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.

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

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.

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

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

:• in the slow-roll approximation and for

E-model

T-model

10-5 10-4 0.001 0.010 0.1000.40

�-0.5Hend

10-5 10-4 0.001 0.010 0.1000

�-0.5 �

(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

• 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

the scale hierarchy:

10-5 10-4 0.001 0.010 0.100

�0.5�

(bottom to top)

�=10-2 �=10-3

�=10-4

0 20 40 60 80-1

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

cosmic time t

a-0.5 �,a-0.5 (d�

��

-2 0 2 4 60.0

�-0.5�

10-5 10-4 0.001 0.010 0.100

PeriodT

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

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

cosmic time

(�-0.5)×

|m3,�

-20 0 20 40 60 80 1000.01

cosmic time

(�-1)×

|m4,�

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

e-folding number N

m�,eff

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

42Effective mass for alpha attractors

100 200 300 400 500t

E model

T model 100 200 300 400 500t

E model

T model

100 200 300 400 500

E model

T model 100 200 300 400 500

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

E model

T model 100 200 300 400 500t

E model

T model

100 200 300 400 500

E model

T model 100 200 300 400 500

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

cosmic time t

0 20 40 60 80-1

cosmic time t

0 20 40 60 80

cosmic time t

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

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

� [ �1/2MPl ]

m�2[�

47WKB approximation

amplification factorafter the first tachyonic region

0 2 4 6 8 10 12

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

[�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/�e

0.0 0.5 1.0 1.5 2.0 2.5

�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

k / �

0.0 0.5 1.0 1.5 2.0 2.50.00

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

� �,�

-1.0 -0.5 0.0 0.5 1.010-2410-2210-2010-1810-1610-1410-12

e-folding number N

� �,�

-0.4 -0.2 0.0 0.2 0.410-2410-2210-2010-1810-1610-1410-12

e-folding number N

� �,�

-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

� �,�

-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

� �,�

-0.1 0.0 0.1 0.2 0.3 0.410-2410-2210-2010-1810-1610-1410-12

e-folding number N

� �,�

E-model

T-model

The E-model can preheat through resonance, when the T-model cannot.

54E-T preheating efficiency

11000000

1100000

110000

� (MPl2 )

1100000

110000

� (MPl2 )

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

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

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

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

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

Log10(�/MPl2 )

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

Log10(�/MPl2 )

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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