Reheating of the Universe after Inflation with f(f)R Gravity: Spontaneous Decay of Inflatons to Bosons, Fermions, and Gauge Bosons

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Reheating of the Universe after Inflation with
f(f)R GravitySpontaneous Decay of Inflatons to
Bosons, Fermions, and Gauge Bosons

• Eiichiro Komatsu Yuki Watanabe
• University of Texas at Austin
• Caltech High Energy Physics Seminar, March 28,
  2007

Reference Phys. Rev. D 75, 061301(R) (2007)
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Why Study Reheating?

• The universe was left cold and empty after
  inflation.
• But, we need a hot Big Bang cosmology.
• The universe must reheat after inflation.
• Successful inflation must transfer energy in
  inflaton to radiation, and heat the universe to
  at least 1 MeV for successful nucleosynthesis.
• however, little is known about this important
  epoch.
• Outstanding Questions
• Can one reheat universe successfully/naturally?
• How much do we know about reheating?
• What can we learn from observations (if possible
  at all)?
• Can we use reheating to constrain inflationary
  models?
• Can we use inflation to constrain reheating
  mechanism?

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Standard Picture
Slow-roll Inflation potential shape is arbitrary
here, as long as it is flat.
Oscillation Phase around the potential minimum
at the end of inflation
Energetics
What determines energy-conversion efficiency
factor, g?
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Perturbative ReheatingDolgov Linde (1982)
Abbott, Farhi Wise (1982) Albrecht et al.
(1982)
Inflaton decays and thermalizes through the
tree-level interactions like
c
y
f
f
c
y
Inflaton can decay if allowed kinematically with
the widths given by
Pauli blocking Bose condensate
Thermal medium effect
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Reheating Temperature from Energetics
Coupling constants determine the decay width, ??
But, what determines coupling constants?
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Fine-tuning Problem?

• To relax fine-tuning, one needs
• High reheat temperature
• -gt unwanted relics (e.g., gravitinos),
• Very low-scale inflation (H10-18 Mpl10 GeV)
• -gt worse fine-tuning, or
• Natural explanation for the smallness of g.

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What are coupling constants? Problem
arbitrariness of the nature of inflaton fields

• Inflation works very well as a concept, but we do
  not understand the nature (including interaction
  properties) of inflaton.
• Arbitrariness of inflaton Arbitrariness of
  couplings
• Can we say anything generic about reheating?
  Universal reheating? Universal coupling?

e.g. Higgs-like scalar fields, Axion-like fields,
Flat directions, RH sneutrino, Moduli fields,
Distances between branes, and many more
Gravitational coupling is universal
-gt however, too weak to cause reheating with
GR. In the early universe, however, GR would be
modified.
What happens to gravitational decay channel,
when GR is modified?
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Conventional Einstein gravity during inflation
Einstein-Hilbert term generates GR.
Inflaton minimally couples to gravity.
Conventionally one had to introduce explicit
couplings between inflaton and matter fields by
hand.
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Modifying Einstein gravity during inflation
Instead of introducing explicit couplings by hand,
Non-minimal gravitational coupling common in
effective Lagrangian from e.g., extra dimensional
theories.
In order to ensure GR after inflation,
Matter (everything but gravity and inflaton)
completely decouples from inflaton and minimally
coupled to gravity as usual.
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Field equations GR
Linearized field equation
Wave modes are gravitational waves. To identify
the wave modes, we usually define
Harmonic (Lorenz) gauge
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Field equations f(?)R gravity
Linearized field equation during coherent
oscillation
Wave modes are mixed up. To extract true
gravitational degrees of freedom, we define
Harmonic (Lorenz) gauge
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New decay channel through scalar gravity waves
y
s
Fermionic (spinor) matter field
y
Yukawa interaction
Bosonic (scalar) matter field
c
s
Three-legged interaction
c
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Spontaneous emergence of Yukawa interaction
analog of spontaneous symmetry breaking
v
-v
Expanding ? around the vev, one gets
New term appeared.
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Spontaneous emergence of Yukawa interaction
analog of spontaneous symmetry breaking
e.g.
Expanding ? around the vev, one gets
Wave mode mixing in the linear
perturbations (appearance of scalar gravity waves)
Yukawa interactions are induced.
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Magnitude of Yukawa coupling

• For f(?)?????g?(v/Mpl)(m/Mpl)
• Natural to obtain g10-7 for e.g., m10-7 Mpl
• The induced Yukawa coupling vanishes for massless
  fermions conformal invariance of massless
  fermions.
• Massless, minimally-coupled scalar fields are not
  conformally invariant. Therefore, the
  three-legged interaction does not vanish even for
  massless scalar fields

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The Results So Far
Phys. Rev. D 75, 061301(R) (2007)

• After inflation with f(?)R gravity, inflatons
  decay spontaneously into
• Massive fermions,
• Massive scalar bosons, or
• Massless scalar bosons with non-conformal
  coupling.
• The smallness of coupling can be explained
  naturally.
• Inflaton decay is built-in and the coupling
  constrants can be calculated explicitly from a
  single function, f(?).
• Rates of decay to fermions and bosons are
  related.
• This mechanism allows inflatons to decay into any
  fields that are not conformally coupled.
• Other possibilities?

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Breaking of conformal invariance by anomaly
Conformally coupled fields at the tree-level may
not be conformally invariant when loops are
included.
Example decay to massless gauge bosons, F
F
f
F
(c.f.) two-photon decay of the Higgs
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Conformal anomaly Lowest order decay channel to
massless gauge fields
F
f
F
Inflaton -gt 2 gauge fields
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Decay Width Summary
Fermions
Scalar Bosons
Probably the most dominant decay channels
Gauge Bosons
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Constraint on f(f)R gravity models from reheating
Constraints from chaotic inflation
e.g.
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Connection to Supergravity?

• Similar effects have been pointed out by Endo,
  Takahashi and Yanagida (2006 2007) in the
  context of supergravity
• Inflatons decay into any fields even if inflatons
  are not coupled directly with these fields in the
  superpotential
• A correspondence may be made as
• f(?)R gravity lt-gt Kahler potential
• Conformal anomaly lt-gt Super-Weyl anomaly
• Our model is simpler and does not require
  explicit use of supergravity -- hence more
  general.
• It may also give physical (rather than
  mathematical) insight into their effects.

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Conclusions

• A natural mechanism for reheating after inflation
  with f(f)R gravity Why natural?
• Inflaton quanta decay spontaneously into any
  matter fields (spin-0, ½, 1) without explicit
  interactions in the original Lagrangian
• Conformal invariance must be broken at the
  tree-level or by loops
• Reheating spontaneously occurs in any theories
  with f(f)R gravity
• Predictability
• All the decay widths are related through a single
  function, f(f).
• A constraint on f(f) from the reheat temperature
  can be found
• A possible limit on the reheat temperature can
  constrain the form of f(f), or vice versa.
• These constraints on f(f) are totally independent
  of the other constraints from inflation and
  density fluctuations
• Further Study
• Preheating? F(?,R) gravity?