The physical mass scales of multi-field preheating · 2020. 10. 28. · In the beginning, there was...

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

• 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

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.


4

CMB

Big Bang nucleosynthesis

Motivation

reheating

The reheating era ispoorly explored and constrained


Why reheating is important? 5

• heats the Universe

[Lineweaver (2003)]APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University


preheating

• It is important source of theoretical uncertainty:

[Planck 2018 results]APEC Seminar, 21 October 2020 Oksana Iarygina, Leiden University


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)]


preheating


[K. D. Lozanov, M. A. Amin (2017)]


• The duration of reheating shifts CMB predictions thus breaking the degeneracy ofinflation models



preheating




• The duration of reheating shifts CMB predictions thus breaking the degeneracy ofinflation models

determined by model of inflation






10


ü

Multi-field inflation


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


Hyperbolic manifolds from UV completions 12

Flattening of the potential is due to hyperbolic manifolds

alpha-attractors provide universal inflationary predictions


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)]

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 …


Plateau models of inflation 14

[R. Kallosh, A. Linde (2013)]


The inflationary plateau appears because of the exponential stretching of the growing branch.

T- and E-models as the prototypical workhorses 15

[J. J. M. Carrasco, R. Kallosh, A. Linde (2015)]





field-space curvature -1




potential steepnessfield-space curvature -1


Lattice simulations for single field alpha attractors 19


efficient preheating through inflaton self-resonance

Alpha-attractors are intrinsically multi-field models 20


N = 1 Supergravity embedding:

the super-potential

T-model E-model






21


ü

ü

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)]


Two-field system on a hyperbolic manifold 23

� ��

��

��

��

�

��

�

��

[ OI, E. Sfakianakis, D.G. Wang, A. Achucarro (2020)][ OI, E. Sfakianakis, D.G. Wang, A. Achucarro (2019)]


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?

.

Two-field system on a hyperbolic manifold 24

� ��

��

��

��

�

��

�

��



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?

Scaling relations for background quantities 25

E

T

:• in the slow-roll approximation and for


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


potential steepnessfield-space curvature -1

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


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

2.0

�

�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�

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.


0 5 10 15

-2

-1

0

1

2

cosmic time t

a-0.5 �,a-0.5 (d�

/dt)

��

��

��

��

-2 0 2 4 60.0

0.2

0.4

0.6

0.8

1.0

�-0.5�

V/�

E

;

10-5 10-4 0.001 0.010 0.100

7

8

9

10

11

12

13

�

PeriodT





28


ü

ü

ü

Covariant formalism to study the evolution of fluctuations 29


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)]


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





potential + field-space + kinematical effects



covariant time derivative in field space

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



The equations of motion for mode functions with and are



The equations of motion for mode functions with and are

curvature of space-time

geometry of field-space

potential contribution

kinematical effects


35Effective mass terms and scaling for hyperbolic manifolds




vanish for


-20 0 20 40 60 80 1000.01

0.05

0.10

0.50

1

cosmic time

(�-0.5)×

|m3,�

2|

-20 0 20 40 60 80 1000.01

0.05

0.10

0.50

1

cosmic time

(�-1)×

|m4,�

2|��

-2



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.



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.


tachyonic vs parametric resonance

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


• Inflationary background is safe• Geometrical destabilization leads to efficient preheating

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!


potential steepness:

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!


potential steepness:

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


E-model

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.


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]


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]

48Floquet charts

is a periodic functionwhere

[T. Krajewski, K. Turzyński, M. Wieczorek (2018)]

The resonance structure looks very different!


49Floquet charts

is a periodic functionwhere

[T. Krajewski, K. Turzyński, M. Wieczorek (2018)]

The resonance structure looks very different!


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


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


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

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.


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 .


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.


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


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.


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.


The physical mass scales of multi-field preheating · 2020. 10. 28. · In the beginning, there was...

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