2. Non-gaussianity of the curvature perturbation from preheating
- We propose “Modulated Preheating” mechanism -
Kazunori Kohri
（郡　和範）
Physics Department, Lancaster University
Based on
Kohri, Lyth, Vlenzuela-Toledo, arXiv: [hep-ph]

3. Abstract We consider ½ m2φ2 preheating models
In expanding universe, narrow resonance does not work. Then massless χ quanta are not so sufficiently produced.
In “Modulated Preheating” in broad resonance, a light field σ contributes to curvature perturbation and produces sizable amount of fNL

4. Reduction of ρφ and resonant production ofρχ
Model of preheating
Motivated by particle physics (Chaotic Inflation, A-term Inflation, Inflection point Inflation.), we may adopt ½ m2φ2 for inflaton potential
See Andrei Frolov’s talk in massless preheating models.
Reduction of ρφ and resonant production ofρχ
See Bond, Frolov, Huang, Kofman, arXiv:

5. How large/small is g2? For no radiative corrections to the potential
Massless fluctuation of χ during inflation
But see Barnaby, Huang, Kofman, Pogosyan, arXiv:

6. Narrow parametric resonance does occur in expanding universe?
Narrow resonance
Conditions for efficient resonance
Big difference from Enqvist, Jokinen, Mazumdar, Vaihkonen (05)

7. We may need another mechanism
Large fluctuation …

8. Modulated Reheating If decay rate Γ=1/tdec depends on another field σ
Dvali, Gruzinov, Zaldarriaga(04)
Kofman (04)
Zaldarriaga (04)
If decay rate Γ=1/tdec depends on another field σ

9. Calculation in modulated reheating

10. Modulated Preheating Coupling constant g can depend on another field
See Podolsky, Felder,Kofman, Peloso (05)
Coupling constant g can depend on another field
Then perturbation produced by σ is important
Ackerman et al (05)
Broad resonance

11. Mathew Equation
Mode expansion
Equation of Motion

12. Instability band
Kofman,Linde,Starobinsky(97)

13. Evolution
Kofman,Linde,Starobinsky(97)

14. End of preheating
Kofman,Linde,Starobinsky(97)

15. Is χ nonrelativistic or relativistic?
χ’ Momentum at the resonance
Mass of χ
After
Relativistic particle for

16. Preheating
Kofman,Linde,Starobinsky(97)
Npreheat
Nend

17. g2=10-8

18. g2=10-9

19. Analytical estimate of 1st stage
During preheating
φand χare massive

20. Analytical estimate of 2nd stage
After preheating
φ is massive, χ is almost massless

21. Spectrum and non-linear parameter

22. Non-gaussianity

23. Conclusion
In expanding universe, narrow resonance (g2<10-10) does not work, and production of massless χ quanta is insufficient, and then Pζχ and fNL　are very small
In “Modulated Preheating” in broad resonance, massless σ quanta contribute to curvature perturbation and fNL
Our resuts should be checked by numerical simulation (by using Andrei’s DEFROST or something)