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Transcript
Cosmology
• Universe – everything we can detect
Questions:
• Infinite or finite?
• Is there an edge, a center?
• How old is it?
Olber’s 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
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  can’t work, because
clouds would heat up and radiate (sky
would still be bright)
were our initial assumptions wrong?
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:
1. Homogeneity – matter uniformly distributed in
space
2. Isotropy – Universe looks the same in all
directions
3. Universality – physical laws we know on Earth
apply everywhere
1) & 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?
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
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:
1. Zero – “flat” Universe – in this case, the area of
circle = π r2 – same for larger radii
2. Positive – “closed Universe – as radius of a
circle increases, the area increases at < π r2
3. Negative – “open Universe – as radius of a circle
increases, the area increases at > π r2
Now, in 3-dimensions, we deal with volumes of
spheres instead of areas of circles.
• In “flat” Universe: volume = 4/3 π 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, it’s closed
Also: both open and flat cases – Universe is infinite;
closed case – Universe is finite, but edgeless (like
the orange)
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, we’d see a redshifted blackbody spectrum
• Penzias & Wilson (early 1960’s ; won Nobel
Prize, 1978) – radio measurements of the sky;
found “noise”
• “Noise” turned out to be Cosmic Microwave
Background Radiation
But…was 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 Way’s motion towards
Virgo Cluster
A timeline:
• At t = 0; matter in state where physics not
well understood
• At t = 10 millionths of a second –T > 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)
• And γ-rays decay  particles, antiparticles
• As Universe expands – wavelengths increase,
Energy decreases  cools off
• At t = 0.0001 sec, T < 1012 K, γ-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
• 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
Photons can’t 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
Future of the Universe:
• Question of density  hence, geometry
• “critical density” – 4 x 10-30 g/cc; results in
a “flat” Universe
• If density < critical density  open
• If density > critical density  closed
• If the Universe is open or flat  will
expand forever; gravity may slow
expansion, but will never stop it
• 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?
• Galaxy counts (but, hard to really determine
the mass); and what about dwarf galaxies?
• Best estimate ~ 5 x 10-31 g/cc
• But > 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
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
Regarding Dark Matter:
• Exotic non-interacting particles (WIMPs)
• Neutrinos (not enough of them); also, can’t
account for galaxy formation (too “hot”)
• MACHOs – massive compact halo objects;
should act as gravitational lenses – a few
detected, but not enough
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
“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
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
Age of Universe:
Distance/velocity = time, but v = H x d;
So, T = (1 / H) x 1012 years
• Doesn’t 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……
Cosmological Constant:
• Einstein (1916) – didn’t know Universe was
expanding --- need force to keep it from
collapsing; Λ – “Cosmological Constant”
• Hubble saw redshifted galaxies, so Λ = 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!!
• Thus, Λ is not = 0; what is going on? Energy from
Q.M. processes in empty space? Maybe….
• Anyhow, if Λ > 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)
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 lookback 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