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Announcements
•Don’t forget about your project.
Presentations will be next Monday May 1 at
3:20pm. A written paper is also due at the
same time. Exam 4 is after the presentations
•Last exam will cover from Chapter 9
Rotating Black Holes through Chapter 13. All
essay exam…pick five from a list of eight to
ten. Exam 4 samples have been updated to
include Chapter 13
What parameters do we
measure?
H0: current value of the Hubble “constant”
k: curvature parameter
WM: mass/energy density parameter
WDM: dark matter density parameter
WL: cosmological constant parameter
q0: deceleration parameter
Determining these parameters will determine
which model best fits the universe
Measuring H0
Simple enough: measure the recessional velocity and
distance to a bunch of galaxies and plot the data on a
Hubble plot…the slope equals H0
A complication for H0:
proper motion
Andromeda
galaxy
approach
speed is
~110 km/s
We are on a collision course with the Andromeda
galaxy. Other galaxies have real motion with respect
to us which may be comparable to the Hubble flow
A major complication: how do
you measure the distance?
Determining the distance to the
closest galaxies is relatively
easy but the farther away it is,
the more difficult it becomes
What is needed are standard
candles
Cepheid variables can be seen from a large
distance but after ~100 Mly they are no longer
distinguishable from the background glow
Type Ia supernovae make the
best standard candle
When a white dwarf star exceeds its mass limit
(1.4MSun) it produces a Type Ia supernova which
can be seen from billions of lightyears away
Results from Type Ia
Supernova observations
Hubble Constant and the Age
of the Universe
Measuring the Shape Factor
The sum of the angles around a triangle depends on
the geometry but you have to measure really big
triangles to see it (i.e. billions of lightyears on a side)
We can get the shape factor from
the CBR
The angular size of the
fluctuations gives us the shape
Watch
Geometry
of the
Universe
WMAP
video
Measuring
the Angular
size of
galaxies and
other
objects also
shows the
shape factor
How much mass is there in the
universe?
WM  ?
And as a sub question
W DM  ?
Gravity Lensing is a means of
measuring the mass in the universe
Observing hot gas in galaxy
clusters also measures mass
Dynamical Methods rely on understanding the dynamics
of galaxy clusters and the hot gas bound by them
Galaxy rotation curves can give
individual galaxy masses
Observations of Large Scale
Structure provides another
independent method of finding WM
Big Bang Nucleosynthesis
also puts constraints on the
amount of baryonic matter
Measuring the relative
abundance of deuterium,
lithium and helium-3 is
one of the most difficult
measurements to make
requiring high precision
spectroscopy
The results indicate more dark
matter than baryonic matter
The next question is: Is it hot
dark matter or cold dark matter?
Most models indicate CDM dominates over HDM
But what is CDM?
Measuring WL
How do you measure
something when you don’t
even know what it is?
For the most part WL is found by
inference
Observations of the CBR tell us the universe is flat (W = 1).
Other observations tell us Wmatter ≈ 0.3 so WL ≈ 0.7
The constituents of the universe
according to Planck
Add all the
observations
together and
the result is a
universe that
has a positive
cosmological
constant and
is accelerating
Planck’s Summery of the
cosmological quantities