dynamics of cosmological relaxation after reheating...conclusion 1. high reheating temperature is...

The 3rd IBS-MultiDark-IPPP WorkshopNovember 24 2016

Dynamics of cosmological relaxation after reheating

Hyungjin Kim

KAIST & IBS CTPU

[Graham, Kaplan, Rajendran 15]


m2h(�0) ⇠ �(90GeV)2


• Relaxion dependent Higgs mass

• Higgs vev dependent Back-reaction potential

• Inflationary Hubble friction

Necessary ingredients for relaxion are

Whole scanning process take place during inflation

What happens after the reheating ?

Two possible scenarios

• Reheating temperature higher than electroweak scale

• Reheating temperature lower than electroweak scale




• thermal correction is small

• barrier is still there

• relaxion does not evolve




• thermal correction is small

• barrier is still there

• relaxion does not evolve

• thermal correction is large

• barrier disappears

• relaxion evolves!

• gauge symmetry is restored

(positive)

To preserve successful selection of electroweak scale

we need small enough field velocity

To preserve successful selection of electroweak scale,

we require

otherwise, the selection of electroweak scale is easily ruined

Dynamically selected EW scale is not stable against high reheating temperature

Alternative possibility?

A possibility:

A new frictional force from Abelian gauge boson

[Choi, HK, Toyokazu; Work in progress]

A possibility:



• Friction from Hubble

• Friction from gauge field production

A possibility:



Anomalous coupling

time-dependent coupling breaks conformal invariance

and develops instability of gauge boson

[Anber & Sorbo, 09]

Dispersion relation

propagatingmode

tachyonicmode

for

Dispersion relation

and exponentially grows in time

tachyonic mode exists for

&

Background evolution of scalar field develops instability

and exponentially produces gauge bosons

Produce X

Background evolution of scalar field develops instability

and exponentially produces gauge bosons

How does X field modify the field velocity of relaxion ?

Produce X

modifies

Evolution of scalar field

force


velocity-dependent

friction


“gauge”friction



terminal velocity is determined as

�̇ = ⇠FXH


terminal velocity is determined as

�̇ = ⇠FXH

decreasing function in time!

When does it stop?

barrier is formed at T ⇠ Tc

�̇2 ⇤4b ?

When does it stop?


�̇2 ⇤4b ?

Yesrelaxion stops at Tc

When does it stop?


�̇2 ⇤4b ?


No

relaxion stops at Tb

�̇2(Tb) ⇠ ⇤4b* Tb is when

When does it stop?

relaxion will stop at

Ts = min(Tc, Tb)


�̇2 ⇤4b ?


No

relaxion stops at Tb

�̇2(Tb) ⇠ ⇤4b* Tb is when


��(ts)

(

�V

�V ⇤2v2


��(ts)

(

�V

�V T 4s ⇤2v2

To prevent overproduction of dark gauge boson

106 107 108 109 1010 1011 1012102

104

106

108

1010

1012

1014

1016

1018

10-2

10-4

10-6

10-8

10-10

10-12

10-14

10-16

10-18

Gauge field overproduction

�Ne↵ �

0.3

✓h� = 10�20

✓h� = 10�15

✓h� = 10�10


Preliminary

106 107 108 109 1010 1011 1012102

104

106

108

1010

1012

1014

1016

1018

100

10-2

10-4

10-6

10-8

10-10

10-12

10-14

10-16


Fifth force

SN1978A

✓h� = 10�20

✓h� = 10�15

✓h� = 10�10

�Ne↵ �

0.3

Preliminary

106 107 108 109 1010 1011 1012102

104

106

108

1010

1012

1014

1016

1018

102

100

10-2

10-4

10-6

10-8

10-10

10-12

10-14

Fifth force


SN1978A

LHC

Globular Cluster

�Ne↵ �

0.3

✓h� = 10�5

✓h� = 10�15

✓h� = 10�10

[Choi & Im 16][Flacke et. al. 16]

regarding constraints on relaxion scenario

Preliminary

Conclusion

1. High reheating temperature is dangerous for cosmological relaxation

2. If relaxion has anomalous coupling to Abelian gauge boson,

it transfer its kinetic energy into gauge bosons

3. Field velocity approaches to terminal velocity,

4. The relaxion can be re-captured by back-reaction potential at EWPT

under reasonable choice of parameters

dynamics of cosmological relaxation after reheating...conclusion 1. high reheating temperature is...

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