Collapse of Small Scales Density Perturbations during Preheating and Production of Gravitational Waves Jérôme Martin Institut d’Astrophysique de Paris (IAP) Cosmo/Cospa 2010 @ Tokyo [In collaboration with K. Jedamzik & M. Lemoine, arXiv:1002.3039, arXiv:1002.3278]

Introduction: large field inflation Outline Introduction: large field inflation Pre-heating and cosmological perturbations: can the power spectrum be affected? Growth of density perturbations on small scales Production of gravitational waves during preheating Conclusions

Inflation: large field model Oscillatory phase p=4 p=2 Slow-roll phase p=4 For p=2 p=2

Cosmological Perturbations Oscillatory phase p=2 p=4 Evolution of the perturbations is characterized by the M-S equation Vacuum fluctuations Radiation-dominated era Matter –dominated era

Equation of motion during preheating Are perturbations affected by (pre)heating? Equation of motion during preheating Mathieu Equation Mathieu Instablity Card with unstable stable

Mathieu Instablity Card Are perturbations affected by (pre)heating? Mathieu Instablity Card unstable stable

Solution: Floquet theory Are perturbations affected by (pre)heating? Solution: Floquet theory Constant curvature perturbation Early structure formation Perturbations grow if the Fourier mode is in the instability band and inside the Hubble radius during Pre-heating

Resonance band

Solution: Floquet theory Are perturbations affected by (pre)heating? Solution: Floquet theory Constant curvature perturbation Early structure formation μ=q/2 is the Floquet index

no Al Gravitational waves The growth of density perturbations will cause the production of GW In the linear regime, this can calculated perturbatively In the non-linear regime, we can estimate the signal using the halo model no Linear radius Non-linearities become important Inflaton halo evaporation Al Virialization

Gravitational Waves Production (III)

Reheating can affect the inflationary predictions Conclusions Reheating can affect the inflationary predictions Preheating can affect the perturbations on small scales, even in the single field slow-roll case Production of gravitational waves; potentially observable Production of black holes? Many things remain to be studied