The 19th Century Universe

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CHAPTER 16Cosmology

• The 19th Century Universe
• Olbers Paradox
• Standard Candles
• Galaxies and Quasars
• The Big Bang
• The Universe
• The Missing Mass
• The Cosmological Constant
• Inflation
• The Future

Edwin Hubble (1889-1953)
Pray that theres intelligent life somewhere up
in space cause theres bugger all down here on
earth. - Monty Python The Meaning of Life
Prof. Rick Trebino, Georgia Tech
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19th Century Cosmology
19th-century scientists knew of the solar system,
other stars, and a wide range of other dim, fuzzy
objects that they couldnt resolve, which they
decided were interstellar cloudsnebulaeand some
of which they called spiral nebulae.
They also thought the universe was static and
unchanging.
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The 19th Century Universe
Aside from the few nearby planets and moons and
some nebulae, 19th-century scientists thought
that the earth and sun were surrounded by
infinitely many fixed stars, roughly uniformly
spaced and extending out to infinity in all
directions.
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The inverse square law for intensity
The light intensity reaching earth from a star of
power P a distance R away is IP/(4pR2).
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Olbers Paradox
Calculate the total amount of light reaching the
earth from all the stars in the universe.
The light intensity reaching earthfrom a star
of power P a distance R away will be
IP/(4pR2).
Let the density of stars be r. Take it to be
uniform throughout the universe. The number of
stars from R to RdR away will be
Each spherical shell of stars yields the same
intensity at earth!
So the total starlight power reaching earth will
be
But this is clearly not the case!
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The big problem in cosmology is determining how
far away objects are.
If an object is close, parallax measurements
relative to the fixed stars (far away) can
determine its distance.
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Parallax allowed the discovery of Pluto.
Percival Lowell estimated the position of ninth
planet from deviations in the orbits of Uranus
and Neptune. It was discovered (in 1930) 14
years after Lowell's death very close to Lowell's
predicted location by American Clyde Tombaugh.
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The 20th Century Universe Standard Candles
Standard candles are celestial objects whose
output power, P, is known. Because intensity
diminishes as 1/R2
Measuring the intensity, I, reaching earth of a
standard candle, its possible to measure its
distance, R, away.
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Standard Candle 1 Cepheid Variables
In 1912, American astronomer Henrietta Leavitt
studied Cepheid variables, stars that have
exhausted their hydrogen and pulsate.
One needs a distance measurement from some other
method for at least one Cepheid. The original
Cepheid variable, Delta Cephei, is close enough
that we have a parallax measurement for it.
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Standard Candle 2 Supernovae
Supernovae are gigantic stellar explosions.
Supernova remnant in the Small Megallanic Cloud
galaxy 190,000 light-years away

• The Crab supernova occurred in 1054 and was
  recorded by the Chinese and Japanese. It was
  bright enough to see during the daytime.
• Other supernovae in our galaxy occurred in 1572,
  1604 and 1987.

Supernova 1604, also known as Kepler's Supernova,
was a supernova that occurred in the Milky Way
and was observed by Kepler in 1604.
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Standard Candle 2 Supernovae
Supernovae are classified according to their
spectra Type I supernovae WITHOUT hydrogen
absorption lines Type II supernovae WITH
hydrogen absorption lines. Type I leaves behind
a gaseous supernova remnant (and no stellar
corpse at the center), very rich in iron. Tychos
Supernova remnant is of a Type Ia supernova (no
helium lines, strong silicon lines). Type Ia
supernovae are all very similar!
Tychos supernova remnant
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Super-novae
The Crab Nebula is the remnant of a Type II
supernova it contains a neutron star at its
center.
Type II leaves a gaseous supernova remnant,
containing elements heavier than iron and a
compressed stellar core, a neutron star or black
hole. Type II supernovae arent as similar as
Type Ia. But theyre worth mentioning.
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Galaxies
Hubble measured the intensities of many standard
candles, yielding the objects distances. This
showed that some objects were very far awaythe
so-called spiral nebulae were really distant
islands of stars galaxies.
Edwin Hubble (1889-1953)
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Okay, so what does our neighborhood of the
universe look like?
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Galaxies
Galaxies are collections of stars bound by
gravitational attraction.
The Milky Way as seen from earth.
Our galaxy is the Milky Way with 200 billion
stars. Its about 100,000 lightyears in diameter
and 10,000 lightyears thick.
The Milky Way as seen from the outside.
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Theres a gigantic black hole at our galaxys
center!
Its mass is about 3,600,000 solar masses. And
its a relatively small one compared to those at
the centers of other galaxies.
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Nearby galaxies
Sagittarius Dwarf Elliptical Galaxy, discovered
in 1994, is 50,000 light-years away. Its passed
through the Milky Way several times so far.
Canis Major Dwarf Galaxy, discovered in 2003, is
about 42,000 light years from the centre of the
Milky Way and only 25,000 light years away from
the solar system. Its doomed by the massive
Milky Way.
Theyre hard to see due to their proximity to the
Milky Ways dusty core.
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The Large and Small Magellanic Clouds
The next closest galaxies (also dwarf galaxies)
to ours are the Large and Small Magellanic
Clouds, distorted by the gravity of the Milky
Way). They were known to mid-east astronomers
from the middle ages, but were brought to
Europeans by Ferdinand Magellan.
Large Magellanic Cloud (180,000 light-years away)
Small Magellanic Cloud (200,000 light-years away)
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The Andromeda Galaxy
Andromeda is the closest large galaxy to ours and
is about a million light-years away.
There are about 100 billion galaxies in the
visible universe.
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Galaxy shapes
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Galaxies and their shapes
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Galaxies and their shapes
Elliptical galaxies
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Quasi-stellar objects Quasars
Quasars are sub-arc-sec objects with tremendously
strong radio signals and strange optical spectra.
They can outshine galaxies. They are among the
most distant and oldest objects in the
universe. They appear to be massive black holes
in the centers of galaxies in early times, eating
stars and other matter and emitting massive
amounts of energy.
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Active Galactic Nuclei (AGN)

• Active galactic nuclei are a category of exotic
  objects that includes luminous quasars, Seyfert
  galaxies, and blazars.
• Its likely that the core of an AGN contains a
  supermassive black hole surrounded by an
  accretion disk. As matter spirals in the black
  hole, electro-magnetic radiation and plasma jets
  spew outward from the poles.

Blazars are AGN with jets spewing relativistic
energies toward the Earth.
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Gamma-ray bursts emit massive amounts of gamma
rays.
Gamma rays are absorbed in the atmosphere, so
GRBs must be observed by satellites.
A new one appears almost every day, and it
persists for lt1 second to 1 minute.
The gamma-ray sky
In 10 seconds, they can emit more energy than our
sun will in its entire lifetime. When shining,
some are brighter than all the other stars in the
visible universe combined.
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Gamma Ray Bursters

• They were recently discovered to come from
  hypernovae (an explosion of a gt20-solar-mass star
  present only in the early universe) in distant
  galaxies.

Jets emerge from the poles, unable to escape from
the rotation disk. We only see one when one of
the jets is pointed at us.
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Gamma Ray Bursters and Hypernova
An interesting property of GRBs is the afterglow
of lower-energy photons including x rays, light,
and radio waves that last for weeks. The
spectra of GRBs are nearly identical to the jet
of a hypernova pointing in our direction.
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But theres another type of gamma ray burster
inside our galaxy!

• Recently, it was realized that a binary neutron
  star collapsing in on itself is also a gamma-ray
  burster that could fry anything within 1000
  light-years. These yield much shorter
  (few-second) bursts.

Binary neutron star in the M15 globular cluster
in our galaxy
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Gamma Ray Bursts and Life on Earth
Its thought that a nearby gamma ray burst caused
the second biggest mass extinction on earth 450
million years ago, and which killed off more than
half earths species at the time. The trilobites
disappeared at this time.
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What about the large-scale structure of the
universe?
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The cosmological constant
Attempting to achieve a static universe, Einstein
realized that he could modify his Field Equations
by introducing a term proportional to the metric
He called the constant ? the cosmological
constant. Einsteins effort was unsuccessful,
however the static universe described by this
theory was unstable.
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Standard Candle 3 Galaxies
Once established as independent entities, entire
galaxies have output powers that could be
considered about the same.
Galaxies are great standard candles because they
shine continuously and are numerous.
Spiral galaxy NGC 4414
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Hubbles measure-ments
Hubble also measured spectra of standard candles,
observing that most were red-shifted. He realized
that this was a Doppler shift. The universe is
expanding!
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Hubbles Law
Hubble also found a linear relation between
distance and recession velocity!
Hubbles law v HR where H is called
Hubbles constant.
Hubbles constant is related to a scale factor a
thats proportional to the distance between
galaxies
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The Expansion of the Universe

• Distances between galaxies are increasing
  uniformly.
• There is no need for a center of the universe.

The expansion of the universe resolves Olbers
Paradox The red-shift reduces the power from
distant sources.
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Event Horizon
The amount of light reaching us is further
reduced by the fact that very distant sources are
receding from us faster than the speed of light,
so no light reaches us from them! This is called
a horizon.
This is consistent with General Relativity.
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Abandoning the cosmological constant
These observations of distant galaxies confirmed
that our universe is, in fact, not static, but
expanding. So the cosmological constant ? was
abandoned, with Einstein calling it the "biggest
blunder he ever made."
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How can the universe be expanding, yet continue
to look the same?

• Proposed in 1948 by Hermann Bondi, Thomas Gold,
  and Sir Fred Hoyle, the Steady-State Theory held
  that the universe is infinite and expanding, and
  matter is continuously created with net constant
  density.
• Only a few atoms per cubic meter per century
  would be required, so no one would ever notice.
• Unfortunately, no mechanism has ever been found
  for matter creation, as required by the
  Steady-State theory.
• Also, in this view, the universe should look the
  same at all distances. But it doesnt. We dont
  see galaxies forming nearby, but we do far away.
  Quasars exist only a billion light-years away or
  more.
• So the universe doesnt actually look the same as
  it expands.

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Extrapolating backward in time, there had to be
one hell of a Big Bang!
And because pV nRT, it mustve been very dense
and hot at t 0!
The Big Bang occurred about 13 billion years ago.
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Age of the Universe
Extrapolating backward, we find that the universe
is 13.7 0.2 billion years old. Radioactive
decay of elements in the oldest meteorites
hitting earth suggest that the universe is
between 8 to 17.5 billion years old.

• Radioactive dating of stars showed that no stars
  were formed earlier than 200,000 years after the
  Big Bang.
• Examining the relative intensities of elemental
  spectral lines of old stars yields ratios of
  thorium/europium and uranium/thorium isotopes,
  indicating an average age of 14 billion years.

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Evidence for the Big Bang Cosmic Microwave
Background Radiation

• In 1964, Penzias and Wilson observed microwave
  background radiation that permeates the universe.
  
• The blackbody radiation of several billion years
  ago has Doppler-shifted to 3K today.
• Satellite measurements show a nearly isotropic
  3K radiation background.

Arno Penzias and Robert Wilson and their
microwave antenna in Crawford Hill, NJ
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Early Universe Nucleo-synthesis

• By considering current ratios of isotopes, we can
  learn more about the early universe.
• We find that it was hot and dense enough to
  create only the lightest few elements.

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Supernovae and nucleo-synthesis

• Supernovae provide the ultrahigh temperature and
  pressure to produce all the heavier elements.

• Steady-state theorists did much of this theory in
  an attempt to save their theory!

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The Cosmological Principle
The cosmological principle says that the universe
looks roughly the same everywhere and in every
direction. Specifically, the universe is both
isotropic and homogeneous.
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Looking into the distance is looking back in time.
While light travels fast, its not that fast. We
can look about 13 billion light-years away, so
were looking back 13 billion years in time.
Modern-day galaxies
Quasars
Quasars
Proto-galaxies
Proto-galaxies
Early stars
Early stars
This is consistent with the Cosmological
Principle.
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The Big Bang

• The Big Bang model rests on two theoretical
  foundations
• The General Theory of Relativity
• The Cosmological Principle
• What does General Relativity have to say?
• RobertsonWalker metric is the simplest
  space-time geometry consistent with an isotropic,
  homogeneous universe.

Ds2 a(t)2 Dx2 Dy2 Dz2 c2Dt2
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Possible geometries of the universe
The density, r, of matter in the universe
determines its shape. W0 r / rcrit where
rcrit 3H2/8pG is the critical density for which
the universe is flat.
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The Future of the Universe

• Looking into the past, there is little question
  that the age of the universe is about 13.7
  billion years.
• What about the future?
• There are three possible futures

Luminous matter only accounts for 3 to 4 of the
critical density of the universe.
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The Missing Mass and Dark Matter
What about dark matter that we cant see?
The Virial Theorem
Using this simple relation, we can estimate the
total mass of the galaxy, M.
The dark matter halo covers the space between
100,000 to 300,000 light-years from the galactic
center. About 70 of the Galaxy is composed of
dark matter.
100,000 light-years
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The Missing Mass
Some of the Universe's missing mass may be hiding
in clusters of galaxies. Astronomers have
discovered previously unseen clouds of hot gas
being pulled into the clusters. The gas has far
greater mass than the observable stars in the
galaxies and so may make up a fraction of the
mass of the universe, but little is known about
it. And most dont think it will suffice.
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Microwave background fluctuations in the
different universe shapes
microwave background intensity vs. q and f.
Recent measurements of the angular variation in
the microwave background by the Wilkinson
Microwave Anisotropy Probe (WMAP) indicate a flat
universe.
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The Missing Mass and Dark Matter
One possibility for dark matter is MAssive
Compact Halo Objects (MACHOs).
Example brown dwarves (objects whose mass is
between twice that of Jupiter and the lower mass
limit for nuclear reactions (8 of the mass of
our sun). Brown dwarfs are failed stars with
insufficient density to start nuclear fusion.
Brown dwarves (artists rendition)
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The Missing Mass and Dark Matter
Another possibility for dark matter is much
smaller particles Weakly Interacting Massive
Particles (WIMPs).
WIMPs are elementary particles with very tiny
interactions with ordinary matter (likely only
the weak force). They don't emit or absorb
photons. With hardly any interactions, they would
be very hard to detect. But they have gravity.
Neutrinos almost fill the bill But their mass
is too low. Maybe the WIMPS needed are a kind of
particle that hasn't been discovered yet.
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The universe expansion seems to be accelerating!
In 1998, observations of Type Ia supernovae
suggested that the expansion of the universe is
speeding up. In the past few years, these
observations have been corroborated by several
independent sources the cosmic microwave
background, gravitational lensing, the age of the
universe, and its large scale structure. The
universe appears to be expanding at an
accelerated rate.
Supernova/Acceleration Probe (SNAP) satellite
observatory proposed to further study Type Ia
supernovae in distant galaxies to better measure
the universe acceleration.
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The cosmological constant revisited
Despite Einstein's misguided motivation for
introducing the cosmological constant term, there
is nothing inconsistent with the presence of such
a term in the equations. Indeed, recent improved
astronomical techniques have found that a
non-zero value of ? is needed to explain some
observations. Einstein thought of the
cosmological constant as an independent
parameter, but its term in the field equation can
also be moved algebraically to the other side and
written as part of the stress-energy tensor
                       The constant
              is called the vacuum energy. The
cosmological constant is equivalent to non-zero
vacuum energy. The terms are now used
interchangeably in general relativity.
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The Friedmann Equation

• The various key constants are related by the
  Friedmann Equation
• Dividing both sides by H2 yields
• Each of the terms in this equation has special
  significance

where k is the curvature parameter
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The cosmological constant rules!

• Visible matter is only 4 of the total mass in
  the universe. Dark matter accounts for 23, and
  73 is mysterious dark energy.
• The star cluster and galaxy data are consistent
  with a low density universe.
• The cosmic microwave background is consistent
  with a flat universe.
• Distance determinations based on Type Ia
  supernovae data are consistent with an
  accelerating universe.
• These sets of data constrain the universe mass
  parameters to the values Ok 0, Om 0.3, and
  OL 0.7.
• The cosmological constant appears to be the
  dominant effect! But why? And what is it
  really?

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We dont have a clue what it really is
Attempts to compute the vacuum energy start with
the zero-point energy of harmonic oscillators,
which turn out to be the model of photons and
other particles in vacuum.
where n is the number of particles present. The
½hw is present for every frequency even in the
absence of particles (vacuum). An infinite
energy density everywhere in space! Considering
this as a vacuum energy that could be responsible
for the cosmological constant, physicists have
limited it to a finite number, yielding an
effective density of rvac 10112 erg/cm3. But
cosmological observations (WL 0.7) yields rvac
10-8 erg/cm3. This is a discrepancy of 120
orders of magnitude!
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Issues for the Big Bang

• Why is the universe flat?
• Why does the universe appear to be homogeneous
  and isotropic? It is amazing that opposite sides
  of the universe that are 27 billion light-years
  apart have the same microwave background in every
  direction.
• Why have we never detected magnetic monopoles?
  Magnetic monopoles would bring symmetry to many
  theories in physics.

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The Inflationary Universe

• A variation of the Big Bang model proposes that
  the universe suddenly expanded by a factor of
  1050 during the time 10-35 to 10-31 seconds after
  the Big Bang. This is called the inflationary
  epoch. It is due to the separation of the nuclear
  and electroweak forces.
• After the inflationary period, it resumed its
  evolution from the Big Bang.
• The inflationary theory requires that the
  universe be flat and the mass density be near the
  critical density.
• The universe reached equilibrium before the
  inflationary period began.
• This explains the homogeneous universe.
• Magnetic monopoles would have to occur along the
  boundaries or walls of different domains. So this
  explains why we dont see them.

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The Inflationary Universe
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Particle physics is the basis of cosmology, and
even this breaks down for early enough times.

• Before 10-43 s after the Big Bang we have no
  theories because the known laws of physics dont
  apply.
• In the beginning, the universe most likely had
  infinite mass density and zero spacetime
  curvature.
• The size of the universe at 10-43 s was lt 10-52
  m.
• The four fundamental forces of strong,
  electromagnetic, weak, and gravity were all
  unified into one force.

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The Future of Earthlings

• The Demise of the Sun
• The sun is about halfway through its life as a
  star, which started 4.5 billion years ago. As its
  hydrogen fuel is exhausted, the sun will
  contract, but then heat up even more as it next
  burns helium.
• The heat will cause it to expand and even consume
  the Earth.
• The sun will become a red giant and the surface
  will cool from 5500 K to 4000 K.
• Eventually the light elements in the outer layers
  will boil off and the sun will contract to the
  size of the Earth with a final mass that will be
  half its current mass.
• The sun will cool down to become a white dwarf
  and then a cold black dwarf.

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The Long-Term Future of the Universe

• The universe is flat, and it is expanding. And
  the expansion is accelerating.
• Eventually all the stars in our galaxy will die
  as well as those in all other galaxies. Black
  holes will consume them and eventually consume
  all available mass.
• It seems that the universe will evolve to a cold,
  dark place. And thats even before protons begin
  to decay
• But theres so much we dont know. We await the
  next revolution