Waves and Bubbles The Detailed Structure of Preheating

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Waves and BubblesThe Detailed Structure of
Preheating

• Gary Felder

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Outline

• Introduction Reheating and Preheating
• The Detailed Structure of Preheating
• A Taxonomy of Preheating
• Conclusions

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Reheating and Preheating

• Originally reheating was considered
  perturbatively and the products of this decay
  were assumed to emerge in thermal equilibrium at
  a calculable reheating temperature, TRH.
• More recently it was found that in a wide variety
  of models reheating begins with an explosive
  stage of non-perturbative particle production,
  which produces a nonthermal spectrum.

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Preheating Parametric Resonance

• Consider reheating in which the oscillating
  inflaton is coupled to a field , e.g.
• The modes of the field will undergo
  oscillations according to the equation
• Since oscillates essentially sinusoidally, the
  modes of undergo parametric resonance.

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Parametric Resonance, cont.

• Each time the inflaton crosses zero the number
  density of particles will increase for all
  modes within the resonance band.

Figure taken from Kofman, Linde, and
Starobinsky, hep-ph/9704452.
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Preheating Tachyonic Preheating

• In many models of inflation such as new inflation
  and hybrid inflation the scalar fields at the end
  of inflation fall down a slope with negative
  curvature.

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Tachyonic Preheating, cont.
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Tachyonic Preheating, cont.

• In many models of inflation such as new inflation
  and hybrid inflation the scalar fields at the end
  of inflation fall down a slope with negative
  curvature.
• As a result, all modes with wave number k smaller
  than the curvature will be exponentially
  amplified.

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The Importance of Preheating

• Thermal effects such as gravitino production and
  phase transitions may occur long before final
  thermalization takes place.
• Nonthermal effects such as baryogenesis can also
  take place shortly after preheating.
• All of these effects (and others) can be highly
  sensitive to the details of preheating.

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The Detailed Structure of Preheating

• Semi-thermalization The spectrum produced by
  preheating
• Bubbles and waves The spatial field distribution
  produced by preheating
• Whats the matter with matter? The equation of
  state after preheating

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The Results of Parametric Resonance
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The Results of Tachyonic Preheating
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A Closer Look at Preheating Tachyonic Preheating
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A Closer Look at Preheating Tachyonic Preheating
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A Closer Look at Preheating Parametric Resonance
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A Closer Look at Preheating Parametric Resonance
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The Equation of State

• Consider the model
• When the energy is dominated by the homogeneous
  inflaton field (after inflation) the equation of
  state is matter domination.
• When the energy is dominated by the conformal,
  quartic term the equation of state is radiation
  domination.

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The Equation of State
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A Taxonomy of Preheating

• Large field models Inflaton decay is dominated
  by parametric resonance.
• Hybrid models Inflaton decay is dominated by
  tachyonic preheating.
• Small field models (new inflation)
• Both effects are important

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Conclusions

• Generically, reheating begins with a rapid stage
  of preheating that produces high occupation
  numbers and a nearly thermal spectrum in infrared
  modes.
• This semi-thermalized state with enormously high
  temperatures is the stage for a lot of
  early-universe physics. The reheating
  temperature is not the most important aspect of
  reheating.

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Additional Slides
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Chaotic Inflation
V

• While the inflaton is high on its potential the
  universe inflates. When it gets low enough
  inflation ends.
• As it oscillates around the minimum the
  homogeneous inflaton decays into fluctuations and
  other fields.

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Key Points of Preheating

• Modes of the fields coupled to the inflaton are
  exponentially amplified.
• These modes are not produced in a thermal
  distribution.
• Rather, the energy is concentrated in
  low-momentum modes.
• However, within those modes the spectrum is
  nearly thermal.

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A Closer Look at Preheating Parametric Resonance
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A Closer Look at Preheating Parametric Resonance
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Chaotic Inflation

• H acts as a damping term for , so as long as H
  is large is nearly constant.
• As long as is nearly constant H will be nearly
  constant.
• Since H /a , a constant H means a increases
  exponentially
• When falls below a certain value H is no
  longer large enough to damp its motion, and
  inflation ends.

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Studying Reheating Two Difficulties

• Unknown Model
• High energy physics not tested in labs
• Use early universe studies to test models
• Complicated Equations
• Cant be solved analytically
• Standard approximations fail
• Must use numerical calculations

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Energy Conservation
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Scale Factor and Energy Density
Scale Factor
Energy Density
Time
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Initial Conditions for Inflation
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Inflaton Decay