14 Cosmology I

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14 - Cosmology - I
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Before the expansion of the universe was
discovered, Part 1
In a finite universe all the stars would fall
into a clump
Newton deduce that the universe had to be
infinite in size for it to be stable against
gravity
In a perfectly uniform infinite universe the
forces are balanced
But the slightest deviation from uniformity will
cause local fragmentation..
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Why is the Night Sky Dark? Olbers Paradox
In an infinite universe, every line of sight
will intersect the surface of a star - so the
entire sky will be as bright as, say, the
observed surface of the Sun It isnt! WHY NOT?
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1901 - Kelvin realizes that universe would need
to be 1014 pc in size and about 3x1014 years old
for light from most distant star to reach us.
Olbers Paradox is avoided if these conditions
are not met. (Note Same viewpoint elucidated in
1848 by American poet Edgar Allen Poe! He
actually listened to astronomy lectures and
thought about the implications..)
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Before the expansion of the universe was
discovered, Part 2
1915 - In order to keep the Galaxies in the
universe from falling into a clump, Einstein
introduced a repulsive term in GR to counteract
gravity - the Cosmological Constant - ?
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1929 - Hubble Humason publish work on expanding
universe. Einstein retracts cosmological
constant, my biggest blunder, as it was no
longer needed,
Galaxy Redshifts the Hubble Law
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The Cosmologists View of the Expansion of the
Universe
NOTE Every galaxy sees the same expansion, the
same H0. While everyone sees themselves as the
center of the expansion, in fact no one is!
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and of the cosmological redshift - NOT a Doppler
shift, but a stretch in the wavelength as the
universe expands while the wave is in flight - as
it expands from a size R0 to a size R, the
wavelength stretches from the emitted value ?0 to
the observed value ?.
Note that all the galaxies were closer in the
past. At what point in time were they touching?
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The Hubble Constant the Age of the Universe
v
R
R
v
In a universe that does not accelerate or
decelerate, the time since expansion started, the
age of the universe, is just 1/H0 - the Hubble
Time
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A Note on Nomenclature
In the case of a universe with no
acceleration/deceleration, vs are constant but
Rs continue to increase Consequence someone who
measures H v/R in the distant future will get a
smaller value! Hubbles constant is not really
a constant, but changes with time - H(t). Many
prefer the term the Hubble Parameter The value
we measure TODAY is given the designation H0
(pronounced aitch-naught)
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But a universe with gravity ought to decelerate!
Expansion makes galaxies move further apart, but
gravity makes them come closer together. Which
one wins?
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In the fight between kinetic energy of expansion
and gravitational (potential) energy of
contraction, whichever one is bigger wins!
for those of you who simply must know
?? is the mass density g/cm3 of matter in space
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3 possible Outcomes
The future depends on the value of critical
density ?c ?(E0)
If ? gt ?c then gravity wins and universe
re-collapses If ? lt ?c then expansion wins and
universe expands forever If ? ?c then expansion
slows to a stop after infinite time
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If ?01 (we are at the critical density), the age
of the universe is precisely 2/3 of the Hubble
Time
size scale
2/(3H0)
time
1/H0
For H072 km/s/Mpc, Hubble time14 billion
years 2/3 of this is 9 billion years. The oldest
stars are 12 billion years old..
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The Geometry of the Universe
In a universe with only expansion gravity,
there is a 1-to-1 correspondence among the
geometric shape of space, the fate of the
universe, and the value of ?0!!
geometry fate