Astronomy 182:The Origin and Evolution of the Universe

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Astronomy 182The Origin and Evolution of the
Universe
Lecture 5


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Assignment
Today Hand in first 3-page essay summarizing
your understanding of Ferris, Chapter 2, along
with 1 page of questions on issues you do not
understand or feel were not presented clearly in
the book or in class. For next week Read
Chapter 2 of B. Greene, The Elegant
Universe Essay on that chapter due April 16.

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Today
Newtonian Cosmology
Alternative cosmologies
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Newtonian Cosmology
How does the size (scale factor) a(t) of the
Universe evolve? Consider
a homogenous ball of matter
Kinetic Energy mv2/2

Gravitational
Potential Energy -GMm/d
(Newton) Conservation of Energy Kinetic
Potential Total E constant

mv2/2 - GMm/d E Now
use vHd (Hubble) and M?V(4?/3)?d3 to find
H2 -
(8?/3)G? 2E/md2 -K/a2 where H Hubble
parameter expansion rate (H quantifies
time rate of change of a(t))
M
m
d
density of Universe
Friedmann equation
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Satellite Analogy
Conservation of Energy Kinetic Potential
Total E constant
mv2/2 - GMm/d E Same equation
governs orbits of satellites around the Earth
v lt vescape Elt0 bound
elliptical orbit (comm. satellites) v
vescape E0 marginally unbound
(barely escapes) v gt vescape Egt0
unbound orbit, satellite escapes to

infinity (e.g., Voyager)

Elt0
E0
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Friedmann Equation
H2 - (8?/3)G? 2E/md2 -K/a2
Define the critical density ?crit
3H02/8?G Subscript

10-29 grams/cm3 0 denotes


present and
the density parameter ?0 ?/?crit
epoch Then ?0 gt 1
implies Elt0 negative Energy, U.
recollapses (closed) ?0 1 implies
E0 Zero Energy, U. marginally expands

forever (open) ?0 lt 1
implies Egt0 positive Energy, U.
expands forever
1 - ?0 -K/a02H02
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Empty constant velocities
Accelerating
Size of the Universe
Open
Today
Will the Universe Expand forever or recollapse in
a Big Crunch?
Closed
Gravity of matter slows down expansion
Cosmic Time
Big Bang
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Friedmann Equation
1 - ?0 -K/a02H02
In Einsteins General Relativity K curvature
of space ?0 gt 1 implies Kgt0 positive
curvature (3-sphere),
U. recollapses (closed) ?0
1 implies K0 zero curvature (flat
Euclidean space),
U. marginally expands forever ?0
lt 1 implies Klt0 negative curvature
(3-d saddle),
U. expands forever
GEOMETRY IS DESTINY (almost)
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Einstein space can be globally curved
Kgt0 K lt 0
K 0 Closed
open
flat
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Fate of the Universe Will the
Universe expand forever or recollapse in a Big
Crunch? Is the average density of matter in the
Universe smaller or larger than the
critical density, i.e., is ?0 smaller or larger
than 1? We will study this question later in the
course. Complications We cannot measure the
average density by just inventorying the
masses of all objects we see in the Universe and
dividing by the volume, because we know
there are objects we do NOT see directly
(i.e., which gravitate but do not emit light)

DARK MATTER ?visible matter 0.01
while best current estimate is ?dark matter
0.3 but even this is not the whole story
Dark Energy with ?dark energy 0.7 is
causing the Universe to accelerate
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Some have (simplistically) characterized
cosmology as the search for 2 numbers
expansion rate H0
density parameter ?0 In fact, if
Dark Energy exists, then additional number(s)
are needed to characterize the cosmological model
describing our Universe. In particular, Dark
Energy breaks the unique correspondence
between Geometry and Destiny (crunch or
continued expansion). This is due to the fact
that Dark Energy exerts a repulsive
gravitational force that causes the
expansion to accelerate, while the attractive
gravity of ordinary matter causes the
expansion to slow down. We will discuss Dark
Energy later in the course as well.
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The Big Bang Singularity at t0 Running
the expansion backward in time, the known laws of
physics break down before one gets back to
the singularity of infinite Temperature and
density. Our basic understanding of Space Time
(spacetime), based upon Einsteins Theory of
General Relativity, must break down when the
Universe was around
tPlanck 10-43 seconds old
TPlanck 1032 degrees At this time, the
classical description of Spacetime (our
notion of space and time) breaks down
quantum fluctuations of spacetime become large.
Requires a theory of Quantum Gravity (perhaps
provided by Superstring Theory) to go beyond
this point. (See B. Greene, The Elegant
Universe)
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Are there plausible Alternative Cosmological
models? Degrees of departure from the
Standard Cosmology 1.
Socialism Models that
incorporate the expansion of the Universe,
but not the Big Bang.
Example Steady State Model
2. Radical anarcho-syndicalist
fringe Models that reject
both expansion and the Big Bang.
Example Tired Light model
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Alternatives to the Big Bang?
Steady State Universe conceived in 1949
by Bondi, Gold, and Hoyle in response to
the Age Crisis of the Big Bang (prompted by
Hubbles too-large value for his
constant) Theoretical Motivation Perfect
Cosmological Principle (Universe homogeneous
in time as well as space) Postulates
continuous creation of matter to fill in space
between galaxies, so that the density remains
constant as Universe expands. Universe
infinite in time space, no Big Bang. This
model is expanding but is not evolving.
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Problems for Steady State Model
Continuous creation of matter violates
well-established Principle of Conservation of
Energy requires new Physics which has no
other fundamental motivation. Galaxy properties
and the density of galaxies and of Quasars
are now observed to evolve with time. Chief
difficulty origin for the isotropic Cosmic
Microwave Background radiation (which arises
naturally in the Big Bang model) is
unexplained and likely inexplicable. Also,
origin of light element abundances (H, He, Li, D)
unexplained (arise naturally in Big Bang).
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Radical alternatives to the expanding Universe
These start from the premise that redshifts are
NOT due to recession velocities, so cannot
infer expansion from Hubbles Law. However,
no alternative explanation for redshift has been
put forward that is physically plausible
consistent with the now very large body of
redshift data (approaching 1 million galaxy
redshifts measured).
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Non-cosmological redshifts?
H. Arp observed a number of high-redshift
quasars which appear to be associated with
low-redshift galaxies. He concluded the
redshift cannot be an indicator of distance.
Are these just chance superpositions of objects
on the sky, or real associations? Arp
there are more such associations than can be
explained by chance superposition. Most other
cosmologists 1) need a carefully done survey
to make such a statistical statementArp did
not do this. 2) such superpositions are
expected by gravitational lensing
foreground galaxy makes background objects
brighter, thus more likely to find (looking
for keys under the lamppost).
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Low- Redshift Galaxy
High- Redshift Quasar
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Gravitational Lensing
Basically, the same effects that occur in more
familiar optical circumstances magnification
and distortion
Objects farther from the line of sight are
distorted less.
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Gravitationally Lensed Quasars
We only find high-redshift objects lensed by
low-redshift galaxies, not the other way around
? redshift IS an indicator of distance
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Clusters of Galaxies Size 1025 cm Megaparsec
(Mpc) Mass 1015 Msun Largest
gravitationally bound objects galaxies, gas,
dark matter
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Cluster of Galaxies
giant arcs are galaxies behind the cluster,
gravitationally lensed by it
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Tired Light Model
Postulates that light loses energy as it travels,
so redshift is not caused by expansion
of the Universe. Objections 1. Requires
an unobserved electromagnetic
interaction to cause light to lose energy this
way. 2. In general, does not predict the
observed linear redshift-distance
relation found by Hubble. 3. Does not
automatically imply that the redshift
is independent of light wavelength, as
observed. 4. Required scattering of
light would smear out appearance
of distant sources, not observed.
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Fractal Universe Model
Postulates that the Universe is not homogeneous
over large scales no well-defined mean
density (in contrast to the Cosmological
Principle). i.e., ?(R) M(R) does not
converge as R ? ? 4?R3
3 Inconsistent with observed spatial
clustering of galaxies. No explanation for
Microwave background its isotropy.
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Evidence in Favor of Expansion Interpretation of
Redshifts How do we know that redshifts
correspond to distance (rather than to
something else)? Redshifts are observed to be
independent of wavelength, linear with
distance, isotropic, always (except for 10
nearby galaxies) positive (i.e.,
recession). Gravitational lenses high-redshift
(background) objects are lensed by
low-redshift (foreground) objects. CMB
temperature at moderate redshift CN (cyanogen)
molecules as thermometer (rotational vibrations
excited by microwave background photons),
consistent with
TT0(1z) Conclusion NO plausible alternatives
to expansion or Big Bang