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

2. 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

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

4. 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

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

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

7. 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

8. Resonance band

9. 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

10. 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

11. Gravitational Waves Production (III)

12. 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