Effective Field Theory in the Early Universe

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Effective Field Theory in the Early Universe

• Inflation, Axions and Baryogenesis

(Collaborations with A. Anisimov, T. Banks, M.
Berkooz, M. Graesser, T. Volansky)
Michael Dine Berkeley Oct. 2004
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In very early universe cosmology, one is
exploring physics at scales well above those
which have been probed experimentally the
relevant laws of nature are at best
conjectural. How to proceed? What can we hope
to learn?
Might hope to guess the correct theory. More
likely, success will come from looking at classes
of theories (Supersymmetric? Large dimensions?
Axions?) Hopefully with connections to
experiment. Crucial tool effective action,
appropriate to the relevant scale of energies,
temperature, curvature
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• Problems to which we might apply these methods
• Dark matter
• Inflation (superluminal expansion, fluctuations)
• Baryogenesis
• In each of these cases, early analyses took some
  renormalizable field theory, and analyzed as if
  space-time were flat. More realistic analysis
  often yields a qualitatively different picture.
  Different possible phenomena sometimes problems
  arise, sometimes problems are resolved.

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• Today we will consider
• Axions as Dark Matter
• Moduli in cosmology
• Inflation
• We will do axions in the greatest detail.

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Axions and the Strong CP Problem
Strong CP Problem QCD is a very successful
theory. But aside from the coupling constant,
it has an additional parameter
In QED, such a term would have no effect, but in
QCD, can show generates CP violating phenomena,
e.g.
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Why is q so small? Axion solution (Peccei,
Quinn, Wilczek, Weinberg) Postulate
field, a(x), symmetry
QCD generates a potential for a(x). If qeff 0,
QCD preserves CP, so ignoring weak interactions,
minimum of axion potential will lie at qeff0.
Can calculate the axion potential (current
algebra)
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A light particle
Constraints from particle searches, red giants
Cosmology can potentially constrain as well.
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The axion hypothesis, at first sight, is
troubling Postulate a symmetry, which is not
broken by anything but small effects in QCD. The
tiniest effects due to unknown interactions at
some high energy scale would lead to too large a
value of q. In the language of effective actions,
one needs to suppress possible operators of very
high dimension which might break the
symmetry. String theory produces exactly such
axions. Typically fa Mp but could be
smaller. (This is one of the attractive features
of string theory).
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Conventional Axion Cosmology
In FRW space-time
Since the mass is so small, at early times
overdamped. At late times, behaves like a
coherent state of zero momentum particles,
diluted by the expansion
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Assuming that the initial angle, q a/fa is of
order one, the axion initially has energy density
vs
The relative proportion of axions and radiation
grows as 1/T one requires that the axions not
dominate the energy density before recombination
time. This limits f_a.
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The axion mass is actually a strong function of
temperature. It turns on quickly somewhat above
the QCD phase transition temperature.
One obtains a limit fa lt 3 1011 GeV
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• Assumptions which go into the axion limit
• Peccei-Quinn phase transition the PQ symmetry
  is a spontaneously broken symmetry axion is the
  corresponding Goldstone boson. Usually assumed
  that there is a transition between an unbroken
  and a broken symmetry phase. Somewhat different
  limits if before inflation (above) after
  (production of cosmological defects)
• Universe in thermal equilibrium from, say, period
  of inflation until decoupling.
• No other light particles which, like the axion,
  might store energy.

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These assumptions are all open to question. E.g.
consider supersymmetry. This is a hypothetical
symmetry between fermions and bosons. A broken
symmetry scale might well be 100s of GeV (I.e.
masses of scalar partners of electrons, quarks,
photon of order 100s of GeV.) Many physicists
believe that this explains why the weak scale is
so much smaller than the Planck scale (mw Mp).
If correct, will soon be discovered at
accelerators. If nature is supersymmetric,
the axion is related by the symmetry to other
fields a fermion and another scalar field.
This scalar field is often called the saxion.
If the saxion exists, it poses much more
serious cosmological problems than the axion.
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The Moduli Problem
The saxion is an example of a modulus a scalar
field with a nearly vanishing potential. Such
fields are common in string theory their
potentials are expected to vanish in the limit
that supersymmetry is unbroken.
m3/2 is gravitino mass size of susy breaking
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In the early universe, the equation for f is
The system is overdamped for Hgtm3/2. At later
times it evolves like dust. Assuming that f
starts a distance Mp from its minimum, when it
starts to oscillate, f stores energy comparable
to H2 Mp2, so quickly dominates. Lifetime
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• Catsrophic for Nucleosynthesis!
• What sorts of solutions are proposed for this
  puzzle
• No supersymmetry, no moduli
• Moduli heavier than m3/2 (1 TeV?) say 100 TeV
• In this case, universe reheats when the
  moduli decay to
• about 10 MeV. Nucleosynthesis restarts. It
  is
• necessary to create the baryons at this time.

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• Implications for axions
• If moduli decays reheat universe to 10 MeV, they
  dilute the axions. This relaxes substantially
  the constraint on fa. In these circumstances,
  saxions decay early and are not a problem.
• Might not have Planck-scale moduli, but in an
  axion model, must at least have saxion. Saxion
  is not a problem if decays early enough (small
  enough fa) then no axion problem.

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Axion Dilution
Axions start to oscillate when H ma. At this
time, ra ma2 fa2 , so
Since both moduli and axions dilute like dust,
this ratio is preserved until moduli decay. T10
MeV, radiation domination. Need radiation
domination to persist until recombination. This
gives fa lt
1015.5 GeV
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This is a much weaker limit than the conventional
one. It relies on speculative but plausible
physics. Even the conventional axion implicitly
assumes some new dynamics at a scale well below
the unification of Planck scale. Suppose that
there are no moduli, other than the saxion. In
this case, the limits may be relaxed as well.
Consider, first, a model for axions with a range
of fa
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Saxions perhaps lower decay constants. One can
construct field theory models for this.
where q carries color and perhaps weak isospin
and hypercharge c is a constant with dimensions
of mass cubed, m is some large integer.
The S vev is of order
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Now we need to consider the saxion cosmology.
If we take this potential as the potential
relevant to the early universe, then again the
saxion starts to oscillate once H m3/2. The
saxion lifetime might be expected to be
There are a number of possibilities. The saxion
may decay before it dominates the energy density.
If not, it will dilute the axions at least to
some extent. Again, the constraints on the axion
decay constant are relaxed.
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Not only are the conventional limits relaxed, but
the basic picture of the PQ phase transition may
also be altered. There need be no phase
transition at all! In our model, the PQ
symmetry is an accident, resulting from discrete
symmetries. The symmetry is explicitly broken by
very high dimension operators. But if the
inflaton transforms under the discrete
symmetries, the symmetry can be explicitly and
badly broken during inflation. As a result,
there need be no PQ phase transition. This leads
to relaxation of constraints from isocurvature
fluctuations. It can eliminate production of
topological defects.
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General lesson considerations of the form of
the effective field theory reveal a range of
phenomena beyond those seen in the lowest
dimension, renormalizable terms. Another
application inflation. There are presently
many models. At the moment, models involving
colliding branes are attracting great attention.
But it was long ago noted by Guth and Randall
that supersymmetric models provide a particularly
natural framework for hybrid inflation.
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Their proposal, however, was harshly criticized.
It was argued to lead to excessive production of
defects (cosmic strings, domain walls) the end
of inflation was said to be complicated, with a
problematic fluctuation spectrum. Both
criticisms result from an overly restrictive view
of the effective action. (In fairness to the
critics, these were features of the original
analysis).
Basic idea inflation at the weak (supersymmetry
breaking) scale. Two fields, the waterfall
field (c) and the inflaton (f).
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(Berkooz, Volansky, M.D.) c naturally a
modulus. To solve moduli problem, need to be
heavy 100 TeV. This leads to sufficient
inflation and a suitable fluctuation
spectrum! The possible problem (Linde et
al) discrete symmetry at the end of inflation,
leads to production of defects, problematic
fluctuation spectrum.
V
f
c
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But (BDV) this problem arises from
oversimplifying the potential. Realistic
potentials (realistic forms of susy breaking)
have no such symmetry and a smooth end of
inflation. Terms like
arise automatically in these models they break
the would-be symmetry and also alter the c
dynamics, bringing a rapid end to inflation.
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In this moduli context, there is also a
natural way to produce baryons. Moduli flat
directions of the MSSM. AD baryogenesis.
Low scale inflation raises a number of issues of
initial conditions, but this is a relatively
compact, simple model. Like virtually all
inflation models, there is a fine tuning, but
this solves problems at once. Again, thinking
carefully about the effective action
considering all of the expected terms opens up
a broader and more realistic set of possibilities.
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