Download in the Universe

How big is the Universe?
How big is a large, expanding object?
Spatial separation NOW, with the positions of both objects
specified at the current time
 This distance NOW is larger than the speed of light times the
light travel time due to the increase of separations
between objects as the Universe expands
 Caused by things being farther apart now than they used to be
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How big is the Universe?
What is the distance NOW to the most distant
thing we can see?
Suppose the Age of the Universe is 10 billion years
 In that time, light travels 10 billion light-years
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But the distance has grown while the light traveled
How big is the Universe?
A Good Rule of thumb
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Universe is three times the speed of light
times the age of the Universe.
What shape is the Universe?
General Relativity leads to geometry of spacetime
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Einstein showed that mass caused space to curve
Objects travelling in curved space have paths deflected, as if a
force had acted on them
What shape is the Universe?
Since Space is curved- 3 possibilities
Tied intimately to the amount of mass (and thus to the total strength of
gravitation) in the Universe
What shape is the Universe?
Flat Surface
Zero curvature
 There is insufficient mass to cause the expansion of the Universe
to stop
 Has no bounds, and will expand forever
 An Open Universe
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Euclidian Universe
What shape is the Universe?
Spherical Surface
Positive curvature
 More than enough mass to stop the
present expansion of the Universe
 Not infinite, but it has no end
 Expansion will eventually stop and
turn into a contraction
 Closed Universe

What shape is the Universe?
Saddle-Shaped Surface
Negative curvature
 Insufficient mass to cause the expansion of the Universe to stop
 Universe has no bounds , and will
expand forever
 Open Universe
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Critical Density
Density Parameter (ratio of actual density of Universe to
critical density that would just be required to cause the expansion
to stop)
Universe is flat (contains just the amount of mass to close it) the
density parameter is exactly 1
 Universe is open with negative curvature the density parameter
lies between 0 and 1
 Universe is closed with positive curvature the density parameter
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is greater than 1
Critical Density
Density Parameter gotten from various methods
Calculating the number of baryons created in the big bang
 Counting stars in galaxies
 Observing the dynamics of galaxies both near and far
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With some rather large uncertainties, all methods point to the
Universe being open (i.e. the density parameter is less
than one)
 And we must remember that they have likely not detected all of

the matter in the Universe yet
Critical Density
Here’s what the experts think...
Current theoretical prejudice is Universe is flat
 Exactly the amount of mass required to stop the expansion
 BOOMERANG, MAXIMA, and supernova data say expansion
of Universe is accelerating
 Universe is geometrically "flat”
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Determining the value of the density parameter and thus the
ultimate fate of the Universe remains one of the major unsolved
problems in modern cosmology. The MAP and Planck missions will
be able to measure the value definitively.
No Edge, No Center
What is the fate of the Universe?
That all depends on
Dark Matter and
Dark Energy!
What is Dark Matter?

Universe is full of "dark matter”
–influences the evolution of the Universe gravitationally
–not seen directly by any of our present methods of observation
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Fritz Zwicky, 50 yrs. ago, realized clusters of galaxies consisted
predominantly of matter in some nonluminous form
Search for dark matter has dominated cosmology for half a
century
Precise measurements obtained over 20 years ago, when dark
matter first mapped in galaxy halos
Only recently has the existence of dark matter over much larger
scales been confirmed
What is Dark Matter?
Astronomers add up masses and luminosities of stars near the
Sun, there are about 3 solar masses for every 1 solar
luminosity
 Total mass of clusters of galaxies and compare that to the total
luminosity of the clusters, they find about 300 solar
masses for every solar luminosity

–Evidently most of the mass in the Universe is dark.
–If the Universe has the critical density then there are about 1000
solar masses for every solar luminosity, so an even greater fraction of
the Universe is dark matter.
What is Dark Matter?

But Big Bang nucleosynthesis says density of ordinary matter
(anything made from atoms) can be at most 10% of the
critical density
–the majority of the Universe does not emit light,
–does not scatter light
–does not absorb light
–is not even made out of atoms
–It can only be "seen" by its gravitational effects
This dark matter can be neutrinos, if they have small masses
instead of being massless
 It can be more exotic particles like WIMPs (Weakly Interacting
Massive Particles),
 It could be primordial black holes.
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Evidence for Dark Matter

First real surprise in outermost parts of galaxies, known as
galaxy halos
–negligible luminosity
–occasional orbiting gas clouds
–allow one to measure rotation velocities and distances
The rotation velocity is found not to decrease with increasing
distance from the galactic center
 This implies that the galaxy's cumulative mass must continue to
increase with the radial distance from the center of the
galaxy, even though the light levels off
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Galactic Halo Mass
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This rise appears to stop at about 50 kiloparsecs
–halo seems to be truncated

We infer that the mass--to--luminosity ratio of the galaxy
including its disk halo, is about five times larger than
estimated for the luminous inner region, or equal to about
50
–This is the first solid, incontrovertible evidence for dark matter
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The rotation velocities throughout many spiral galaxies have
been measured, and all reveal dominance by dark matter
MACHOs
What else could it be?
• MACHOs
(MAssive Compact
Halo Objects)
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- baryonic dark
matter
- strong evidence
from gravitational
microlensing
Microlensing
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MACHO in our galaxy's halo passes very close to line of sight
from Earth to a distant star, the gravity of the otherwise
invisible MACHO acts as a lens that bends the starlight
–star splits into multiple images that are separated by a milliarcsecond, far too small to observe from the ground
–background star temporarily brightens as the MACHO moves across
the line of sight in the course of its orbit around the Milky Way halo
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To overcome the low probability of observing a microlensing
event, the experiments were designed to monitor several
million stars in the Large Magellanic Cloud
–stars observed hundreds of times over the course of a year
–revealed several events that had microlensing signatures
Microlensing
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Microlensing
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Measuring Mass through
Microlensing
The duration of the microlensing event directly
measures the mass of the MACHO
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The event duration is time cross the Einstein ring radius
–approximately equal to the geometric mean of the Schwarzschild
radius of the MACHO and the distance to the MACHO
–for a MACHO half-way to the Large Magellanic Cloud, that distance
is 55 kiloparsecs
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The Einstein ring radius is about equal to 1 astronomical unit, or
the Earth-Sun distance
–MACHOs must be smaller than the lens, so roughly the radius of a
red giant star.
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Event durations suggest typical mass around 0.1 solar masses;
–at least a factor of 3 uncertainty in either direction.
Measuring Mass
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Mass-to-light ratio can also be evaluated by studying galaxy
pairs, groups, and clusters
–measure velocities and length scales
–determine total mass required to provide the necessary self-gravity to
stop the system from flying apart
–inferred ratio of mass to luminosity is about 100M/L for galaxy
pairs, which typically have separations of about 100 kiloparsecs
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The mass-to-luminosity ratio increases to 300 for groups and
clusters of galaxies over a length scale of about 1
megaparsec
–over this scale, 95 percent of the measured mass is dark
What is the fate of the Universe?
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ROSAT image
–hot gas seen in X-rays would have dispersed if it were held in place
ONLY by gravity of mass that is producing light in this image (the socalled "luminous mass")
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The nature of this dark matter, and the associated "missing mass
problem", is one of the fundamental cosmological issues
of modern astrophysics.
More Ways to Measure Mass
Superclusters: largest scale of mass density
–aggregate of several clusters of galaxies, extending over about 10
megaparsecs
–our local supercluster is an extended distribution of galaxies centered
on the Virgo cluster, some 10 to 20 megaparsecs distant
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The mass between us and Virgo tends to decelerate the recession
of our galaxy relative to Virgo, as expected according to
Hubble's law, by about 10 percent.
–deviation from the uniform Hubble expansion can be mapped out for
the galaxies throughout this region, and provides a measure of the
mean density within the Virgo supercluster.
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Over the extent of our local supercluster, about 20 megaparsecs
–ratio of mass to luminosity equal to approximately 300.
Hot vs Cold
Scientific discussions of dark matter typically consider two
extremes
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Hot Dark Matter
Cold Dark Matter
Hot Dark Matter
Composed of particles that have zero or near-zero mass (the
neutrinos are a prime example)
 The Special Theory of Relativity requires that massless particles
move at the speed of light and that nearly massless
particles move at nearly the speed of light

–must move at very high velocities
–form (by the kinetic theory of gases) very hot gases
Cold Dark Matter
Objects sufficiently massive that they move at sub-relativistic
velocities
 Form much colder (that is, slower moving) gases.
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The difference between cold dark matter and hot dark matter is
significant in the formation of structure
–high velocities of hot dark matter cause it to wipe out structure on
small scales.
Current Beliefs on Dark Matter
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All theories and observations currently point to 90 – 99% of the
mass of the Universe being in the form of dark matter
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What type of particles can make up this material?
Current Beliefs on Dark Matter

The known neutrinoes have problems as candidates for dark
matter because they are relativistic (hot dark matter)
–they erase fluctuations on small scales
–relativistic neutrinos could form large structures like superclusters,
but would have trouble forming smaller structures like galaxies
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These arguments might be at least partially invalidated if one of
the types of neutrinos (the tau neutrino is the obvious
candidate) is considerably more massive than the electron
or muon neutrino.
Current Beliefs on Dark Matter
On smaller scales (galaxies and clusters of galaxies), dynamical
estimates of mass indicate that 90% of the total mass is
not seen
–implies that the mass density of the Universe is 10% of the closure
density
–sub-luminous mass could be normal (baryonic) and be locked up in
stellar remnants (white dwarfs, neutron stars, black holes) or just in
very dim stars called "Brown Dwarfs”
–recent evidence for possible observation of one of these very dim
Brown Dwarfs
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The big bang nucleosynthesis puts the 10% limit on this idea
–missing mass is more than 90%, it cannot be (entirely) baryonic
Current Beliefs on Dark Matter
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Large scale structure (e.g. the distribution of galaxies) very hard
to understand
–smooth microwave background as measured by the COBE satellite
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To accommodate this, go to a mixed dark matter model in which
you have some hot dark matter (for the large scale) and
some cold dark matter to act as a seed for galaxy
formation
–None fit the data using the critical density
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Best models to date suggest mixed dark matter and an overall
cosmological mass density of 20-30% of closure
–to retain inflation, with its inescapable prediction that the Universe
must be flat, requires re-invoking Einstein's cosmological constant meaning the Universe has vacuum energy (negative pressure) and is
currently accelerating.
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This makes our cosmology complicated, but much recent data is
pointing this way.
Current Beliefs on Dark Matter
Neutrinos have mass
Supernova 1987a neutrino time of flight studies
 Solar Neutrino experiment
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–not a mass that can cosmologically dominate.
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We cannot currently test for various supersymmetric particles
which would only be created at very high energy (e.g. the
early Universe)
–many viable potential particles that are consistent with the Standard
Model of particle physics, that would remain unnoticed in any
accelerator experiments.
Dark Energy

Einstein's Law of General Relativity concluded the Universe
must collapse under the relentless pull of gravity
–assumed the Universe to be static and unchanging
–added something he called the "cosmological constant" whose
gravity is repulsive, though he had no idea if it was real
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Shortly afterwards, astronomer Edwin Hubble says: Universe
is expanding!
–assumed that the Universe slowing down under gravity and might
even come to a halt
–leads Einstein later to say that his cosmological constant was the
biggest blunder of his career
–now appears Einstein was on the right track after all!
What is “Dark Energy”?
The source of the repulsive gravity may be something akin to
Einstein's cosmological constant -- referred to as the energy of the
"quantum vacuum," a subatomic netherworld pervading space -- or
it may be something entirely new and unexpected.
Universal Expansion
We now have observations which suggest the expansion of the
Universe is accelerating rather than slowing down. Whatever is
driving this acceleration is unknown at present and is referred to as
“dark energy”.
Evidence for an accelerating expansion comes from observations of
the brightness of distant supernovae. We observe the redshift of a
supernova which tells us by what factor the Universe has expanded
since the supernova exploded. This factor is (1+z), where z is the
redshift. But in order to determine the expected brightness of the
supernova, we need to know its distance now. If the expansion of
the Universe is accelerating, then the expansion was slower in the
past, and thus the time required to expand by a given factor is
longer, and the distance NOW is larger.
Yes, This IS Confusing...
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If the expansion is decelerating, it was faster in the past and the distance
NOW is smaller. Thus, for an accelerating expansion the supernovae at
high redshifts will appear to be fainter than they would for a decelerating
expansion because their current distances are larger.
Just believe me…we can tell by observations.
Expansion is Accelerating!
The Hubble discovery reinforces the startling idea that the Universe
only recently began speeding up; it offers tantalizing observational
evidence that gravity began slowing down the expansion of the
Universe after the Big Bang, and only later did the repulsive force
of dark energy win out over gravity's grip. The record-breaking
supernova appears relatively bright, a consequence of the Universe
slowing down in the past (when the supernova exploded) and
accelerating only recently
HST Observation Image
What We See
This supernova appears to be one of a special class of explosions
that allows astronomers to understand how the Universe's
expansion has changed over time, much as the way a parent follows
a child's growth spurts by marking a doorway. It shows us the
Universe is behaving like a driver who slows down approaching a
red stoplight and then hits the accelerator when the light turns
green.
Long ago, when the light left this distant supernova, the Universe
appears to have been slowing down due to the mutual tug of all the
mass in the Universe. Billions of years later, when the light left
more recent supernovae, the Universe had begun accelerating,
stretching the expanse between galaxies and making objects in
them appear dimmer.
What is the fate of the Universe?
Understanding Dark Energy will
provide crucial clues in the quest
to unify the forces and particles
in the Universe.