Astronomy 10

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Astronomy 10

• Lecture 24

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The History of the Universe
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Deepest picture ever taken by HST. Thousands of
galaxies out to z3 !!
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Using HST to Study the Past
Galaxies of the past dont look like z0 galaxies!

• Z 2
• Z 1

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The Cosmological Principle

• The observed clustering of galaxies is very
  pronounced on small scales, but becomes weaker on
  large scales
• On largest scales, the universe appears
  homogeneous (same in all locations) and isotropic
  (same in all directions)
• Cosmological Principle states that at any instant
  of time, a typical observer in a randomly chosen
  galaxy sees the same Universe on large scale as
  us.
• All observers see an isotropic Hubble expansion,
  a Universe that all condensed at a point at time
  approximately 1/H0 in the past.
• As Universe expands, its density must decrease,
  and in the past its density must have been
  extremely high.

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• Consider an imaginary coordinate grid on which
  there is a set of observers. (e.g. fixed
  latitudes and longitudes on an expanding balloon
• Characterize the expansion of the Universe by a
  scale factor R(t). Observers sit on fixed grid
  points Universe expands.
• The problem of cosmology is then to describe R(t)

R(t) is the scaling of, e.g. the distance between
points C and D
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• Einstein, after completing General Theory of
  Relativity in 1915, studied cosmological
  implications of his theory, and soon realized
  that R(t) constant (a static Universe), was not
  a solution of his equations R(t) had to either
  increase or decrease with time
• This was prior to discovery of expansion of
  Universe, and even Einstein could not conceive
  that the Universe was expanding, so he added a
  fudge factor to his beautiful equations, known as
  the cosmological constant ?. This term made it
  possible for R(t)constant to be a solution.
• After discoveries of Hubble in 1929, Einstein
  rejected the ? term, labeling it "the biggest
  mistake of my life". Prediction of expansion of
  the Universe would have been 4th major prediction
  of G.R.

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Evolution of Expansion parameter

• We can get a good sense of how R(t) behaves by
  carving a spherical volume out of homogeneous
  Universe.
• Mass contained within sphere of radius r
• M(4?/3) ?0 R3, where ?0 is the mean density.
• Energy conservation equation for galaxy on edge
  of sphere E mv2/2 (-GMm/R)
  constant (with M (4?/3) ?0 R3 and
  v H0R )
• This is same equation we saw in Newtonian
  gravity!
• Bound Universe. if Elt0,
• unbound Universe. if Egt0,
• critical U. if E0 critical density ?0 (3H02
  /8?G)
• 5x10-30 gm/cm3
• 3 H atoms/m3 !!!
• (contrast to galaxy, in which density is ? 1
  atom/cm3 106 atom/m3 )
• Note how expansion of Universe is slowing down,
  age of Universe is less than 1/H0.
• For the case of critical density, age 2/(3H0)
  
  9 (70/H0) billion yrs.

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Curvature in the Universe

• Flat (If E0) -- Euclidean geometry there is
  one unique line parallel to another, passing
  through a given point. (C 2?R --- no curvature
  in circle)
• This universe is infinite, expands forever,
  barely.
• Positive Curvature (e.g. surface of sphere) (if
  Elt0) all lines eventually intersect. (Clt 2?R )
• This universe is finite, no edge, eventually
  recollapses.
• Negative Curvature (e.g. surface of saddle) (if
  Egt0) there are many parallel lines to a given
  line
• (C gt 2?R)
• This universe is infinite, no edge, has escaped
  its own self-gravity and expands forever.

Note, in contrast to black hole, the space
curvature is uniform. Matter generates
curvature.
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What is R(t) for our Universe?
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The Cosmological Redshift

• It is incorrect to attribute the observed
  redshift of galaxies to Doppler velocities. In
  fact, the distant galaxies are not moving at all
  it is space that is expanding.
• Wavelengths are stretched simply because of the
  expansion of space.
• If a wave is emitted at time te and received at
  time t0, then the ratio of emitted to observed
  wavelength is simply ?0/?e
  R(t0)/R(te)
• Thus when we observe a quasar with ?0/?e 5, we
  infer that when those photons were emitted, the
  Universe was 5 times smaller than today.
• Note also that Universe is not expanding into
  anything it already is everything. The space
  does not exist until Universe expands to create
  it. Think only of a grid of comoving observers
  with scale factor R(t) connecting them.
• The Big Bang is not an explosion in any ordinary
  sense it has no center and may have infinite
  extent. Furthermore, there exists a distant shell
  of Universe that, in Doppler interpretation, is
  receding from us at speed vc (infinite
  redshift!). Beyond this shell, matter recedes at
  vgtc this is OK in G.R., since it is not a
  velocity at all.

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Expansion is the growth of the grid pattern!
Balloon could be infinite in extent!

• The fabric of spacetime is manufactured by the
  gravitation of all the mass-energy existing in
  the Universe.

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• Imagine a two dimensional Universe on the surface
  of an expanding balloon. Suppose you were an ant
  living on this Balloon.
• Common Misconception of Expanding Ant world of
  Finite Area
• Expansion of ant world (closed Universe) takes
  place not along observable two spatial dimensions
  (three spatial dimensions) but by world
  (universe) being carried in time to a new 2D
  surface (3D volume) in an unobservable third
  (fourth) spatial dimension. There is NO
  preexisting 2D surface (3D volume) not occupied
  by ants (galaxies) into which the ant world
  (universe) expands.
• The evolution of the
• amount of space available is
• governed by Einstein's theory of
• gravitation (general relativity).
• In a crucial sense, therefore, the
• fabric of spacetime is
• manufactured
• by the gravitation of all the
• mass-energy existing in the
• Universe.

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Measuring the Universe

• How can we determine the curvature of the
  Universe?
• 1. Measure the density, compare it with ?crit
  Define ? ? / ?crit . ?lt1 for
  open
  ?gt1 for closed
• 2. Measure expansion rate long ago to see how
  fast Universe is decelerating (not real
  practical)
• 3. Look at geometrical properties of space
• Sum of angles in triangle 1800 if flatgt1800 if
  positive curvaturelt1800 if negative curvature
  (but space is so close to flat that it is very
  hard to do this!)

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The Critical Density

• We have seen that gravitational attraction
  between galaxies can overcome the expansion of
  the Universe in localized regions.
• how strong must gravity be to stop the entire
  Universe from expanding?
• it depends on the total mass density of the
  Universe
• We refer to the mass density required for this
  gravitational pull to equal the kinetic energy of
  the Universe as the critical density.
• if mass lt critical density, the Universe will
  expand forever
• if mass gt critical density, the Universe will
  stop expanding and then contract
• The value of Ho tells us the current kinetic
  energy of the Universe.
• this being known, the critical density is 1029 g
  / cm3
• all the luminous matter that we observe accounts
  for lt 1 of critical density
• for dark matter to stop Universal expansion, the
  average M/L of the Universe would have to be
  1,000 Msun/ Lsun a few times greater than
  clusters
• This line of research suggests the Universe will
  expand forever!

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How Mass Density affects the Expansion of the
Universe
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Does Gravity alone Influence the Expansion?

• Recent observations of white dwarf supernovae in
  very distant galaxies have yielded unexpected
  results.
• remember, white dwarf supernovae make very good
  standard candles. The supernovae are apparently
  fainter than predicted for their redshifts

• At a given cosmological redshift
• galaxies should be closer to us
• i.e. shorter lookback time
• for greater Universal mass densities
• these supernova are farther back in time than
  even the models for an ever-expanding (coasting)
  Universe predict
• This implies that the Universal expansion is
  accelerating!
• there must be an as yet unknown force which
  repels the galaxies
• a dark energy

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How Mass Density and Dark Energy affectthe
Expansion of the Universe
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The Fate of the Universe
?gt1 ?1 ?lt1 ?lt1 , ?gt0
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How to determine ?

• Diameter of Galaxies, or luminosity of galaxies
  or such standard candles as Supernovae
  (especially of Type I)
• If all galaxies are same size, then curvature of
  Universe can change apparent angular size of
  distant object, or cause deviations from the
  Euclidean law b L/4?d2
• Number of galaxies as a function of distance
  Volume V(4?/3) R3 is true only if space is
  flat.
• Doubling distance ? 8x as many galaxies(lt 8x if
  positive curvature gt 8x if negative curvature)
• Look for signature of flat Universe in CMBR

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Problems with Cosmological Measurements

• Space is very nearly flat and one must look over
  enormous distances to see any curvature effects.
• Effects even at large distances are NOT large, so
  very difficult
• Distances are so large that objects have probably
  evolved considerably in light travel time to
  reach us. How do we know that the intrinsic size
  or luminosity of a distant galaxy is the same as
  typical galaxy near to us?
• Measurements can be fooled by inhomogeneities
  toward object, which introduce extra noise, and
  can lead to biased estimates due to gravitational
  lensing effects (extra focusing and
  magnification)
• We know that there is abundant dark matter. Do
  galaxies act as a fair tracer of the dark matter?

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Atoms are only 4 !!

• Measuring cluster masses shows the CDM is only
  23 of the total. (CDM is an undiscovered
  particle)
• Atoms (like us!) amount to 4. If all mass shines
  about as much as a collection of stars, then ? lt
  0.01 ( a Universe that is very open!!)
• The overwhelming majority is Dark Energy! What
  is the Dark Energy?

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Alternatives to the Big Bang

• Steady State Cosmology (F. Hoyle )
• Based on "perfect cosmological principle". The
  Universe is not only the same to all observers,
  but its properties do not change with time.
• No beginning of time, no end of time.
• Since the Universe is expanding, to keep density
  constant in time, new matter is constantly being
  created (? 1 hydrogen atom/m3/109 years!-- not
  likely to have been noticed locally)
• Problems
• Radio galaxies and quasars are more common at
  large look-back time than at present-- so
  Universe does evolve
• Discovery of the 30 K background radiation in
  1964 killed this theory. Fatal flaw
• Lots of other theories cross my desk every year,
  but none fit the considerable body of evidence
  that is consistent with the Hot Big Bang model

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The Cosmic Microwave Background Radiation (CMBR)

• Penzias and R. Wilson (1964), working for Bell
  Labs in NJ, could not get rid of a persistent
  radio noise affecting a very sensitive
  measurement. Noise came from all directions, was
  extremely isotropic. They scratched their heads
  over what it could mean.
• Meanwhile, Dicke, Peebles, Roll, and Wilkinson,
  were building an experiment at Princeton to
  search for a possible remnant of an early phase
  of the Big Bang.

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Cosmic Microwave Background

• The spectral distribution of this radiation was
  the same as radiation from a 3,000 K object.
• It last interacted, scattered, when T3000 K.
• like the surface of a red giant
• Since then, the Universes size has expanded
  1,000 times.
• cosmological redshift has turned this radiation
  into microwaves.

• This Cosmic Microwave Background, predicted by
  theory
• was accidentally discovered in 1965 by Arno
  Penzias Robert Wilson
• appeared to come from every direction
• had a perfectly thermal spectrum with a
  temperature of 2.73 K

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1st all-sky map of CMBR 70 resolution
WMAP Satellite is still flying. Resolution 20
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The Spectrum of CMBR fluctuations

• The solid curve is the expectation of LCDM model.
  
• The points with error bars are the data (pretty
  close!)

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Conditions in the Early Universe

• The most distant galaxies we observe come from a
  time when the Universe was a few billion years
  old.
• The cosmic microwave background prevents us
  viewing light from before the Universe was
  380,000 years old.
• So how do we know what conditions were like at
  the beginning of time?

• We know the conditions expansion rate of the
  Universe today.
• By running the expansion backwards
• we can predict the temperature density of the
  Universe at anytime in its history using basic
  physics
• we study how matter behaves at high temperatures
  densities in laboratory experiments
• current experimental evidence provides info on
  conditions as early as 1010 sec after the Big
  Bang

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Brief History
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Evolution of a Universe

• Temperature variations in the 380,000 year-old
  Universe serve as a genetic code for the
  structure of the Universe today!

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WMAP full sky map of Anisotropy
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Cosmic Microwave Background Uniform
Homogeneous Universe
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CMB Doppler Effect due toOur Peculiar Motion
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CMB Fluctuations in Temperature
COBE
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