Cosmology

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Cosmology

• Universe everything we can detect
• Questions
• Infinite or finite?
• Is there an edge, a center?
• How old is it?
• Olbers Paradox (actually discussed much earlier,
  by Digges, Kepler, Halley)
• Why is the sky dark at night?
• Assumptions static and infinite Universe
• Universe is uniformly
  filled with stars

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• Then, in any direction, line-of-sight will
  intersect a star ? the sky should be as bright as
  the surface of a star?
• (of course, L is proportional to 1/distance2, but
  number of stars increases as distance2)
• Olbers suggested light blocked by intervening
  clouds of matter ? cant work, because clouds
  would heat up and radiate (sky would still be
  bright)
• were our initial assumptions wrong?

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• A solution suggested by E.A. Poe (yes, him!)
• What if the Universe were created at some time in
  the past?
• With a long enough look-back time, there would
  be no stars.
• Basic Assumptions of Cosmology
• Homogeneity matter uniformly distributed in
  space
• Isotropy Universe looks the same in all
  directions
• Universality physical laws we know on Earth
  apply everywhere

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• 2) are known as the Cosmological Principle
• Note the assumptions only apply on the largest
  scales there is ample evidence for local
  inhomogeneity, anisotropy (e.g. galaxies)
• Also evolutionary changes not considered
• Expansion of the Universe
• Hubble detected redshifts of galaxies
• Velocity proportional to distance (like raisins
  in a rising loaf of bread)
• But are redshifts really due to motion?

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• General Relativity
• Expansion of Universe is really an expansion of
  space-time itself
• Photons are stretched when traveling through
  expanding space-time ? hence, shifted to longer
  wavelengths
• Curvature of Space-Time
• General Rel. mass curves space-time
• We experience the curvature as a gravitational
  field
• The total amount of mass defines the geometry of
  the Universe

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• How can we comprehend this?
• Imagine an ant walking on an orange e.g., a
  two-dimensional Universe finite, but unbounded
  (i.e., edge-less)
• 3 different curvatures (geometries) possible
• Zero flat Universe in this case, the area
  of circle p r2 same for larger radii
• Positive closed Universe as radius of a
  circle increases, the area increases at lt p r2
• Negative open Universe as radius of a circle
  increases, the area increases at gt p r2

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• Now, in 3-dimensions, we deal with volumes of
  spheres instead of areas of circles.
• In flat Universe volume 4/3 p r3
• How can we determine the curvature?
• Count galaxies if the number increases
  proportional to r3, Universe is flat if the
  number increases more quickly with radius, the
  Universe is open, if more slowly, its closed
• Also both open and flat cases Universe is
  infinite closed case Universe is finite, but
  edgeless (like the orange)

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• Big Bang Theory
• Universe began in a high temperature, high
  density state ? not at a single point, the Big
  Bang filled entire volume of the Universe
• We can look back to the era of the Big Bang
  radiation from that time is highly redshifted (to
  IR, radio)
• Gamov (1948) predicted that early Big Bang was
  hot, emitted blackbody radiation ? in present
  era, wed see a redshifted blackbody spectrum

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• Penzias Wilson (early 1960s won Nobel Prize,
  1978) radio measurements of the sky found
  noise
• Noise turned out to be Cosmic Microwave
  Background Radiation
• Butwas it a black-body?
• Cosmic Background Explorer (COBE) 1989 confirmed
  it was B-body (T 2.7 K, in agreement with
  predictions) z 1000
• Originally from gas clouds of T 3000K
• Almost perfectly isotropic some blueshift in
  direction of the Milky Ways motion towards Virgo
  Cluster

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• A timeline
• At t 0 matter in state where physics not well
  understood
• At t 10 millionths of a second T gt 1012K,
  density 5 x 1013 gm/cc (same as an atomic
  nucleus)
• At this point, Universe was entirely in the form
  of radiation (but, E M c2)

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• And ?-rays decay ? particles, antiparticles
• As Universe expands wavelengths increase,
  Energy decreases ? cools off
• At t 0.0001 sec, T lt 1012 K, ?-ray decay can no
  longer produce protons, neutrons (although
  electron/positron pairs can be produced until t
  4 seconds)
• Cooling/expanding continue until atomic nuclei
  form

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• At t 2 minutes p n ? deuterium
• At t 3 minutes deuterium ? helium
• But, nothing heavier (no stable atomic nuclei
  with atomic weights 5 8)
• At t 30 minutes nuclear reactions mstop 25
  of mass in He nuclei rest is in H nuclei (i.e.
  protons) same as oldest stars
• Up until t 106 years dominated by radiation
  gas ionized

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• Photons cant travel far (interact with
  electrons) matter and radiation are coupled
• At t 106 years cool enough to form atoms gas
  becomes transparent to radiation (Recombination)
  T 3000 K this is the point where the CMB
  radiation originates
• Matter now dominates

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• Future of the Universe
• Question of density ? hence, geometry
• critical density 4 x 10-30 g/cc results in a
  flat Universe
• If density lt critical density ? open
• If density gt critical density ? closed
• If the Universe is open or flat ? will expand
  forever gravity may slow expansion, but will
  never stop it

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• If Universe is closed expansion stops, followed
  by contraction and collapse to high density state
  (Big Crunch)
• Oscillating Universe? Probably not.
• How do we measure the density?

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• Galaxy counts (but, hard to really determine the
  mass) and what about dwarf galaxies?
• Best estimate 5 x 10-31 g/cc
• But gt 90 may be in form of Dark Matter from
  study of lensing, mass 10 times greater than
  estimated from luminosity halos 10 to 20 times
  larger than visible parts of galaxies ? so, 10 x
  more mass

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• Deuterium
• Amount depends on density of early Universe
• Can be destroyed, but no longer created
• In gas near Quasars, 25 D per every 106 H atom
  tells us that the Universe was not so dense that
  more D ? He
• Taking all into account, maybe 5 of mass
  required for a flat Universe

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• Regarding Dark Matter
• Exotic non-interacting particles (WIMPs)
• Neutrinos (not enough of them) also, cant
  account for galaxy formation (too hot)
• MACHOs massive compact halo objects should act
  as gravitational lenses a few detected, but not
  enough

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• Quantum Universe
• flatness why a flat Universe (note, we are
  within a factor of 10 of critical density)
• horizon problem isotropy of CMB (same to 1
  part in 1000)
• At time of recombination, gas was transparent to
  radiation but not enough time for signals to
  travel from one region to another

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• Inflationary Universe
• Sudden expansion when Universe very young
• 4 fundamental forces Gravity, Electromagnetism,
  Strong, Weak Unification Electromagnetism and
  Weak force same at high energies
• Grand Unification Theories in early Universe,
  all 4 forces unified
• At t 10-35 sec, fundamental forces separated
  huge amounts of energy released, Universe
  inflated by factor of 1020 to 1030

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• Solves problems inflation forces curvature to
  zero (Flatness) and temperatures equalized
  before inflation (Horizon)
• Quantum Mechanics predicts spontaneous creation
  of matter/anti-matter -- maybe how Universe
  appeared in the first place

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• Age of Universe
• Distance/velocity time, but v H x d
• So, T (1 / H) x 1012 years
• Doesnt account for gravity
• If H 80, Universe is younger than oldest
  globular clusters!
• Best current values age of globulars 11 x 109
  years, H 70 Universe is 13.5 x 109 years, so
  OK, but a concern

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• Cosmological Constant
• Einstein (1916) didnt know Universe was
  expanding --- need force to keep it from
  collapsing ? Cosmological Constant
• Hubble saw redshifted galaxies, so ? 0,
  everything Ok, right?
• By looking at Type Ia Supernovae in very distant
  galaxies, get distances expected to see
  expansion slow down ? But saw just the
  opposite!!

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• Thus, ? is not 0 what is going on? Energy from
  Q.M. processes in empty space? Maybe.
• Anyhow, if ? gt 0, Universe could be older than
• 1 / H (so, no worries about stars older than the
  Universe)
• Also critical mass normal matter 5 dark
  matter 25 rest in form of empty space (E Mc2)

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• Structure of Universe
• Superclusters groups in filaments/walls
• CMB is uniform
• How did the structure form out of the hot gas in
  the Big Bang?
• Also must have occurred early (Quasars at
  look-back time 93 of the age of the Universe)
• Cold dark matter galaxies
• Hot dark matter filaments
• But, what are the galaxy seeds QM
  fluctuations, magnified by Inflation consistent
  with small CMB fluctuations detected by COBE