Chapter 28 Cosmology

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Chapter 28Cosmology

• In the beginning. And what we know about it, and
  how we know about it.

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Way out there...

• For about 10 days the Hubble Space Telescope
  pointed at one spot in space. As far as we knew,
  nothing was there - at least nothing had been
  observed there before.
• Hubble Deep Field - the oldest galaxies
• 10 to 12 billion years old
• How old is the Universe? Is it infinitely old
  and infinitely large?
• How did it all begin? Or has the universe always
  been there?

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Newtons Universe

• Cosmology deals with the structure and the
  evolution of the universe as a whole.
• According to Newtonian cosmology, we live in a
  static, infinitely old and infinitely large
  universe with stars randomly scattered throughout
  the universe.
• In the early 1800s , the German astronomer
  Heinrich Olbers pointed out that something was
  wrong with this picture - Olberss Paradox.

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Olberss Paradox

• If the Universe is infinite, why isnt the sky
  bright at night?
• We should be able to have a line of sight to
  galaxy or star in any direction we look, if the
  line of sight extends far enough.
• But sky is dark, so there must be an end.
• End is due to expansion of Universe and resulting
  cosmic horizon - some of light from Universe has
  not reached us yet.

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Expansion of the Universe

• Einsteins relativity gave an entirely different
  picture of spacetime and gravity.
• His calculations showed that the universe must
  expand or contract, so he included a fudge factor
  into his equations - Cosmological Constant - so
  that his theory would support a static universe.
• Later, when it was established that the Universe
  is indeed expanding, he said that it was the
  biggest blunder in his life.

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Expansion of the Universe

• While some disagree about how the universe came
  into existence, no one argues that the Universe
  is expanding.
• The first person to discover this was Edwin
  Hubble. He observed that all remote galaxies are
  moving away from us.
• Hubbles Law - The further away something is from
  us, the faster it is receding from us.
• v H0 d v recession velocity,
  H Hubbles constant, d
  distance

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Conceptualizing the expansion of the Universe

• What does it actually mean to say that the
  universe is expanding?
• Think of small coins representing the galaxies
  glued on a balloon as it is blown up.
• As the balloon expands, the the amount of space
  between the coins gets larger and large.
• Similarly,as the universe expands, the amount of
  space between the widely separated galaxies
  increases.

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Conceptualizing the expansion of the Universe
The expanding balloon analogy.
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Conceptualizing the expansion of the Universe

• Expansion occurs only in the space between
  galaxies and clusters of galaxies.
• Galaxies (or stars, or us) themselves do not
  expand, just like the coins do not expand.
• Think of a line of galaxies. The distance between
  each galaxy doubles in a certain time. There is
  no center, and all observers notice Hubbles Law
  
• No matter which galaxy you call home you will see
  all other galaxies receding from you in
  accordance with the same Hubble Law

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The expanding universe and the Hubble law
The greater the original distance between the
galaxies, the greater the amount that the
distance has increased.
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Creating space

• What is the universe expanding into?
• NOTE! The Universe is not expanding into
  pre-existing space - it creates space as it
  goes (!?), just as the surface of a balloon gets
  bigger as it is blown up.
• There is nothing beyond the universe, because
  there is no beyond.
• Asking what is beyond the universe is a
  meaningless question.

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What we observe about the Universe The
Cosmological Principle

• Over very large distance scales the universe
  homogeneous
• i.e. every region looks the same as every other
  region
• The universe is isotropic
• The universe looks the same in every direction
• These two assumptions constitute the
  cosmological principle.
• Gives precise meaning to the idea that we do not
  occupy a special location in space.

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The Big Bang

• According to Hubble law the universe has been
  expanding for a very long time, and thus the
  matter in the past must have been closer together
  and denser than today.
• Therefore, a very long time ago all matter was
  compressed to single point (as energy). For some
  reason, point began to expand initiated by a
  colossal explosion known as the Big bang. As it
  expanded, it cooled, and developed into the
  Universe we see today.

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The Hubble constant

• The Hubble constant H0 tells how fast the
  Universe is expanding. v H0d
• H0 seems to be around 65 (km/s)/Mpc, though
  scientists still debate this.
• The age of the universe(T0) can be calculated
  from the equation T0 1/H0 14 billion yrs.
• age problem (limit to how large H0 can be) if
  we use an H0 that is too big then the universe
  gets younger but the oldest stars observed are
  older than Universe!

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The Cosmic Horizon

• There is a limit to how deep in the Universe we
  can peer. We are at the center of the limits of
  our vision (a.k.a. the Cosmic Particle Horizon)
• limit set by how old Universe is and speed of
  light light from distant galaxies must have had
  time to reach us
• our cosmic horizon is different from other
  galaxies - they are at their own center
• This solves the Olberss Paradox. We do not
  receive light from galaxies beyond our horizon.

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The cosmic horizon
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The Cosmic Singularity

• At the moment of the Big Bang
• A state of infinite density filled the universe
• A condition of infinite curvature existed, giving
  rise to a situation where space and time were
  jumbled.
• Therefore, we cannot apply laws of physics to
  describe the moment of the Big bang.
• This is very similar to the condition at the
  center of a black hole - i.e. at the black hole
  singularity
• For this reason we refer to the black hole as the
  Cosmic Singularity.

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Plank Time

• Due to the state of the universe during the BB,
  we cannot use laws of physics to describe this
  event.
• Nor can science answer what existed before the BB
  - these are fundamentally unknowable things.
• In fact, from the beginning of the BB until
  10-43 seconds after The BB, space time was so
  jumbled-up that laws of Physics fails us
• This time interval tP 10-43 sec. is referred
  to as the Plank time.

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Cosmic microwave background radiation (CMB)

• Amount of helium in the universe is more than
  expected if we believe that .
• The universe originally contained only hydrogen.
• all of the helium was produced inside stars
• Indicates that some helium was formed in early
  Universe before stars were formed.
• The presence of so much helium posed a major
  problem for astronomers.
• The answer to this dilemma was discovered during
  the 60s.

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It was once hot here...

• In 1960 Dicke Peebles working on an idea put
  forward by Alpher Hermann discovered that the
  abundance of helium can be accounted for if the
  early universe was hotter than the core of our
  Sun.
• In such a universe thermonuclear reactions
  occurred everywhere throughout the space, thus
  converting hydrogen to helium.
• Therefore, it was believed that the early
  universe must have been full of high-energy
  short-wavelength photons (radiation).

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Cosmic microwave background radiation (CMB)

• This radiation is blackbody radiation and depends
  on the temperature, just like the radiation from
  the Sun.
• This radiation which fills all space is referred
  to as the Cosmic Microwave background radiation
  (CMB).
• It was discovered by Arno Penzias Robert Wilson
  in the early 60s.

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Cosmic microwave background radiation (CMB)

• Cosmic no identifiable point source - comes
  from all directions - cosmic in origin
• Microwave wavelengths (frequencies) in the
  microwave region of the electromagnetic spectrum
• Background permeates all space
• Radiation Electromagnetic radiation

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The CMB

• Continuous spectrum from a source with
  temperature of 2.7 K
• Source seems to be space itself
• Source is really the hot early Universe itself,
  just before it cooled.
• We are seeing EM radiation as it reaches us for
  the first time from the farthest reaches of the
  Universe
• as many light years away as the Universe is old

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Why 2.7 K?

• Original temperature about 1013 Kelvin and
  density 1010 g/cm3, but expansion has cooled it.
• Cooling occurs as space is stretched by
  expansion, and wavelengths get longer - redshift.
• The redshift caused by the expansion of the
  universe is called the cosmological redshift.
• The Big Bang happened EVERYWHERE in space - right
  here included!!

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The CMB

• The discovery of the CMB radiation was the nail
  in the coffin for all the other competing
  cosmological theories of the time which avoided
  the big Bang scenario.
• The Steady state Theory was the main challenger
  to the Big bang theory at the time.
• CMB radiation has no other explanation but the
  Big Bang.

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Will the universe expand forever?What is the
shape of the Universe?The density of the Universe

• Hard question to answer - requires knowing how
  much matter and radiation is in the Universe
  (equivalently Energy density)
• Which plays a more important role in the
  Universe Matter or energy?
• Depends on when!
• At present the matter radiation densities
• Radiation density ?rad 4.6 x 10-31 kg/m3
• Matter density ?m 2 to 4 x 10-27 kg/m3 ( 1 to 2
  H atoms in 1 m3)

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The density of the Universe

• Today, mater prevails over radiation in the
  Universe - matter-dominated Universe
• However, as you go back in time towards the BB,
  as the universe was more compressed, both
  densities were higher, but in addition photons
  were not so redshifted gt higher energy.
• Early universe was a radiation-dominated Universe
• The transition from radiation dominated to matter
  dominated universe happened about 2500 yrs. after
  the BB

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The Evolution of mass (energy) density of the
Universe.
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History of the Universe

• Very exciting in the beginning, very dull now.
  Hot early, cool later.
• Radiation dominated At first, Universe very hot.
  Exotic forms of matter present, but were quickly
  destroyed. Mostly EM radiation like gamma rays
  present. Would see brightness everywhere.
• Matter dominated (Like now) Universe dark,
  cooler. Matter forms and stays formed.
• Transition between two eras is where CMB came from

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What shape is the Universe?

• Open Universe Will expand forever. Negative
  curvature. Parallel lines always diverge.
• Closed Universe Stops expanding and collapses
  again. Positive curvature. Parallel lines always
  converge.
• Flat Universe exactly stops expanding but
  doesnt collapse (really doesnt exactly stop
  until infinite time). Zero curvature. Parallel
  lines remain parallel

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What shape is the Universe?

• The curvature (Shape) of the universe depends on
  the combined matter radiation density - ?0
• Critical Density ?C
• If ?0 ?C the universe is flat
• If ?0 gt ?C the universe is closed
• If ?0 lt ?C the universe is open
• Using H0 70 km/s/Mpc we get
• ?C 9.2 x 10-27 kg/m3
• 5.5 hydrogen atoms per cubic meter

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What shape is the Universe?

• Astronomers prefer to use the Density parameter
  instead of density
• ?0 ?0 / ?C
• Therefore, the shape of the universe can be
  understood in terms of ?0 .
• Critical Density ?C
• If ?0 1 the universe is flat
• If ?0 gt 1 the universe is closed
• If ?0 lt 1 the universe is open

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Flat space
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Curved space
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Measurements of open vs. closed universe

• These measurements are underway with a new
  generation of telescopes
• From current observations astrophysicists find
  that ?0 1.0 with an uncertainty of 10.
• This means that the universe is flat.
• The flatness of the universe presents a major
  dilemma.

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Dark Energy

• The matter Radiation density parameter ?m/R
  lies between 0.2 - 0.4.
• But ?0 1.0 and if there is only matter
  radiation in the Universe then ?0 ?m/R !!
• The source of the missing density must be some
  form of energy that we cannot detect from its
  gravitational effects (like astronomers do with
  dark matter) nor does it emit any radiation.
• This mysterious energy is called Dark Energy

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Dark Energy

• Therefore, the density parameter of the universe
  has two components ?0 ?m/R ?? , where ?? is
  the dark energy density parameter.
• ?? should be between 0.6 0.8 (since ?m/R 0.2
  to 0.4 and ?0 1.0).
• That is dark energy accounts for 60 to 80 of
  the contents of the universe!!
• It is believed that this dark energy to be a form
  of energy that provides an anti-gravity like
  effect that cause the universe to accelerate mare
  rapidly.
• This concept goes back to Einstein and his
  cosmological constant.

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Recent measurements Is the expansion speeding up?

• Recently published measurements of velocity vs.
  distance using supernovae as distance indicators
  suggest that the rate of expansion is increasing.
  
• Where is the energy driving this rate of increase
  coming from? Dark Energy?

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Long ago galaxies receded more slowly than now
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The Ultimate fate of the Universe

• How the universe is going to evolve depends on
  the matterradiation density and the dark matter
  density of the universe.
• The rate of cosmological expansion is given in
  terms of the deceleration parameter q0 .
• Unbounded universe q0 lt 1/2. Expands for ever.
• Bounded Universe q0 gt 1/2. Gravity will
  eventually stop the expansion and then the
  universe will contract inward. At the end will
  contract to a point of infinte density in an
  event called the Big Crunch.

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Key concepts

• Big Bang
• Cosmic horizon
• Hubbles Law
• Definition and origin of the CMB
• The role of temperature during history of
  Universe
• Dark Energy
• The shape of the Universe, significance in terms
  of its future.