1. Preheating with Higher Dimensional Interaction PASCOS 2014@Warsaw Tomohiro Matsuda / Saitama Institute of Technology References ``Preheating with higher dimensional interaction,‘’ 1405.3012 (E.Enomoto, N. Maekawa, TM) ``Beauty is more attractive: particle production and …,'' JHEP 1401, 141 (2014) / 1310.4751 (E.Enomoto, S.Iida, N, Maekawa, TM)

2. Why reheating ? However, just after inflation the Universe is On the other hand, what we see is ? Something happened after inflation Reheating Cold Vacuum Energy Inflaton kin. E. Inflation explains … Origin of the large-scale structure of the cosmos Inflation solves … Horizon problem, Flatness problem, Monopole etc…

3. Why “p”reheating ? Very Old View Modern view (preheating) AND MORE (apart from “reheating after inflation”) These non-trivial dynamics may affect observables e.g. Non-Gaussianity, Stochastic GW background, Cosmological relics of Defects/ Particles Reheating explains relation between … the end of inflation and beginning of old Big-Bang cosmology Curvaton decay Flat direction, Moduli oscillation to decay Rich Dynamics: Many stages before thermalization (Osc, resonant prod., Phase Trans,..)

4. Reheating (Basics) 1. Perturbative decay Boltzmann Equation Oscillation decays when No extra dynamics. * Boltzmann equation and can be derived as “Adiabatic limit of preheating ” Kofman ‘96 coincides with conventional particle decay rate.

5. 2. Non-Perturbative decay with 1.Inflaton Oscillation 2.Non-adiabatic particle production 3.Rescattering of the product 4.Non-linear fragmentation/turbulent cascading/P.T. 5.Thermalization Non-perturbative Reheating may include: Usually start with Causes sinusoidal oscillation This problem has been well studied for Then, what do you think if the inflaton is “decoupled” * in the effective action? * ”decoupling” could not be exact since: May be coupled above a Cut-off scale Gravitational int. may not be avoidable Normally, one will expect perturbative decay Stop, are you sure?

6. 3. Non-Perturbative particle production with Higher dimensional Int. Normally one might think “Suppression of the Interaction is crucial !” But in reality is time-dependent Non-adiabatic area is wider => Enhancement? Tension? Note also For a Late-time oscillation : a cold / non-thermal “decoupled” sector might cause preheating via HDI and may avoid “thermal blocking”) Higher Dimensional Interaction Could be Important. One cannot simply neglect HDI.

7. 3. Non-Perturbative particle production with Higher dimensional Int. (1 st step) Consider potential and int. Around j-th zero crossing at t j we assume sinusoidal oscillation which leads to Linearize the equation using Recovers usual preheating if higher terms can be neglected (At least within the non-adiabatic area) 1 st point (transparency) For the transparency of the calculation we first consider Quadratic approximation. Although the parameter space is narrow, conventional calculation may apply there.

8. 3. Non-Perturbative particle production with Higher dimensional Int. (2 nd step) 1. Quadratic approximation is useful for the transparency, because it recovers conventional calculation of preheating 2. However it is valid when μ is not small 3. Obviously the approximation underestimates the particle production 4. Therefore the Quadratic approximation can only give a modest lower bound. For the amplitude as large as M, the quadratic approximation suggests 25 times of collision is needed for the energy transfer. Numerical calculation suggests 8.

9. 3. Non-Perturbative particle production with Higher dimensional Int. (3 rd step) Quadratic Quartic After integration / approximations we found =>

10. (j-th collision) 2collision=1osc If we take, energy transfer becomes significant after 8-th collision In good agreement with the numerical calculation. 3 rd point A very useful result!

11. In our studies we have been trying to remove the most essential assumption among preheating studies. No need to assume renormalizable int! Conclusions and discussions In our first paper “beauty is more attractive” we showed “trapping” could be efficient for higher dimensional int. However (at that moment) it was not quite obvious if the resonant particle production occurs with modest kinetic energy. Also, most people might have been skeptical about resonant particle production with a Planck-suppressed int. Therefore, in our recent study we tried to find a transparent view and a useful result to show why higher int. is important. “I” (personally) believe the result is surprising. Preheating works with HDI. Be free from RI!