Zhong-Zhi Xianyu Center for high energy physics, THU

November 9, 2014

IN THE NAME OF GOD PARTICLE

Inflation

Quantum fluctuations Large scale structure

⇢v(a) ⇠ const.

⇣1a

da

dt

⌘2=

8⇡G

3⇢(a)

a(t) ⇠ exp(Ht)a(t)

vacuum energy

Who drives?

V (�)

(MP = 1)

✏ = 12 (V

0/V )2

⌘ = V 00/V

Scalar tilt ns = 1� 6✏+ 2⌘

Tensor-to-scalar ratio r = 16✏

Scalar amplitude

(V/✏)1/4 ' 0.027

… and more

Inflaton

0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.000.0

0.1

0.2

0.3

0.4

ns

r

Planck+WP+highLPlanck+WP+highL+BICEP2

Observables

Scalar tilt ns = 1� 6✏+ 2⌘

Tensor-to-scalar ratio r = 16✏

(MP = 1)

Scalar amplitude

(V/✏)1/4 ' 0.027

… and more

v

14�v

4

V (�) =1

4�(�2 � v2)2

� ' 0.13 v ' 246GeV

Standard Model Higgs field

V (�) =1

4�(�2 � v2)2

� ' 0.13 v ' 246GeV

Standard Model Higgs field

LSM + LGR

Unknown Fundamental Theory

High energy

Low energy

Unknown Fundamental Theory

LSM + LGR + 12

p�g⇠R�2

High energy

Low energy

LJp�g

= 12R+ 1

2⇠R�2 + 12 (@µ�)

2 � V (�)

(MP = 1)

LJp�g

= 12R+ 1

2⇠R�2 + 12 (@µ�)

2 � V (�)

LEp�g

= 12R+

3(@µ⌦)2

⌦2+

(@µ�)2

2⌦2� V (�)

⌦4

gµ⌫ ! ⌦�2gµ⌫

⌦2 ⌘ 1 + ⇠�2

Weyl Transformation

(MP = 1)

V (�) = 14�(�

2 � v2)2

102GeV

V (�) = 14�(�

2 � v2)2

V (�) =�(�2 � v2)2

4(1 + ⇠�2)2

102GeV

1016GeV

0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.000.0

0.1

0.2

0.3

0.4

ns

r

Planck+WP+highLPlanck+WP+highL+BICEP2

Higgs inflation

r ' 0.003ns ' 0.967

⇠ ' 104

(V/✏)1/4 ' 0.027

A Large would ruin perturbation expansion

⇠ ⇠ 104

ZZ Xianyu, J Ren, HJ He, Phys. Rev. D 88 (2013) 096013

Unitarity Bound for Nonminimal Coupling

Unitarity: probability 1 amplitude Coupled channel analysis:

(MP = 1)

|a0| 12

W+

W�

Z0

Z0

|a0| =9⇠2E2

16⇡|⇠|

p8⇡E

3

Generalization to arbitrary background field channel:

J Ren, ZZ Xianyu, HJ He, JCAP 1406 (2014) 032

Unitarity of Higgs Inflation

�

(MP = 1)

WW ! ZZ

|a0| =1 + ⇠�2

16⇡�2

✓1� 1� ⇠�2

1 + 6⇠2�2

◆E2

� ⌧ 1/⇠ |a0| '3⇠2E2

8⇡

|a0| '⇠E2

16⇡� � 1/

p⇠

E . 1/⇠

E . 1/p

⇠

103 106 109 1012 1015 10181

103

106

109

1012

1015

1018

E (GeV)

|ξ|

Unitarity Bound

Large ϕUnitarity

Bound

InflationScale

(BICEP2)

Higgs inflation

J Ren, ZZ Xianyu, HJ He, JCAP 1406 (2014) 032

Unitarity of Higgs Inflation

Perturbation theory validated

Then we do it order by order

Firstly classical …

Perturbation theory validated

Then we do it order by order

1011GeV

Firstly classical …

Then quantum corrections …

Perturbation theory validated

Then we do it order by order

1000 106 109 1012 1015 1018

-0.05

0.00

0.05

0.10

m HGeVL

l

Metastable

Unstable

Central Values

4s in Mt

4s in MH

4s in a3

Instability of Higgs potential

from A. Spencer-Smith, 1405.1975

Instability of Higgs potential

µd�

dµ=

1

16⇡2

�24�2 � 6y4t + · · ·

�

Bosonic Fermionic

yt =Mtp2v

� =M2

h

2v2

Instability of Higgs potential

120 122 124 126 128 130 132168

170

172

174

176

178

180

MH HGeVL

MtHGe

VL

from A. Spencer-Smith, 1405.1975

HJ He, ZZ Xianyu, JCAP 1410 (2014) 019

Higgs inflation with TeV New Physics

Simplest extension: 1 boson + 1 fermion @ TeV scale

V (H,S) = � µ21H

†H � 12µ

22S

2 + �1(H†H)2

+ 14�2S

4 + 12�3S

2H†H + S

LY =� y1Q̄3LH̃tR � y2Q̄3LH̃TR

� 1p2y3ST̄LTR � 1p

2y4ST̄LtR + h.c.

HJ He, ZZ Xianyu, JCAP 1410 (2014) 019

Higgs inflation with TeV New Physics

Simplest extension: 1 boson + 1 fermion @ TeV scale

103 106 109 1012 1015 1018

0

0.05

0.10

0.15

m HGeVL

l il HSML l1

l2

l3Sample A��1 =1

16⇡2

�24�2

1 � 6y4t

+ 12�3 + 12�1y

22

� 6y42 � 12y21y22

+ · · ·�

HJ He, ZZ Xianyu, JCAP 1410 (2014) 019

Higgs inflation with TeV New Physics

Inflation potential

0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.000.0

0.1

0.2

0.3

0.4

ns

rPlanck+WP+highLPlanck+WP+highL+BICEP2

HJ He, ZZ Xianyu, JCAP 1410 (2014) 019

Higgs inflation with TeV New Physics

Nearly critical

Large ⇠

ZZ Xianyu, HJ He, JCAP 1410 (2014) 083

Asymptotically Safe Higgs inflation

Unknown Theory

SM+GR+…

Conformal field theory?

Criticality in Higgs+top sector?

106 108 1010 1012

0

0.02

0.04

0.06

0.01

0.03

0.05

m HGeVL

l

Gaussian fixed point

106 108 1010 1012

0

0.02

0.04

0.06

0.01

0.03

0.05

m HGeVL

l

1015 1016 1017 10181014

1015

1016

h HGeVLV1ê4 HG

eVL

mh=125GeV

mh=126GeV

mh=127GeV

ZZ Xianyu, HJ He, JCAP 1410 (2014) 083

Asymptotically Safe Higgs inflation

3M2P (H)H2 = V = 1

4�(H)�4 －minimally coupled

ZZ Xianyu, HJ He, JCAP 1410 (2014) 083

Asymptotically Safe Higgs inflation

125.0 125.5 126.0 126.5172.0

172.5

173.0

173.5

174.0

174.5

mh HGeVL

m tHGeV

L

0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.000.0

0.1

0.2

0.3

0.4

ns

r

Planck+WP+highLPlanck+WP+highL+BICEP2

Planck+WP+BICEP2 Hdust amp. unfixedLCollider

CMB

•  (In)equivalence of Jordan and Einstein frame at quantum level?

•  Higgs inflation in more complete new physics models. Supersymmetry? Supergravity?

•  Enhanced tensor-to-scalar ratio without critical point (fine-tuning)?

Outlook

Thank you