1. Waves and Bubbles The Detailed Structure of Preheating Gary Felder

2. Outline Introduction: Reheating and Preheating Introduction: Reheating and Preheating The Detailed Structure of Preheating The Detailed Structure of Preheating A Taxonomy of Preheating A Taxonomy of Preheating Conclusions Conclusions

3. 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, T RH. Originally reheating was considered perturbatively and the products of this decay were assumed to emerge in thermal equilibrium at a calculable reheating temperature, T RH. 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. 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.

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

5. Parametric Resonance, cont. Each time the inflaton crosses zero the number density of particles will increase for all modes within the resonance band. 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.

6. 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. 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.

7. Tachyonic Preheating, cont.

8. 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. 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. As a result, all modes with wave number k smaller than the curvature will be exponentially amplified.

9. The Importance of Preheating Thermal effects such as gravitino production and phase transitions may occur long before final thermalization takes place. 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. 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. All of these effects (and others) can be highly sensitive to the details of preheating.

10. The Detailed Structure of Preheating Semi-thermalization: The spectrum produced by preheating Semi-thermalization: The spectrum produced by preheating Bubbles and waves: The spatial field distribution produced by preheating Bubbles and waves: The spatial field distribution produced by preheating What’s the matter with matter?: The equation of state after preheating What’s the matter with matter?: The equation of state after preheating

11. The Results of Parametric Resonance

12. The Results of Tachyonic Preheating

13. A Closer Look at Preheating: Tachyonic Preheating

15. A Closer Look at Preheating: Parametric Resonance

17. The Equation of State Consider the model 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 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. When the energy is dominated by the conformal, quartic term the equation of state is radiation domination.

18. The Equation of State

19. A Taxonomy of Preheating Large field models: Inflaton decay is dominated by parametric resonance. Large field models: Inflaton decay is dominated by parametric resonance. Hybrid models: Inflaton decay is dominated by tachyonic preheating. Hybrid models: Inflaton decay is dominated by tachyonic preheating. Small field models (new inflation) Small field models (new inflation) Both effects are important

20. Conclusions Generically, reheating begins with a rapid stage of preheating that produces high occupation numbers and a nearly thermal spectrum in infrared modes. 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. 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.

21. Additional Slides

22. Chaotic Inflation 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. V

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

24. A Closer Look at Preheating: Parametric Resonance

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

27. Studying Reheating: Two Difficulties Unknown Model Unknown Model High energy physics not tested in labs High energy physics not tested in labs Use early universe studies to test models Use early universe studies to test models Complicated Equations Complicated Equations Can’t be solved analytically Can’t be solved analytically Standard approximations fail Standard approximations fail Must use numerical calculations Must use numerical calculations

28. Energy Conservation Time Kinetic Energy Potential Energy Time Scalar Field Energy

29. Scale Factor and Energy Density Time Scale Factor Energy Density

30. Initial Conditions for Inflation

31. Inflaton Decay