1 Parametric resonance with Multi-frequencies in preheating José Pedro Mimoso University of Lisboa...
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Transcript of 1 Parametric resonance with Multi-frequencies in preheating José Pedro Mimoso University of Lisboa...
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
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Outline:
Motivations
(P)reheating after Inflation
Preheating with multi-frequencies
Conclusions
ERE08 –Salamanca: September 15, 2008
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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
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[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
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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
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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
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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
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Narrow Resonance
Broad Resonance
ab
a
b
ab
02cos tba
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Broad ResonanceNarrow Resonance
02cos tba
g
m
gRadiab
2
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Narrow Resonance
ICG –Portsmouth: May 16, 2008
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Narrow Resonance
ERE08 –Salamanca: September 15, 2008
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Narrow resonance
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arXiv: 0807.4805v1 [hep-ph]
[Dufaux et al, PRD (2006) hep-ph/0602144v2Tachyonic Resonance]
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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
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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…
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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
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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 ]
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ERE08 –Salamanca: September 15, 2008
29Kofman, Linde and Starobinski, Phys. Rev. D 56 (1997) 3258-3295
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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
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