… but the equilibrium is unstable. In order
to prevent the universe from either
expanding or contracting, Einstein
introduced a scalar field that was called
The Cosmological Constant
in order to keep the universe static.
The Age of the Universe
No gravity: v = Hor 
to = r/v = Ho-1
Newtonian gravity for a flat universe:
½ mv2 - GmM/r = 0  v = dr/dt = (2GM/r)½
so we can integrate r½dr = (2GM)½dt to get
to = 2/3 (r3/2GM)½ = 2/3 (r/v) = 2/3 Ho-1
Ho = 73.8 ± 2.4 (km/s)/Mpc.
to = 13.7 billion years
Oscillations on many scales
Source: Wayne Hu:
Power Spectrum
cosmic variance
limited for l<354
for l<658
Evidence for the Hot Big Bang
Hubble flow
Ho measures the universe at approximately t = 1010 yrs
Cosmic microwave background radiation
CMB measure the universe at approximately t = 4 x105 yrs
Abundances of the light elements
BBN measures the universe at approximately t = 200 s
Galactic Rotation Curves
For a star of mass m a distance r from the center of
a galaxy, where the total mass interior to r is M(r):
mv2/r = GM(r)m/r2
so that we would expect
v= [GM(r)/r] ½
so that v should go like r -½
Size and Scale of the Universe
Image courtesy of The Cosmic Perspective by Bennett, Donahue, Schneider, & Voit; Addison Wesley, 2002
The Milky Way Galaxy
The Milky Way Galaxy is a giant disk of stars 160,000 light-years across and 1,000 light-years
The Sun is located at the edge of a
spiral arm, 30,000 light-years from
the center
It takes 250 Million years for the Sun
to complete one orbit
You Are Here
There are over 100 Billion stars in
the Milky Way
The Spiral arms are only 5% more
dense than average, and are the
locations of new star formation
The Local Group
• Contains 3 large spiral galaxies--Milky
Way, Andromeda (M31), and Triangulum
(M33)—plus a few dozen dwarf galaxies
with elliptical or irregular shapes.
• Gravitationally bound together—orbiting
about a common center of mass
• Ellipsoidal in shape
• About 6.5 million light-years in diameter
• A cluster of many groups
and clusters of galaxies
The Local Supercluster
• Largest cluster is the Virgo
cluster containing over a
thousand galaxies.
• Clusters and groups of
galaxies are gravitationally
bound together, however the
clusters and groups spread
away from each other as the
Universe expands.
• The Local Supercluster gets
bigger with time
• It has a flattened shape
• The Local Group is on the
edge of the majority of
• The Local Supercluster is
about 130 Million light-years
1.3 Billion light-years
The Universe
• Surveys of galaxies reveal a web-like or
honeycomb structure to the Universe
The plane of the Milky Way Galaxy obscures
our view of what lies beyond. This creates the
wedge-shaped gaps in all-sky galaxy surveys
such as those shown here.
• Great walls and filaments of matter
surrounding voids containing no galaxies
• Probably 100 Billion galaxies in the
The Universe
The observable
Universe is ~26
Billion light-years
in diameter.
Computer Simulation
The Universe
The distance to the center
of the Milky Way is about
104 pc, whereas the size of
the solar system is about
10-4 pc. If the distance to
the center of the Milky
Way were scaled to the
size of this room (10
meters), then on the same
Elements of an Interactive
• Feedback (Clicker questions)
• Peer education (Think pair share)
• Formative and summative assessment (JiTT)
• Inquiry based learning (workshop style classrooms)
• Web-based activities & resources (facebook, youtube, twitter &
• Visualizations (Phet Simulations, demos)
A "Hubble diagram" is a graph of:
A. Brightness versus wavelength or frequency;
B. Luminosity versus temperature;
C. Mass versus radius;
D. Size versus time;
E. Velocity versus distance.
What is the principal observational evidence that the age of the
Universe is about 14 billion years?
A. The oldest rocks (carbonaceous chondrites) in the solar system
indicate an age of 14 billion years;
B. Radioactive decay of heavy elements created in the Big Bang
indicates an age of 14 billion years;
C. The main sequence turn-off point in the HR diagrams of globular
clusters indicates ages of about 14 billion years;
D. Light from the most distant galaxies and quasars appears to be about
14 billion years old;
E. The reciprocal of Hubble's constant gives an estimate of the age of
the Universe.
How can astronomers measure that a galaxy is rotating?
A. From the rotating motion of the galaxy on the sky;
B. From its redshift;
C. From the difference in the redshift of the galaxy from one side to the
D. From the swept back appearance of its spiral arms;
E. From Cepheid variables in the galaxy.
The distance to the center of the Milky
Way is about 104 pc, whereas the size of
the solar system is about 10-4 pc. If the
distance to the center of the Milky Way
were scaled to the size of this room (10
meters), then on the same scale the solar
system would be about the size of:
A. An atom (10-10 m);
B. A molecule of DNA (10-7 m);
C. A pin head (10-3 m);
D. A foot (10-1 m);
E. You (1 meter).
There was a revolution in cosmology, leading to the "Standard Model
of Cosmology" (according to which the Universe contains 70% Dark
Energy, 26% non-baryonic Dark Matter, 4% baryonic matter). What
observational discovery caused the revolution?
A. The redshifts of galaxies showed that the Universe is expanding;
B. The discovery of the Cosmic Microwave Background.
C. The rotation of spiral galaxies showed the existence of Dark Matter;
D. All of the above
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