Standard Big Bang

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Standard Big Bang
Topics Standard theory Nucleosynthesis Matter-an
timatter problem CMB
Motivation What is the Big Bang really? A first
exposure to the Universes spatial curvature.
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The Standard Big Bang

• In order to properly understand the timeline of
  the Big Bang theory from t0 to the current, you
  need the following tools
• Special Relativity
• Nuclear Physics
• Particle Physics
• General Relativity
• We have three out of four for now we can fake
  the GR.

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Origins of the theory

• Various mathematicians had proposed the concept
  of an expanding Universe because of various
  theoretical considerations, but the real impetus
  began from Hubbles 1929 discovery of Hubbles
  Law
• vHd
• In the decades that followed, a number of
  theories competed with this theory, most notably
  the Steady State hypothesis which said stable
  matter appeared out of a vacuum, to generate new
  galaxies as the already-existing galaxies grew
  farther apart.
• The name Big Bang was coined in 1949 by Fred
  Hoyle, ironically enough, one of the developers
  of the Steady State hypothesis.
• (Hoyle later developed the concept of how the
  more massive elements in the Universe were
  created by stars conducting hydrogen and helium
  fusion.)
• The Big Bang theory won out with the detection of
  the cosmic microwave background in 1964.

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Are you a closet steady stater?

• The premise of the Steady State was that the
  Universe is infinitely large, and that the
  Universe is infinitely old. Do you agree, in your
  heart, with
• The Universe is infinite, without bounds, and has
  always been around!
• If that is the case, along any sight line, you
  should see a star.
• The fact that the night sky is not as bright as
  the surface of a star is observational proof that
  the Steady State notion of the Universe is
  untenable.

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The Big Bang history

• Themes
• The expanding Universe is much like an expanding
  cloud of gas.
• As a gas cloud expands, it decreases in density
  and temperature.
• Looking back into time, the Universe was
  progressively more densely packed.
• Looking back into time, the Universe was
  progressively hotter.

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The Big Bang history

• Matter and energy densities
• Note that as the Universe gets larger by some
  factor R, its volume increases by R3, so its
  matter density (mass/volume) decreases by a
  factor R3.
• The energy density, stored in the photons, also
  decreases by this factor R3.
• But photons also stretch as the Universe expands.
  Recall that longer wavelength photons have less
  energy.
• This means that the photons decrease in energy by
  another factor of R, so energy density decreases
  by R4.
• The ancient Universe was ENERGY DOMINATED.
• The current Universe is MATTER DOMINATED.

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The Big Bang history

• Timeline
• We will start at the early Universe (the VERY
  early Universe) and follow the best models of the
  Universe through to the times of protogalactic
  gas clouds.
• We will defer a detailed discussion of
  inflation for later.
• The history of the Universe is traditionally
  broken into seven eras.
• Our two main measures during this narrative will
  be the time from the Big Bangs beginning (t0)
  and the Universes initial temperature (T 8).

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Era 0 the Era of the Unknown

• Time ZERO, or even earlier.
• This is a matter of pure speculation. Does time
  even have a meaningful definition? Was there any
  form of space?
• Did the Big Bang have a previous iteration?
• Was the physics in a previous Universe anything
  like our current physics?
• Hartle-Hawking state
• String landscapes
• Brane intersections (ekpyrotic models)
• Did the Universe emerge from some kind of virtual
  particle, or violation of physics?
• Was a supernatural entity involved?
• We do not know, nor is it likely we will ever
  resolve this question in a satisfactory way.

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Era 1 the Planck era
Time Less than about 10-43 sec Conditions The
vast energy density and small scales correspond
(via the Heisenberg Uncertainty Principle) to
enormous virtual mass-energy fluctuations on
space. The four forces (gravitational,
electromagnetic, strong, and weak) were
indistinguishable and essentially explained by
one (as-yet undeveloped) overarching force law
called the Theory of Everything (T.O.E).

• Particles and antiparticles regularly combined
  into virtual photons, and back again. In the
  Planck Era, photons had arbitrarily high
  energies, so enormously large particles could be
  spontaneously formed.
• These massive fluctuations resulted in a
  spacetime that was far from flatit was not just
  curved, it was so bumpy it was foamlike!

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Era 1 the Planck era (contd.)

• Problems with understanding the Planck Era
• General Relativity (Einsteins theory of gravity)
  is based on the assumption that the curvature in
  spacetime is relatively smooth clearly this was
  not the case in the foamlike early Universe.
• Meanwhile, Quantum Physics is built upon the
  premise of a flat spacetime.
• The very early Universe, and black holes, are the
  two places where the irreconcilable differences
  between General Relativity and Quantum Physics
  end up in divorce court. New physics is needed!
• Why Planck Era?
• Plancks constant is very small 6.610-34 J-sec
• Plancks length is derived by c, G, h, is
  1.610-35 m
• Plancks length/c 10-43 sec
• These Planck units are anticipated as being
  important if/when a theory of quantum gravity is
  ever developed.

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Era 2 the GUT era
Time Temperature 10-43 sec to about 10-36
sec 1032 K to about 1029 K Conditions At the
beginning of the GUT Era, the T.O.E. force split
into two forces T.O.E. ? Gravity GUT force

• The GUT force (electronuclear force) was the high
  energy version of electromagnetic, weak, and
  strong forces, which is described by the as-yet
  undeveloped Grand Unified Theory.
• The only particle expected to be stable in this
  early era was the Higgs Boson.
• Problems with understanding the GUT Era
• The TOE and GUT are still purely theoretical!

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Era 3 the electroweak era
Time Temperature 10-36 sec to about 10-12
sec 1029 K to about 1015 K Conditions At the
beginning of the Electroweak Era, the GUT force
froze out into two forces GUT force ? Strong
Electroweak force The Electroweak force was the
high energy version of electromagnetic and weak
forces.

• It is theorized that at some point here, the
  equation
• energy ? matter antimatter
• was not perfectly obeyed hence the excess of
  matter over antimatter in todays Universe.
• Unlike the earlier unified forces, the
  electroweak force has actually been successfully
  described in Quantum Physics.

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Era 3 the electroweak era (contd.)
Time Temperature 10-36 sec to about 10-12
sec 1029 K to about 1015 K

• Inflation
• During the period of 10-36 sec to about 10-32
  sec, the Universe experienced a massive stage of
  inflation, in addition to its expansion.
• Saving a discussion on inflation for a future
  class, for now, we simply note it existed and it
  was associated with energy released when the GUT
  force separated into the strong and electroweak
  interactions.
• Inflation increased the size of the Universe from
  that of an atom to that of the Solar System.
• At the end of the Electroweak Era, the
  Electroweak force froze out into two forces (this
  is the current situation)
• Electroweak force ? Weak Electromagnetic force

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Era 4 the particle era
Time Temperature 10-12 sec to about 1 sec
1015 K to about 1010 K

• Major events
• Time 10-12 sec to 10-6 sec.Free quarks became
  stable. Constituents quarks, leptons, gluons,
  ?, antimatter equivalents.
• Time 10-6 sec to 0.01 sec.Quarks bonded to
  hadrons (such as protons and neutrons).Constituen
  ts p, n, leptons, ?, antimatter equivalents.
• Time 0.01 sec to 1 sec.Photons no longer had
  energy to produce n.Photons no longer had energy
  to produce pProtons and neutrons combined with
  their antiparticles.For every 109 pairs of
  matter-antimatter particles, one particle
  remained. (Why, oh WHY this asymmetry from the
  electroweak era?)Constituents p, n, leptons, ?

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Era 5 the nucleosynthesis era
Time Temperature About 1-10 sec to 300 sec
1010 K to about 109 K

• Major Events
• Photons could no longer turn into p and
  n.Photons could still turn into e- and
  e.Since matter and energy were coupled, clumps
  of matter could not form. Why? Because clumps of
  matter would generate clumps of photons, which
  would blow apart the clumps of matter.
• At around 10 seconds, photons could no longer
  turn into e- and e.Clumps of matter are still
  prevented from forming, because the free
  electrons could interact with photons. The
  photons drag electrons around, and the electrons
  drag the protons around.

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Era 5 the nucleosynthesis era (contd.)

• The story of the neutrons
• Since neutrons are slightly more massive than
  protons, they are easier to make from virtual
  photons. The Big Bang predicts that, at this
  time, there were about 7 as many protons as
  neutrons. As the Universe cooled, eventually
  deuterium (D 2H, a hydrogen isotope) became
  stable, which started pulling the relatively rare
  neutrons out of circulation
• n p ? D ?
• Butbefore all the neutrons were gobbled up,
  helium became stable the remaining neutrons were
  quickly stored in helium atoms
• 2p 2n ? He ?
• Also, the deuterium that was created was mostly
  converted into helium
• D D ? He ?

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Era 5 the nucleosynthesis era and neutrons

• This entire business was complicated by the fact
  that neutrons are not stable!
• While they are stable when bound in atomic
  nuclei, outside a nucleus a free neutron will
  decay
• n ? p e- ?e
• The half-life for this process is about 886 sec
  15 min.
• Let us now explore what happened to the neutrons
  and protons in the early Universe.
• Start with the initial ratio of 142
  protonsneutrons, as predicted by the Big Bang.

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Era 5 the nucleosynthesis era and neutrons

• Neutrons started getting stored into deuterium
• Next, neutrons rapidly got stored in helium
• Most (but not all) of the deuterium was converted
  into helium...
• The Universe expanded until the density was too
  low for continued nucleosynthesis, freezing the
  initial cosmic abundances of elements.
• Summary 14p 2n ? 12p (2p2n) 12H He
• This predicts the Universe should be 75 H by
  mass, 25 He by mass.
• Butduring all these steps, neutrons were
  decaying into protons. As a result, some neutrons
  decayed before they could be sequestered into He.
  This modifies the amount of He predicted to be in
  the modern Universe.
• The abundances of deuterium, Li, and 3He in the
  Universe are also predicted.
• Ralph Alpher, George Gamow ? Alpher,
  Gamow (1948)
• a ß ?
• 300 people attended Alphers dissertation defense!

(Hans Bethe),
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Era 6 the era of nuclei

• Time Temperature
• About 300 sec to 370,000 years 109 K to about
  3000 K
• Conditions
• The Universe consisted of nuclei H, He, and Li
  nuclei and electrons.
• The nuclei were positively charged, the electrons
  were negatively charged.
• Photons do not have enough energy to make
  virtual particles, but they do have enough energy
  to strip electrons from nuclei. So any nuclei
  that acquire an electron are quickly re-ionized.
• Matter and photons were coupled (colliding
  frequently, changing their directions of travel).

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Era 6 the Era of Nuclei

• Events
• At the end of the era of nuclei, the temperature
  dropped to 3000 K.Photons no longer had enough
  energy to ionize hydrogen.
• Hydrogen and helium nuclei began to capture
  electrons, forming neutral atoms.Neutral atoms
  do not interact much with photons, so photons
  were free to pass by nuclei ? the Universe became
  transparent! This is called decoupling.
• Consequences of decoupling
• The matter density (atomic nuclei) and the energy
  density (photons) were no longer intimately
  connected. They had decoupled.
• Even today, we still see these ancient photons,
  but they have been cosmologically redshifted into
  a cosmic microwave background.
• Decoupling was a critical instant, one to which
  we will return.

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Eras 7 8 the eras of atoms and galaxies
Era of atoms Era of galaxies 370,000 years to
109 years 109 years to today (13.7109
years) During the era of atoms, matter was
allowed to form clumps. During the era of
galaxies, the clumping became so significant that
protogalactic clouds began to emerge and the era
of galaxies began.

• Quasars as Tools of the Era of Galaxies
• The light from quasars passes great distances to
  reach us.
• Every gas cloud the quasar light passes through
  produces an absorption spectrumthe spectrum of
  each gas cloud has its own redshift. This lets us
  probe physical conditions in galactic clouds, in
  space, and through the Universes history.
• The furthest known objects are galaxies and
  quasars near z8.6 (600 MY after the big bang).
  Note z ??/? ? v/c

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The Cosmic Background Radiation

• At the end of the Era of Nuclei, matter and
  energy decoupled.
• At this point, the Universe was filled with a
  radiation field corresponding to an object at
  T3000Kthe temperature of the Universe at that
  time.
• In 1948, Alpher and Herman predicted the Universe
  should be filled with 5K radiation.
• This was discovered in 1965 by Penzias and
  Wilson, Bell Labs in New Jersey. The temperature
  currently measured is 2.73K.
• Weins Law lmax 2.9mm/T
• T1 3000K, T2 2.73K ?
• l1 2.9mm/T1 l2 2.9mm/T2 ? l2/l1 T1/T2
  3000/2.73 110
• ? The Universe is about 110 larger than it was
  at decoupling.

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Big Bang Strengths and Weaknesses

• Strengths
• It predicts the relative abundances of H, D, He.
• It predicts the presence of the cosmic microwave
  background.
• Weaknesses
• Why is it that we have an asymmetry of matter vs.
  antimatter?(During the particle era, 109
  matter-antimatter pairs per matter residue.)
• Why is it that the cosmic microwave background is
  so very, very, very smooth?
• There are additional surprises, and fixes, that
  we will look at next.
• Preview Inflation!

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