Higgs-portal assisted Higgs inﬂationcftp.tecnico.ulisboa.pt/~2hdmwork/Slides/2016/Day4/Jinsu_Kim.pdf · Higgs-portal assisted Higgs inﬂation Jinsu Kim in collaboration with Wan-il

Higgs-portal assistedHiggs inflation

Jinsu Kimin collaboration with

Wan-il Park and Pyungwon Ko

KIAS - Quantum Universe Center

Sep. 9, 2016 @ IST, Lisboa, Portugal

Jinsu Kim @ KIAS Workshop on Multi-Higgs Models 2016

Our whole Universe was in a hot and dense state, then nearly14 billion years ago (accelerating) expansion started, ..., Thatall started with the Big Bang!

– The Big Bang Theory



Can Higgs be the inflaton?


Higgs inflation [Bezrukov Shaposhnikov 2008][Cervantes-Cota Dehnen 1995]


Higgs inflation

Zd

4x

p�g

M

2P

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

� Zd

4x

p�g

M

2P

2R+

1

2⇠hh

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

�

[Bezrukov Shaposhnikov 2008][Cervantes-Cota Dehnen 1995]


Higgs inflation

Zd

4x

p�g

M

2P

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

� Zd

4x

p�g

M

2P

2R+

1

2⇠hh

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

�

�h ⇠ 10�12 �h/⇠2h ⇠ 4⇥ 10�10



Higgs inflation

Zd

4x

p�g

M

2P

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

� Zd

4x

p�g

M

2P

2R+

1

2⇠hh

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

�

�h ⇠ 10�12 �h/⇠2h ⇠ 4⇥ 10�10

�h 6= 1/8 �h ⇠ 0.1 & ⇠h ⇠ 104 � 105



Higgs inflation

Zd

4x

p�g

M

2P

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

� Zd

4x

p�g

M

2P

2R+

1

2⇠hh

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

�

�h ⇠ 10�12 �h/⇠2h ⇠ 4⇥ 10�10

�h 6= 1/8 �h ⇠ 0.1 & ⇠h ⇠ 104 � 105


Higgs inflation

Zd

4x

p�g

M

2P

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

� Zd

4x

p�g

M

2P

2R+

1

2⇠hh

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

�

�h ⇠ 10�12 �h/⇠2h ⇠ 4⇥ 10�10

�h 6= 1/8 �h ⇠ 0.1 & ⇠h ⇠ 104 � 105

Ruled out ! Favoured !


Wait! Quantum Corrections?

In the pure SM case, assuming that the SM is valid all the wayup to the (nearly) Planck scale, �h can be very small due to theRG effects.


[Hamada et al. 2014][Allison 2014]

[Simone et al. 2009]

[Cook et al. 2014]

[Bezrukov et al. 2014]

Sketch:• The Einstein-frame potential is

U(h) =�h(t)h4

4(1 + ⇠hh2/M2

P

)2.

• Tensor-to-scalar ratio, for example, is given by

r ⇡ 64

3⇠2h

✓M2

P

h

◆4

1 + x

⇠hh2

4M2

P

�2

,

where

x ⌘ 1

�h

d�h

dt.


Cosmological observables :

x ⌘ 1

�h

d�h

dt, y ⌘ 1

d�h/dt

d2�h

dt2



Higgs inflation

Zd

4x

p�g

M

2P

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

� Zd

4x

p�g

M

2P

2R+

1

2⇠hh

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

�

�h ⇠ 10�12 �h/⇠2h ⇠ 4⇥ 10�10

�h 6= 1/8 �h ⇠ 0.1 & ⇠h ⇠ 104 � 105

�h ⇠ 10�12 small ⇠h & large r ⇠ O(0.01)�O(0.1)


Higgs inflation

Zd

4x

p�g

M

2P

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

� Zd

4x

p�g

M

2P

2R+

1

2⇠hh

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

�

�h ⇠ 10�12 �h/⇠2h ⇠ 4⇥ 10�10

�h 6= 1/8 �h ⇠ 0.1 & ⇠h ⇠ 104 � 105


Still ruled out ! Okay, but…


Higgs inflation

Zd

4x

p�g

M

2P

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

� Zd

4x

p�g

M

2P

2R+

1

2⇠hh

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

�

�h ⇠ 10�12 �h/⇠2h ⇠ 4⇥ 10�10

�h 6= 1/8 �h ⇠ 0.1 & ⇠h ⇠ 104 � 105


Still ruled out ! Okay, but…

[Salvio 2013]


Realisation with Higgs portal

The SM needs to be extended anyway in order to explain, atleast, the existence of DM.

We shall see that Higgs-portal interaction, which is generic inhidden-sector DM models, revives the Higgs inflation byweakening the dependence on Mt.

In this work, we choose to work with the SFDM model, wherethe hidden sector consists of a singlet scalar field S and afermionic DM-candidate field .

The SM sector and the hidden sector communicate through theHiggs-portal interaction:

Vportal

= µSHSH†H +1

2�SHS2H†H .


Important point is to note that

1

2⇠SS

2R

is generated via RG runnings.



Numerical Analysis

Relevant parameter list:• �S : quartic coupling of S field• � : coupling between S and , � S • �SH : portal coupling• ↵ : mixing angle between the dark Higgs and the SM Higgs• mS : mass of S field• ⇠S : Nonminimal coupling of S to gravity

Note that ⇠h is NOT a free parameter; shall be determined bythe Planck normalisation,

PS ⇡ 2.2⇥ 10�9 .




PS ⇡ 2.2⇥ 10�9 .




PS ⇡ 2.2⇥ 10�9 .


• LEP bound

• oblique parameters

• DM relic density

• DM direct detection

0 |� | . 0.6 ,

�0.2 .�SH . 0.4 ,

0 �S . 0.2



PS ⇡ 2.2⇥ 10�9 .


We are interested in the Higgs inflation !

⇠S = 0



PS ⇡ 2.2⇥ 10�9 .


⇠h = 220 , ⇠S = 0 ,mS = 500GeV ,

�SH = 0.2 ,�S = 0.2 ,� = 0.25


, , :

• perturbativity

• vacuum stability

• Planck 2015 data

�S = 0.1 ,

�SH = 0.25 ,

� = 0.15


, , :

• perturbativity

• vacuum stability

• Planck 2015 data


Summary

In this talk, we discussed• Higgs inflation in the presence of Higgs-portal interaction• and how a large tensor-to-scalar ratio can be achieved

without resort to a strong dependence on Mt.

Especially, using the model of singlet fermion dark matter as aconcrete model, we performed a numerical analysis andshowed how it is realised.

We find it amusing that the dark Higgs guarantees the darkmatter stability and improves the stability of electroweakvacuum as well as assisting the Higgs inflation at the same time.


Thank you


Backup


gµ⌫ ! gEµ⌫ = ⌦2 gµ⌫

, : ,

⌦2 = 1 +⇠�2

M2P

S =

Zd

4x

p�g

M

2P

2R� 1

2g

µ⌫@µ�@⌫�� U(�)

�

U(�) =V

⌦4

,

d�

d�=

1

⌦2

"⌦2 + 6⇠2

✓�

MP

◆2#1/2

Weyl rescaling[Bezrukov Shaposhnikov 2008][Cervantes-Cota Dehnen 1995]

S =

Zd

4x

p�g

M

2P

2R+ ⇠�

2R� 1

2g

µ⌫@µ�@⌫�� V (�)

�

,


Higgs inflation

Zd

4x

p�g

M

2P

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

�

Zd

4x

p�g

M

2P

2R+

1

2⇠hh

2R� 1

2g

µ⌫@µh@⌫h� 1

4�hh

4

�




PS ⇡ 2.2⇥ 10�9 .


⇠h = 220 , ⇠S = 0 ,mS = 500GeV ,

�SH = 0.2 ,�S = 0.2 ,� = 0.25

16⇡2��H= 6(1 + 3s2h)�

2H + 12�H�2

t � 6�4t

� 3�H(3g22 + g21) +3

8

�2g42 + (g22 + g21)

2�

+1

2s2s�

2HS

Documents

Higgs-portal assisted Higgs inﬂationcftp.tecnico.ulisboa.pt/~2hdmwork/Slides/2016/Day4/Jinsu_Kim.pdf · Higgs-portal assisted Higgs inﬂation Jinsu Kim in collaboration with Wan-il