Lecture 30: Cosmology II: The Fate of the Universe
Astronomy 101/103
Terry Herter, Cornell University
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Lecture
Topics
  • The Evolution of the Universe
    • The Critical Density
    • The Age of the Universe
  • The Cosmological Constant
  • The Accelerating Universe


Universe's Fate?

  • Consider a planet; shot a spacecraft from the surface (single shot)
  • At the escape velocity (intermediate between the high and low velocity cases) the spacecraft just escapes.




  • Looking at the evolution of the universe similar to escaping from a planet.

Evolution of the
Universe
  • Possible "histories" of the universe



Critical Density
  • Will the universe keep expanding forever or stop expanding and collapse?
  • If the mass density is:
    • large eventual collapse (bound)
    • small expansion forever (unbound)
  • The critical density is the dividing line between the bound and unbound cases.
  • For H0 = 75 km/sec/Mpc
    • critical density ~ 10-29 g/cm3, or about 6 H-atoms/m3
  • This corresponds to 1 MW galaxy/Mpc3
  • Define WM as the ratio of the actual density to the critical density
    • Sometimes this will simply be called W.

WM and Ho
  • WM determines the fate of the universe.
    • Expanding forever vs. eventual collapse
  • H0 determines the age of the universe
WM
Age
 Comment
0
1/H0
Empty Universe
1
(2/3)x(1/H0)
Critical Universe
  • We've already discussed H0.
  • But what is omega? (numerically)

Age of the Universe
(again)


Measuring
WM
Two ways to determine WM are:
  • Galaxy Counts -
    • Directly measure amount of mass in the universe.
  • Deceleration of the Universe -
    • Measure how much faster galaxies were moving in the past.

Galaxy Counts
  • Counting galaxies and adding up their mass yields WM ~ 0.045.
  • But... This misses most of the mass.
  • Masses can be found from (gravity):
    • the motions of stars in galaxies
    • the motions of galaxies in clusters
  • Gravity implies much more mass than we see in stars/galaxies dark matter.

 

  • We can't "see" > 90% of the mass in the universe, except by gravity!
  • Possible presence of:
    • MACHOs (Massive Compact Halo Objects)?
    • WIMPs (Weakly Interacting Massive Particles)?
  • Correcting for the missing mass due to dark matter gives WM ~ 0.35.

Deceleration of the Universe
  • We need a "standard candle" to measure distances and recessional velocities independently.
  • It is difficult to find a standard candle.
  • Galaxies were different in the past
  • Type Ia Supernovae now appear to work very well. (Caused by accretion onto a white dwarf.)

A Funny Thing
Happened ...
  • Type Ia SN results indicate that the universe is accelerating!
    • Acceleration => the expansion rate is increasing
  • Contrary to our initial bias the it should be decelerating
    • Deceleration => the expansion rate is slowing

The
Cosmological
Constant

The Cosmological Constant (L)

  • Introduced by Einstein into General Relativity
    • Thought the universe was static
    • Can be repulsive or attactive
    • Called it his biggest mistake
  • But now we may need it!
    • As a repulsive force

  • This is not the only way to handle this problem, but you still need a repulsive force to explain the acceleration of the universe.
  • A fifth force dubbed "Quintessence" has been postulated.

The Three
Omegas
  • Besides H0 we need three more parameters to determine the evolution of the universe
  • WM, WL, and Wk as
    • WM, is defined as before
    • WL defines the Cosmological Constant part
    • Wk defines the geometry of the universe (more later)
  • However, Wk can be written in terms of the other two so we really only need two Omegas
    • Wk = 1 - WM - WL
  • Will the universe keep expanding forever or stop expanding and collapse?

The Two
Omegas
  • So now we only need to know WM and WL.
  • With no (zero) cosmological constant
    • Have WM and Wk with Wk = 1 - WM
  • With a non-zero cosmological constant
    • Have WM, WL, and Wk with Wk = 1 - WM - WL
  • These determine the dynamics and geometry of the Universe
    • WM and WL set acceleration/deceleration
    • Wk sets the geometry

Accelerating
Universe


  • The expansion velocity in the past depends upon WM and WL.
  • Galaxies would be moving faster in the past for a non-empty universe.

Type Ia SN
Results
  • Observations of the distance modulus (m-M) for Type Ia supernovae and WMAP (Microwave Anisotropy Probe) seem to be best fit with
    • WM = 0.27 and WL = 0.73 (and from Hubble measurements H0 = 71 km/sec/Mpc)
  • Good spectroscopic data exists only for supernovae at z < 1.
  • Infrared observations of the light curve of a more distant supernova in the Hubble Deep field show agreement with the above Omegas.
    • These latter measurements do not have detailed spectroscopy because the source was too faint, so they are more uncertain.
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