Matthew von Hippel
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Outline
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What is Big Bang Nucleosyntheis?
How does it work?
How can we check it?
The Primordial Lithium Problem
Problem or problem?
Possibility of New Physics
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“We are star-stuff” –Carl Sagan
• Well not exactly.
Many elements come from stars or
supernovae, but the lightest need another
origin
• Hence, Big Bang Nucleosynthesis (BBN)
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Big Bang Nucleosynthesis
• First proposed by Ralph Alpher, Hans
Bethe, and George Gamow, 1948
– Bethe wasn’t actually involved in the
research, but was added for the alphabeta-gamma pun
• They proposed that all elements were
formed in the Big Bang. This turns out
to be false: there is no stable nucleus
of mass number five or eight, which
prevents the process from going
beyond Lithium.
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BBN At a Glance
• Einstein’s Equations in a universe with an isotropic distribution of
matter and energy give us the Friedmann Equations:
𝑎2 𝑡
𝑎2 𝑡
𝑘𝑐 2
+ 𝑅2 𝑎 2 𝑡
0
=
8𝜋𝐺𝑁
3
𝜌
𝑎 (𝑡)
𝑎(𝑡)
=−
4𝜋𝐺𝑁
𝑐2
1
3
(𝑝 + 𝜌𝑐 2 )
Where a(t) is a universal scale factor and k is related to the
universe’s curvature
• With these and the equation of state for gas we can write the scale
factor in terms of the density
• The early universe was very hot, thus dominated by radiation.
Because of this the density near the Big Bang is approximately the
radiation density, which thermodynamics lets us relate to the
temperature
• Put all this together, and we get
−1
𝑇~𝑎
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The Reactions
• From this relation, we get the temperature of the early
universe, which tells us which reactions take place
• Light elements are produced by the following
reactions:
+
𝑝+𝑛
𝐷+ + 𝑝
3 +
𝐻 +𝑝
4
𝐻𝑒 + 𝐷
3
𝐻𝑒 ++ + 𝛾
4
𝐻𝑒 ++ + 𝛾
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𝐿𝑖 + 𝛾
𝐷 +𝛾
3 +
𝐷+ + 𝑛
𝐻 +𝛾
3
4
𝐻𝑒 ++ + 𝑛
𝐻𝑒 ++ + 𝛾
4
𝐻𝑒 + 3𝐻
7
𝐿𝑖 + 𝛾
• Inputting 11 key nuclear cross sections, the baryonphoton ratio, and the neutron lifetime, we can predict
the relative abundances of Deuterium, Lithium-7,
Helium-3, and Helium-4 compared to Hydrogen
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Cosmic Microwave Background
• The angular power spectrum
of the Cosmic Microwave
Background can give us a value
for the baryon-photon ratio
• The ratio of heights between
odd and even peaks increases
with baryon density. Other
parameters move the peaks in
synch
• There were some early
discrepancies, but more recent
measurements (WMAP) give
baryon-photon ratio 6.23±0.17
• This is then used in the BBN
formulas
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What do we compare it to?
• To observe whether the ratios calculated by BBN hold,
we measure old parts of the universe where fusion
has been of limited scope.
In particular, three areas for Lithium:
Metal-poor halo stars: Li in these
stars correlates with Fe, so by taking
Fe to zero we get a value for Li in the
early universe
Globular clusters: Similar situation
Metal-poor high velocity clouds: Not
pursued in detail yet, may offer a
check on the above two
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What do we get?
• Yellow and Empty
curves are
observations, Blue is
theory
• Y=He/(H+He)
• Helium 3 is hard to
measure, since most
stars burn it, so there
is no yellow curve
• Remaining curves
within expected
error…except Lithium.
Is this a problem?
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Problems vs. problems
• To find discrepancies that indicate new physics, we first have to be
sure the discrepancy isn’t caused by more prosaic sources of
inaccuracy in our measurements/calculations.
– Essentially, whether it is a Problem that can spark a new theory, or
merely a problem with our current calculation
• What else could go wrong?
– Nuclear Cross Sections: in general, we might have missed some key
nuclear reactions that reduce cosmic Lithium. However, the nuclear
theory involved is well understood. Those parts that are more poorly
understood are constrained by the role they play in models of stars,
which end up meaning that corrections here will likely be in the wrong
direction.
– More observations: current observations could be supplemented by
unexplored areas(high velocity clouds). However, we will likely still
have to use halo stars as a standard measurement, so this might cause
dramatic change.
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New Physics!
• If it really is a Problem, not just an issue with our
methods, then that means new physics.
• In general:
– Today’s Li-7 from primordial Li-7 and Be-7. In the early
universe the following reaction would get rid of Be-7:
7
𝐵𝑒 + 𝑛
7
𝐿𝑖
4
4
𝐻𝑒 + 𝐻𝑒
where Li-7 is destroyed by proton reactions
– So to reduce Li, we need more neutrons.
• WIMP decays an early speculation, but insufficient
• Decays of GeV scale SUSY particles might bring more
neutrons through more complex paths (Pospelov and
Pradler, 2010)
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Conclusion
• Big Bang Nucleosynthesis allows predictions of
present-day light element abundances, once
we have CMB anisotropy data
• These match observations well, except for
Lithium
• The missing Lithium is likely a sign of physics
beyond the standard model
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Bibliography
• Cheng, T.-P. (2005). Relativity, Gravitation, and Cosmology: A Basic
Introduction. Oxford, Oxford University Press.
• Cyburt, R. H. and et al. (2008). "An update on the big bang
nucleosynthesis prediction for 7 Li: the problem worsens." Journal
of Cosmology and Astroparticle Physics 2008(11): 012.
• Kaplinghat, M. T., Michael S. (2001). "Precision Cosmology and the
Density of Baryons in the Universe." Physical Review Letters 86(3):
4.
• Pospelov, M. a. P., Josef (2010) Metastable GeV-scale particles as a
solution to the cosmological lithium problem. arXiv:1006.4172
• Turner, M. S. (1996) Big-bang Nucleosynthesis: Is the Glass Half Full
or Half Empty? arXiv:astro-ph/9610158v1
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