the physical mass scales of multi-field preheating · 2020. 10. 28. · in the beginning, there was...
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The physical mass scalesof multi-field preheating
Oksana Iarygina
Based on:
[ OI, E. Sfakianakis, D.G. Wang, A. Achucarro: JCAP 1906, no. 06, 027(2019) [arXiv:1810.02804][ OI, E. Sfakianakis, D.G. Wang, A. Achucarro: arXiv:2005.00528 (2020)]
21 October 2020
APEC Seminar
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• Why do we need to know the physics of preheating?
• Why multi-field?
• Scaling relations in multi-field alpha-attractors
• Mass scales for preheating
Outline: 2
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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In the beginning, there was (probably) inflation 3
preheatingRadiation & matterdominance
ü Solves horizon, flatness problems
ü Explains fluctuations as stretched quantum perturbations seeds for all structure
ü Predicts a nearly scale invariant spectrumtogether with Gaussian perturbations
A simple mechanism: scalar field with a flat potential.
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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4
CMB
Big Bang nucleosynthesis
Motivation
reheating
The reheating era ispoorly explored and constrained
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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Why reheating is important? 5
• heats the Universe
[Lineweaver (2003)]APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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Why reheating is important? 6
preheating
• It is important source of theoretical uncertainty:
[Planck 2018 results]APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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Why reheating is important? 7
preheating
• inefficient preheating can lead to prolonged matter-dominated phase after inflation, changing the time during inflation when the CMB modes exit the horizon
comoving Hubbleradius
[A. Liddle, S. Leach (2003)]
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University[M. Amin at al (2014)]
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Why reheating is important? 8
preheating
comoving Hubbleradius
[K. D. Lozanov, M. A. Amin (2017)]
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
• The duration of reheating shifts CMB predictions thus breaking the degeneracy ofinflation models
[A. Liddle, S. Leach (2003)]
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Why reheating is important? 9
preheating
comoving Hubbleradius
[K. D. Lozanov, M. A. Amin (2017)]
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
• The duration of reheating shifts CMB predictions thus breaking the degeneracy ofinflation models
determined by model of inflation
[A. Liddle, S. Leach (2003)]
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• Why do we need to know the physics of preheating?
• Why multi-field?
• Scaling relations in multi-field alpha-attractors
• Mass scales for preheating
10
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
ü
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Multi-field inflation
preheatingRadiation & matterdominance
field-space metric potential
[figure courtesy Yi Wang]
Energy scale of the very early universe could be as high as 10#$GeV.Could contain scalar fields to participate in inflationary dynamics.
Two types of perturbations:
• Adiabatic (curvature)• Non-Adiabatic (isocurvature)
Derivative interaction/random trajectory turns:couple the fluctuations and modify their dispersion relations and correlators.
11
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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Hyperbolic manifolds from UV completions 12
Flattening of the potential is due to hyperbolic manifolds
alpha-attractors provide universal inflationary predictions
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
ü Supergravityü String theory compactification: Fibre inflationü …
[R. Kallosh, A. Linde (2013)][S. Ferrara, R. Kallosh, A. Linde and M. Porrati (2013)][J. J. M. Carrasco, R. Kallosh, A. Linde and D. Roest (2015)]
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Hyperbolic manifolds from UV completions 13
[R. Kallosh, A. Linde (2013)][S. Ferrara, R. Kallosh, A. Linde and M. Porrati (2013)][J. J. M. Carrasco, R. Kallosh, A. Linde and D. Roest (2015)]
Flattening of the potential is due to hyperbolic manifolds
alpha-attractors provide universal inflationary predictions
ü Supergravityü String theory compactification: Fibre inflationü …
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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Plateau models of inflation 14
[R. Kallosh, A. Linde (2013)]
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
The inflationary plateau appears because of the exponential stretching of the growing branch.
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T- and E-models as the prototypical workhorses 15
[J. J. M. Carrasco, R. Kallosh, A. Linde (2015)]
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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T- and E-models as the prototypical workhorses 16
[J. J. M. Carrasco, R. Kallosh, A. Linde (2015)]
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
field-space curvature -1
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T- and E-models as the prototypical workhorses 17
[J. J. M. Carrasco, R. Kallosh, A. Linde (2015)]
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
potential steepnessfield-space curvature -1
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T- and E-models as the prototypical workhorses 18
[J. J. M. Carrasco, R. Kallosh, A. Linde (2015)]
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
Lattice simulations for single field alpha attractors 19
[K. D. Lozanov, M. A. Amin (2017)]
efficient preheating through inflaton self-resonance
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Alpha-attractors are intrinsically multi-field models 20
[J. J. M. Carrasco, R. Kallosh, A. Linde (2015)]
N = 1 Supergravity embedding:
the super-potential
T-model E-model
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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• Why do we need to know the physics of preheating?
• Why multi-field?
• Scaling relations in multi-field alpha-attractors
• Mass scales for preheating
21
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
ü
ü
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Lattice simulations for two-field alpha attractors 22
showed very efficient preheating with the presence of spectator field
[T. Krajewski, K. Turzynski, M. Wieczorek (2018)]
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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Two-field system on a hyperbolic manifold 23
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[ OI, E. Sfakianakis, D.G. Wang, A. Achucarro (2020)][ OI, E. Sfakianakis, D.G. Wang, A. Achucarro (2019)]
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
curvature of the field-space
,• The two-stage inflation leading to single-field motion at
• The two models during inflation are the same in the multi-field case, up to slow roll corrections.
• Does it hold during preheating?
.
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Two-field system on a hyperbolic manifold 24
� �� �� �� �� �� �� ����
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[ OI, E. Sfakianakis, D.G. Wang, A. Achucarro (2020)][ OI, E. Sfakianakis, D.G. Wang, A. Achucarro (2019)]
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
curvature of the field-space
,.• The two-stage inflation leading to single-field motion at
• The two models during inflation are the same in the multi-field case, up to slow roll corrections.
• Does it hold during preheating?
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Scaling relations for background quantities 25
E
T
:• in the slow-roll approximation and for
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
E-model
T-model
10-5 10-4 0.001 0.010 0.1000.40
0.45
0.50
0.55
0.60
0.65
�
�-0.5Hend
10-5 10-4 0.001 0.010 0.1000
1
2
3
4
�
�-0.5 �
end
(bottom to top)
• the scaling is similar for the E- and T-models, with slightly different pre-factors
[ OI, E. Sfakianakis, D.G. Wang, A. Achucarro (2020)][ OI, E. Sfakianakis, D.G. Wang, A. Achucarro (2019)]
potential steepnessfield-space curvature -1
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Hierarchy between the frequency of background oscillations and the Hubble scale
26
ET
E
T
• More background oscillations occur per Hubble time for smaller values of alpha
• For small alphas the Hubble scale can be neglected, as it takes a large number of background oscillations for any considerable red-shifting to occur.
• More damping of the background motion per oscillation for the E-model
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
10-5 10-4 0.001 0.010 0.1001
510
50100
�
�/H
end
the scale hierarchy:
10-5 10-4 0.001 0.010 0.100
0.5
1.0
1.5
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�
�0.5�
/Hend
(bottom to top)
�=10-2 �=10-3
�=10-4
0 20 40 60 80-1
0
1
2
3
cosmic time t
�-0.5�
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Asymmetric motion of the E-model 27
ET• the T-model starts “higher up on the plateau" at the end of inflation
• the background motion is asymmetric for the E-model, spending much more time near the plateau and far less time near the steep potential wall.
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
0 5 10 15
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a-0.5 �,a-0.5 (d�
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• Why do we need to know the physics of preheating?
• Why multi-field?
• Scaling relations in multi-field alpha-attractors
• Mass scales for preheating
28
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
ü
ü
ü
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Covariant formalism to study the evolution of fluctuations 29
preheatingRadiation & matterdominance
The gauge-invariant perturbations obey
[H. Kodama and M. Sasaki (1984)][M. Sasaki, E. D. Stewart (1995)][D. Langlois and S. Renaux-Petel (2008)][D. I. Kaiser, E. A. Mazenc, and E. I. Sfakianakis (2013)]
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
To study fields at the end of inflation, we consider scalar metric perturbations around a spatially flat FLRW line element
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Covariant formalism to study the evolution of fluctuations 30
preheatingRadiation & matterdominance
The gauge-invariant perturbations obey
[H. Kodama and M. Sasaki (1984)][M. Sasaki, E. D. Stewart (1995)][D. Langlois and S. Renaux-Petel (2008)][D. I. Kaiser, E. A. Mazenc, and E. I. Sfakianakis (2013)]
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
To study fields at the end of inflation, we consider scalar metric perturbations around a spatially flat FLRW line element
covariant time derivative in field space
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Covariant formalism to study the evolution of fluctuations 31
preheatingRadiation & matterdominance
The gauge-invariant perturbations obey
[H. Kodama and M. Sasaki (1984)][M. Sasaki, E. D. Stewart (1995)][D. Langlois and S. Renaux-Petel (2008)][D. I. Kaiser, E. A. Mazenc, and E. I. Sfakianakis (2013)]
potential + field-space + kinematical effects
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
To study fields at the end of inflation, we consider scalar metric perturbations around a spatially flat FLRW line element
covariant time derivative in field space
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32Covariant formalism to study the evolution of fluctuations
When the background motion is restricted along the direction
the field-space structure simplifies and the quantization of the fluctuations proceeds as usual.
The quadratic action becomes
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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33Covariant formalism to study the evolution of fluctuations
The equations of motion for mode functions with and are
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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34Covariant formalism to study the evolution of fluctuations
The equations of motion for mode functions with and are
curvature of space-time
geometry of field-space
potential contribution
kinematical effects
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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35Effective mass terms and scaling for hyperbolic manifolds
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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36Effective mass terms and scaling for hyperbolic manifolds
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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37Effective mass terms and scaling for hyperbolic manifolds
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
vanish for
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38Effective mass terms and scaling for hyperbolic manifolds
-20 0 20 40 60 80 1000.01
0.05
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cosmic time
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|m3,�
2|
-20 0 20 40 60 80 1000.01
0.05
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-2
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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39Effective mass terms and scaling for hyperbolic manifolds
the field spaceRicci curvature scalar
Our focus: fluctuations can undergo tachyonic excitation, more efficient than parametric amplification and is a truly
multi-field phenomenon with a crucial dependence on the field-space geometry.
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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40Effective mass terms and scaling for hyperbolic manifolds
the field spaceRicci curvature scalar
Our focus: fluctuations can undergo tachyonic excitation, more efficient than parametric amplification and is a truly
multi-field phenomenon with a crucial dependence on the field-space geometry.
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
tachyonic vs parametric resonance
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Geometrical destabilization 41
[S. Renaux-Petel and K. Turzynski (2016)]
Alpha-attractors are safe against geometric destabilization effects until close to the end of inflation.
During inflation the effective super-horizonisocurvature mass in the slow-roll approximation
-1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.010-6
10-5
10-4
0.001
0.010
0.100
1
e-folding number N
m�,eff
2
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
• Inflationary background is safe• Geometrical destabilization leads to efficient preheating
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42Effective mass for alpha attractors
100 200 300 400 500t
-0.5
0.5
1.0
1.5
2.0
m�
E model
T model 100 200 300 400 500t
-1.0
-0.5
0.5
1.0
m�
E model
T model
100 200 300 400 500
-0.5
0.5
1.0
E model
T model 100 200 300 400 500
-1.0
-0.5
0.5
1.0
E model
T model
massive case
massless case
no tachyonic resonance in massive E-model!
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
potential steepness:
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43Effective mass for alpha attractors
100 200 300 400 500t
-0.5
0.5
1.0
1.5
2.0
m�
E model
T model 100 200 300 400 500t
-1.0
-0.5
0.5
1.0
m�
E model
T model
100 200 300 400 500
-0.5
0.5
1.0
E model
T model 100 200 300 400 500
-1.0
-0.5
0.5
1.0
E model
T model
massive case
massless case
no tachyonic resonance in massive E-model!
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
potential steepness:
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44Effective mass terms for massive fields
m1,�2 m2,�2
0 20 40 60 80-1
0
1
2
3
4
cosmic time t
meff
2
0 20 40 60 80-1
0
1
2
3
4
5
cosmic time t
meff
2
0 20 40 60 80
0
2
4
6
8
cosmic time t
meff
2
parametric resonance is suppressed for
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
E-model
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45Effective mass terms for massless fields
m1,�2 m2,�2
0 20 40 60 80
-1012345
cosmic time t
�-0.5�
m1,�2 m2,�2
0 20 40 60 80-1
0
1
2
3
4
cosmic time t
�-0.5�
E-model
For n < 2 the wavenumber contribution is less important than potential after few oscillations, for n > 2 it dominates over the potential at late times, for sufficiently large wave-numbers.
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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46Effective mass terms and scaling for alpha attractor potentials
In the E-model with n = 1 the potential term can dominate over the tachyonic field-space curvature
-1.0 -0.5 0.0 0.5 1.00.0
0.5
1.0
1.5
2.0
2.5
� [ �1/2MPl ]
m�2[�
2]
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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47WKB approximation
amplification factorafter the first tachyonic region
0 2 4 6 8 10 12
-4
-2
0
2
4
t
Re[� k]
WKB (red) before, during and after a tachyonic transitionAPEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
0 2 4 6 8 10 12
-4
-2
0
2
4
tIm
[�k]
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48Floquet charts
is a periodic functionwhere
[T. Krajewski, K. Turzyński, M. Wieczorek (2018)]
The resonance structure looks very different!
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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49Floquet charts
is a periodic functionwhere
[T. Krajewski, K. Turzyński, M. Wieczorek (2018)]
The resonance structure looks very different!
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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Floquet charts for symmetric potentials 50
With a proper rescaling
the resonance structure is identical, regardless ofthe exact value of the field-space curvature
“master diagram”
emerges a unifying picture
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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51Floquet charts E-model
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
k/�
�0/�e
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
k/�
�0/�e
The E-model has a richer resonance structure during (p)reheating, due to competing mass scales
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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52Full floquet diagram vs potential contribution
0.0 0.5 1.0 1.5 2.0 2.50.00
0.05
0.10
0.15
0.20
k / �
� k
0.0 0.5 1.0 1.5 2.0 2.50.00
0.05
0.10
0.15
0.20
k / µ
� kAPEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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53Preheating efficiency
-1.0 -0.5 0.0 0.5 1.0 1.5 2.010-2410-2210-2010-1810-1610-1410-12
e-folding number N
� �,�
�(M
Pl4)
-1.0 -0.5 0.0 0.5 1.010-2410-2210-2010-1810-1610-1410-12
e-folding number N
� �,�
�(M
Pl4)
-0.4 -0.2 0.0 0.2 0.410-2410-2210-2010-1810-1610-1410-12
e-folding number N
� �,�
�(M
Pl4)
-1.0 -0.5 0.0 0.5 1.0 1.5 2.010-2410-2210-2010-1810-1610-1410-12
e-folding number N
� �,�
�(M
Pl4)
-0.2 0.0 0.2 0.4 0.6 0.8 1.010-2410-2210-2010-1810-1610-1410-12
e-folding number N
� �,�
�(M
Pl4)
-0.1 0.0 0.1 0.2 0.3 0.410-2410-2210-2010-1810-1610-1410-12
e-folding number N
� �,�
�(M
Pl4)
E-model
T-model
The E-model can preheat through resonance, when the T-model cannot.
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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54E-T preheating efficiency
11000000
1100000
110000
11000
0.0
0.5
1.0
1.5
� (MPl2 )
Nreh
1100000
110000
11000
1100
0.0
0.5
1.0
1.5
� (MPl2 )
Nreh
Preheating for massive fields• The T-model: tachyonic resonance of the field for
• The E-model: self-resonance of the field for , while the T-model does not preheat!
For massless fields and steeper potentials • tachyonic resonance of a spectator field, starting at
For alphas preheating is practically instantaneous for any .
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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The sum up of the scaling results for hyperbolic manifolds 55
ET
The amplification per Hubble time grows as
• The amplification factor during each tachyonic regime is approximately the same
• There are oscillations per Hubble time
• We can ignore the slow red-shifting of the background
For :
The Floquet chart is ”universal” and can be scaled between different values of alpha.
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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56Outlook
• Inflation along spectator direction and turning around horizon crossing can have observational consequences
• Non-linear effects and backreaction?
0 200 400 600 800 1000-0.1
0.0
0.1
0.2
0.3
0.4
cosmic time t
�(t),�(t),H(t)
0.0 0.2 0.4 0.6 0.8 1.010-1210-1010-810-610-410-2
e-folding number N
� �V,BR
1,BR
2
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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57Multi-field preheating reduces theoretical uncertainties
Single-field simulations are unable to capture the most important time-scales,
which control the tachyonic growth of the spectator field.
-5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.00.0
0.5
1.0
1.5
2.0
Log10(�/MPl2 )
Nreh
Effective field theory of preheating leads to reducing of error bars of the plot.
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University
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58Multi-field preheating reduces theoretical uncertainties
Single-field simulations are unable to capture the most important time-scales,
which control the tachyonic growth of the spectator field.
-5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.00.0
0.5
1.0
1.5
2.0
Log10(�/MPl2 )
Nreh
Effective field theory of preheating leads to reducing of error bars of the plot.
APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University