1

Parametric resonance with Multi-frequencies in preheating

José Pedro Mimoso

University of Lisboa

Collaboration with:

Ana NunesTiago Charters

ERE08 –Salamanca: September 15, 2008

Physics Dep. Science Fac. & CFTC

arXiv: 0807.4805v1 [hep-ph]

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

Outline:

Motivations

(P)reheating after Inflation

Preheating with multi-frequencies

Conclusions

ERE08 –Salamanca: September 15, 2008

4

Inflation: as much of a problemas of a solution?!

The accelerated expansion dilutes the matter content

The universe becomes too cold Trad ~ e-60 Tinit

0)3(3

42 p

ma

a

p

Φ

V(Φ)

))(( 2 V

Slow roll

Fast oscillations

Inflation exhausts the Universe:

initnen 180

ERE08 –Salamanca: September 15, 2008

5(A. Linde)

So

First, inflation

Second, recreate Hell

ERE08 –Salamanca: September 15, 2008

6

[Chaotic inflation - A. Linde]

Hm

The expansion of the universe can be neglected

[M. S. Turner, 1983]

0'3 VH

Coherent oscillations of

mtt

Asin

ERE08 –Salamanca: September 15, 2008

7

Old Reheating

“Old” reheating

Phenomenological perturbative decay of the inflaton

Temperature reheating

Thermalization

decmH 23

m

g

8

24

8

4mh

mmm ,H

pltotreheat mg

T

1002.0

ERE08 –Salamanca: September 15, 2008

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

0

,3

2int

2

2

2

kkk

V

a

kH

Parametric Resonance of

2222int ,, ghV

0,3 int22 VVaH

ERE08 –Salamanca: September 15, 2008

9

Parametric Resonance

DistinguishBroad Resonance

Narrow Resonance

Exponential Production of Particles

02

22

22

2

kk m

g

am

k

te tk

Floquet theor.

Periodic

Ignore expansion

Minkowski 02cos tbaMathieu Equation

ERE08 –Salamanca: September 15, 2008

10

Narrow Resonance

Broad Resonance

ab

a

b

ab

02cos tba

ERE08 –Salamanca: September 15, 2008

11

Broad ResonanceNarrow Resonance

02cos tba

g

m

gRadiab

2

ERE08 –Salamanca: September 15, 2008

12

Narrow Resonance

ICG –Portsmouth: May 16, 2008

13

Narrow Resonance

ERE08 –Salamanca: September 15, 2008

14ERE08 –Salamanca: September 15, 2008

15

Narrow resonance

ERE08 –Salamanca: September 15, 2008

16ERE08 –Salamanca: September 15, 2008

17ERE08 –Salamanca: September 15, 2008

18ERE08 –Salamanca: September 15, 2008

19ERE08 –Salamanca: September 15, 2008

arXiv: 0807.4805v1 [hep-ph]

[Dufaux et al, PRD (2006) hep-ph/0602144v2Tachyonic Resonance]

20ERE08 –Salamanca: September 15, 2008

21

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

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 amplitudeL 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

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!

25ERE08 –Salamanca: September 15, 2008

26

27

Broad Resonance

0)( 2 kjkk ttba

t

k

t

k dssi

k

jk

dssi

k

jkj

k ee 00

)()(

22

|| 2kkn

[Kofman, Linde and Starobinski, Phys. Rev. D 56 (1997) 3258-3295 ]

ERE08 –Salamanca: September 15, 2008

28

ERE08 –Salamanca: September 15, 2008

29Kofman, Linde and Starobinski, Phys. Rev. D 56 (1997) 3258-3295

ERE08 –Salamanca: September 15, 2008

30

jtot

jk

jk

KK

jk

KKjk

nnee

neen

sin)1(12

)(22

22

)2/(

1

jtot

KK

Kjk

ee

e

sin12

1ln(2

1

22

2

)2/(

Charters, Mimoso & Nunes

ERE08 –Salamanca: September 15, 2008

31ERE08 –Salamanca: September 15, 2008

32ERE08 –Salamanca: September 15, 2008

33ERE08 –Salamanca: September 15, 2008

34ERE08 –Salamanca: September 15, 2008

35ERE08 –Salamanca: September 15, 2008