PHYS 182 Lecture Notes - Lecture 22: Hubble Volume, Antiparticle, Quantum Fluctuation
PHYS182: Our Evolving Universe
2017-11-28 LEC 22
Evidence for the Big Bang Theory
1. Hubble’s Law: The further away the object is the larger the recessional velocity measured in terms of
the redshift
2. Existence and black body nature of the CMB
o Recall: Start with plasma full of protons, then there is recombination where there exists
thermal equilibrium
o Photons left over from this period should have a black body distribution, which is predicted
by the Big Bang Theory
3. Nucleosynthesis
o Goal: compute the abundances of light elements
o Go way back into the past, you have a plasma no protons/electrons/netrons are bound together
§ These particles lose kinetic energy and eventually nuclei can bind
o Through a reaction chain of proton à deuterium à tritium à helium
§ First: p+ + n à 2H (deuterium)
§ Second: 2H + 2H à 3H + p (tritium)
§ Third: p + 3H à 4He
§ Deuterium and He nuclei are unstable
o Why does one quarter of the mass of the starting protons and neutrons become helium?
§ In an empty space, the mass of a neutron (mn) is slightly larger than the mass of a
proton (mp)
§ Once T < m (E=mc2), then the abundance of the particle decreases
§ Eventually mp < T < mn, so ¯ abundance of neutrons, while abundance of protons
does not change
• While T>mn, you have enough energy to go back and forth between protons
and neutrons
§ But to form He, you need the same number of protons and neutrons
§ According to the Big Bang model, ~25% of the mass of nuclei is in 4He, and the rest
is protons
Predictions vs. observations of nucleosynthesis
- Observational abundance limits for He, deuterium, and lithium
- There is a small range of baryon density for which you can fit the observed abundances
- So nucleosynthesis supports the Big Bang Theory because it can correctly predict the abundance of
several light elements, provided that the number density of nuclei divided by the number density of
photons ~10-8
o This is the baryogenesis puzzle, which as of now has no well-established solution
- Why is the number density of nuclei not 0?
o There is matter and anti-matter, which annihilate into photons
- We don’t know if the Big Bang is correct before nucleosynthesis, but up until then it is a good model
Problems of Big Bang
1. Isotropy of the CMB: the horizon problem
o Measure the intensity, translate it to colour
o We see that the temperature in the universe
is the same in every direction of the sky
o Tells us that matter in the early universe
had to be homogenous
Document Summary
These particles lose kinetic energy and eventually nuclei can bind: through a reaction chain of proton deuterium tritium helium. First: p+ + n 2h (deuterium) Second: 2h + 2h 3h + p (tritium) In an empty space, the mass of a neutron (mn) is slightly larger than the mass of a proton (mp) Once t < m (e=mc2), then the abundance of the particle decreases. Eventually mp < t < mn, so abundance of neutrons, while abundance of protons does not change: while t>mn, you have enough energy to go back and forth between protons and neutrons. But to form he, you need the same number of protons and neutrons. According to the big bang model, ~25% of the mass of nuclei is in 4he, and the rest. Observational abundance limits for he, deuterium, and lithium. There is a small range of baryon density for which you can fit the observed abundances.
