1. 1 Parametric resonance with Multi-frequencies in preheating José Pedro Mimoso University of Lisboa Collaboration with: Ana Nunes Tiago Charters ERE08 –Salamanca: September 15, 2008 Physics Dep. Science Fac. & CFTC arXiv: 0807.4805v1 [hep-ph]

2. 2 We study the decay of the inflaton field to another scalar field χ in the parametric resonance preheating mechanism. We consider the presence of several simultaneous couplings between the fields. This amounts to the existence of extra harmonic terms in the perturbation of the χ field dynamics. For the case of two frequencies we compute the geometry of the resonance regions, which is significantly altered due to the presence of non-cuspidal resonance regions associated to higher harmonics and to the emergence of instability `pockets'. We discuss the effect of this change in the efficiency of the energy transfer process for the simplest non-homogeneous coupling. We find that the presence of a finite number of higher harmonics has limited cosmological implications. Abstract

3. 3 Outline: Motivations (P)reheating after Inflation Preheating with multi- frequencies Conclusions ERE08 –Salamanca: September 15, 2008

4. 4 Inflation: as much of a problem as of a solution?! The accelerated expansion dilutes the matter content The universe becomes too cold T rad ~ e -60 T init Φ V(Φ) Slow roll Fast oscillations Inflation exhausts the Universe: ERE08 –Salamanca: September 15, 2008

5. 5 (A. Linde) So First, inflation Second, recreate Hell ERE08 –Salamanca: September 15, 2008

6. 6 [Chaotic inflation - A. Linde] The expansion of the universe can be neglected [M. S. Turner, 1983] Coherent oscillations of ERE08 –Salamanca: September 15, 2008

7. 7 Old Reheating “Old” reheating Phenomenological perturbative decay of the inflaton Temperature reheating Thermalization ERE08 –Salamanca: September 15, 2008

8. 8 Preheating Thermalization “New” Reheating Inflaton – homogeneous field –> large occupation of k=0 mode Φ ~ Classical field acting on quantum fields χ, ψ Makes masses of χ, ψ to vary periodically Parametric Resonance of ERE08 –Salamanca: September 15, 2008

9. 9 Parametric Resonance Distinguish Broad Resonance Narrow Resonance Exponential Production of Particles Floquet theor. Periodic Ignore expansion Minkowski Mathieu Equation ERE08 –Salamanca: September 15, 2008

10. 10 Narrow Resonance Broad Resonance ERE08 –Salamanca: September 15, 2008

11. 11 Broad Resonance Narrow Resonance ERE08 –Salamanca: September 15, 2008

12. 12 Narrow Resonance ICG –Portsmouth: May 16, 2008

13. 13 Narrow Resonance ERE08 –Salamanca: September 15, 2008

14. 14 ERE08 –Salamanca: September 15, 2008

15. 15 Narrow resonance ERE08 –Salamanca: September 15, 2008

16. 16 ERE08 –Salamanca: September 15, 2008

17. 17 ERE08 –Salamanca: September 15, 2008

18. 18 ERE08 –Salamanca: September 15, 2008

19. 19 ERE08 –Salamanca: September 15, 2008 arXiv: 0807.4805v1 [hep-ph] [Dufaux et al, PRD (2006) hep-ph/0602144v2 Tachyonic Resonance]

20. 20 ERE08 –Salamanca: September 15, 2008

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22. 22 Expanding Universe There is particle production if the frequency does not redshift out of the resonance band in a time interval shorter than the amplification period ERE08 –Salamanca: September 15, 2008

23. 23 Differs very little from the contribution coming from the first band. The reason are that in the second resonance band the values of μ are shifted up and are smaller for the same peturbation amplitude L is much smaller. Moreover the distortion created by the emergence of the instability pocket narrows the instability band as the perturbation amplitude is increased… ERE08 –Salamanca: September 15, 2008

24. 24 Conclusion The assumption that the particle production in the narrow resonance regime is only due to the first instability band is justified and so are the conclusions regarding the lesser effectiveness of this regime to contribute to the particle production and reheating. ERE08 –Salamanca: September 15, 2008 THANKS FOR LISTENING!

25. 25 ERE08 –Salamanca: September 15, 2008

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27. 27 Broad Resonance [Kofman, Linde and Starobinski, Phys. Rev. D 56 (1997) 3258-3295 ] ERE08 –Salamanca: September 15, 2008

28. 28 ERE08 –Salamanca: September 15, 2008

29. 29 Kofman, Linde and Starobinski, Phys. Rev. D 56 (1997) 3258-3295 ERE08 –Salamanca: September 15, 2008

30. 30 Charters, Mimoso & Nunes ERE08 –Salamanca: September 15, 2008

31. 31 ERE08 –Salamanca: September 15, 2008

32. 32 ERE08 –Salamanca: September 15, 2008

33. 33 ERE08 –Salamanca: September 15, 2008

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35. 35 ERE08 –Salamanca: September 15, 2008