substantial fraction of the total size
of the Universe - galaxies would be closer together on
average than they are now, owing to the expansion and
early curvature of the Universe. (Recall: far away = far
back in time; spacetime is warped close to singularities.)
 Evolution: very distant (young) galaxies should be
qualitatively different on average from nearby galaxies.
 We should be able to see the blast of the Big Bang itself,
by looking far enough away. It would look like a hot,
opaque body, but with its light Doppler-shifted to
extremely long wavelengths because it is so far away. (V =
H0D and  = 0(1 + V/c):  much larger than 0.)
4 December 2001
Astronomy 102, Fall 2001
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Observational tests of cosmological models
(continued)
And for their part, those studying the steady-state model
predicted:
 that galaxies would appear to be distributed uniformly,
and spacetime would appear to be flat, no matter how far
away we look.
 no evolution: the internal properties of galaxies – what
kinds of stars they have in them, what concentrations of
heavy elements they possess, etc. – would be the same, on
the average, everywhere in the Universe. That is, there
should be no tendency for distant galaxies to look young.
A few steady-state proponents even predicted that galaxy
redshifts would turn out not to be of cosmological origin, but
instead would represent material ejected at high speeds by
galaxies with small Doppler shifts.
4 December 2001
Astronomy 102, Fall 2001
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Observational tests I: radio galaxies at large
redshifts
Soon after radio galaxies were identified in the 1950s it was
realized that most of the faint radio sources in the sky must
be radio galaxies, mostly at distances much greater than those
determined for visible galaxies.
 Counting the numbers of these faint sources as a function
of their brightness basically provides a repeat of Hubble’s
demonstration that galaxies are distributed
homogeneously on large scales.
 However, the faint radio sources should be much farther
away than the faint galaxies observed by Hubble: far
enough away to expect these galaxies to be closer together
on average than present-day galaxies in a Big Bang model.
4 December 2001
Astronomy 102, Fall 2001
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Number or radio galaxies
per square degree of sky
Data
Observational tests I:
radio galaxies at
large redshifts
(continued)
Results by Pooley and
Ryle (1968) (points) and a
big-bang model (curve) in
black, compared to a
steady-state Universe, in
red.
Steady-state
Universe
Brightness
(power per cm2 of telescope area)
4 December 2001
Astronomy 102, Fall 2001
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Observational tests I: radio galaxies at large
redshifts (continued)
Implications of radio-source counts like those by Pooley and
Ryle:
 As one looks back through time, the number of radio
galaxies per unit volume increases (or typical separation
decreases) up to very great distances.
 At the largest distances, the number of radio galaxies per
unit volume decreases again.
 Thus either the Universe is not homogeneous, or is not
flat, or contains galaxy populations that evolve (with
radio-galaxy appearance as one phase of development), or
all three.
 In any case, this is inconsistent with the predictions of the
Steady State model, but explicable in Big Bang models.
4 December 2001
Astronomy 102, Fall 2001
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Observational tests II: direct observation of the Big
Bang
In the 1940s, George Gamow’s students, Ralph Alpher and
Bob Herman, predicted that the blast from the Big Bang
should be detectable someday.
 Specifically: light would be seen that arose at the time
when the Universe had cooled to the point that atoms
could form.
 The light started off visible, but owing to the great
distance of its source it would be redshifted into the
microwave band (wavelengths of a millimeter to a few
centimeters), and look like a black body with a
temperature a few degrees Kelvin (above absolute zero).
 Since it was close to a singularity when emitted, the light
should appear isotropic: spread uniformly across the sky.
(We’ll explain why it should look like this, in a bit.)
4 December 2001
Astronomy 102, Fall 2001
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Observational tests II: direct observation of the Big
Bang (continued)
In 1965, Bob Wilson and Arno Penzias (AT&T Bell Telephone
Laboratories) were working on a very sensitive microwave
receiver and antenna they built for satellite communication.
They were trying to tune it up to reach ideal performance,
but persistently found extra noise power for which they
couldn’t account. They knew nothing of Gamow’s prediction.
 The extra power was like that of a black body with
temperature 2.7 K (2.7 degrees above absolute zero).
 It was the same no matter which direction they pointed
their antenna. ( If it comes from the sky, it’s isotropic.)
They were grasping at straws for an explanation, when they
were paid a visit by radio astronomer Bernie Burke, a
professor at MIT.
4 December 2001
Astronomy 102, Fall 2001
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Observational tests II: direct observation of the Big
Bang (continued)
Burke knew of efforts at Princeton U. by Dicke and Peebles to
build a sensitive microwave receiver and antenna to look for
the Big Bang radiation predicted by Gamow, but were having
technical troubles. He introduced the Bell Labs group to the
Princeton group.
 It was quickly noticed that Penzias and Wilson had
indeed detected that relict radiation (now called the
Cosmic Microwave Background).
 Thus the blast from the Big Bang is seen directly. This is
the sturdiest nail in the coffin of the Steady-State
Universe.
 For this epochal discovery, Penzias and Wilson shared the
1978 Nobel Prize in Physics.
4 December 2001
Astronomy 102, Fall 2001
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