Transcript Slide 1

Standard Big Bang
Topics
Standard theory;
Nucleosynthesis;
Matter-antimatter problem
CMB
Motivation
What is the Big Bang really?
A first exposure to the Universe’s spatial curvature.
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The Standard Big Bang
In order to properly understand the timeline of the Big Bang theory
from t=0 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 Hubble’s 1929
discovery of Hubble’s Law:
v=Hd
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 Bang’s beginning (t=0) and the Universe’s initial
temperature (T ≈ ∞).
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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 massenergy 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
flat—it 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 (Einstein’s 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?
– Planck’s constant is very small: 6.6×10-34 J-sec
– Planck’s length is derived by c, G, h, is 1.6×10-35 m
– Planck’s 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
10-43 sec to about 10-36 sec
Temperature
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
10-36 sec to about 10-12 sec
Temperature
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 today’s 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
10-36 sec to about 10-12 sec
Temperature
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
10-12 sec to about 1 sec
Temperature
1015 K to about 1010 K
Major events
1. Time: 10-12 sec to 10-6 sec.
Free quarks became stable.
Constituents: quarks, leptons, gluons, γ, antimatter equivalents.
2. Time: 10-6 sec to 0.01 sec.
Quarks bonded to hadrons (such as protons and neutrons).
Constituents: p, n, leptons, γ, antimatter equivalents.
3. Time: 0.01 sec to 1 sec.
Photons no longer had energy to produce n.
Photons no longer had energy to produce p
Protons 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, γ
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Era #5: the nucleosynthesis era
Time
About 1-10 sec to 300 sec
Temperature
1010 K to about 109 K
Major Events
1. 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.
2. 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
3. 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+γ
4. But…before all the neutrons were gobbled up, helium became stable; the
remaining neutrons were quickly stored in helium atoms:
2p +2n → He + γ
Also, the deuterium that was created was mostly converted into helium:
D + D → He + γ
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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- +νe
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 14:2 protons:neutrons, 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 + (2p+2n) = 12H + He
This predicts the Universe should be ~75% H by mass, 25% He by mass.
But…during 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, (Hans Bethe), Gamow (1948)
α
β
γ
300 people attended Alpher’s dissertation defense!
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Era #6: the era of nuclei
Time
About 300 sec to 370,000 years
Temperature
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
1. At the end of the era of nuclei, the temperature dropped to 3000 K.
Photons no longer had enough energy to ionize hydrogen.
2. 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
370,000 years to 109 years
(13.7×109 years)
Era of galaxies
109 years to today
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
spectrum—the spectrum of each gas cloud has its own redshift. This lets us
probe physical conditions in galactic clouds, in space, and through the
Universe’s history.
The furthest known objects are galaxies and quasars near z=8.6 (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 T=3000K—the 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.
Wein’s Law: max = 2.9mm/T
T1 = 3000K, T2 = 2.73K: →
1 = 2.9mm/T1
2 = 2.9mm/T2 → 2/1 = 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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