Collapse of Small Scales Density Perturbations during Preheating

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, ar. Xiv: 1002. 3039, ar. Xiv: 1002. 3278]1

Outline q Introduction: large field inflation q Pre-heating and cosmological perturbations: can the power spectrum be affected? q Growth of density perturbations on small scales q Production of gravitational waves during preheating q Conclusions 2

Inflation: large field model Oscillatory phase p=2 p=4 Slow-roll phase p=4 p=2 q For p=2 3

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 4

Are perturbations affected by (pre)heating? q Equation of motion during preheating q Mathieu Equation Mathieu Instablity Card with unstable 5

Are perturbations affected by (pre)heating? Mathieu Instablity Card unstable 6

Are perturbations affected by (pre)heating? q Solution: Floquet theory q Constant curvature perturbation q Early structure formation Perturbations grow if the Fourier mode is in the instability band inside the Hubble radius during Pre-heating 7

Resonance band 8

Are perturbations affected by (pre)heating? q Solution: Floquet theory μ=q/2 is the Floquet index q Constant curvature perturbation q Early structure formation 9

Gravitational waves q The growth of density perturbations will cause the production of GW q In the linear regime, this can calculated perturbatively q In the non-linear regime, we can estimate the signal using the halo model no Linear radius Non-linearities become important Inflaton halo evaporation A l Virialization 10

Gravitational Waves Production (III) 11

Conclusions q Reheating can affect the inflationary predictions q Preheating can affect the perturbations on small scales, even in the single field slow-roll case q Production of gravitational waves; potentially observable q Production of black holes? q Many things remain to be studied 12