Inflation and Higgs Fuminobu Takahashi (Tohoku & IPMU) 14th - - PowerPoint PPT Presentation

Inflation and Higgs

Fuminobu Takahashi (Tohoku & IPMU)

14th February 2015 HPNP2015@Toyama

Planck data out

Color: CMB temperature Texture: direction of polarization

(ns, r)

Planck, 1502.01589

Quadratic chaotic inflation is disfavored.

(ns, r)

Planck, 1502.01589

Quadratic chaotic inflation is disfavored.

Neff

Neff = 3.15 ± 0.23

(Planck TT, lowP, BAO)

U1' with fermions Nf 5 U1' SU2' SU2'SU2' SU3'

3 4 5 6 7 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Log10ΦGeV N eff

Br(h → invisible) = 0.2

0.1 0.01

• K. Jeong, FT, 1305.6521

Leff = 1 Λ2

φ

F 0

µνF 0µν|H|2

The bound now starts to constrain interesting scenarios such as Higgs portal dark radiation.

U1' with fermions Nf 5 U1' SU2' SU2'SU2' SU3'

3 4 5 6 7 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Log10ΦGeV N eff

Br(h → invisible) = 0.2

0.1 0.01

• K. Jeong, FT, 1305.6521

Leff = 1 Λ2

φ

F 0

µνF 0µν|H|2

The bound now starts to constrain interesting scenarios such as Higgs portal dark radiation.

Accelerated cosmic expansion solves various theoretical problems of the std. big bang cosmology.

Inflation

V

• δφ = H

2π

One way to realize the inflationary expansion is the slow- roll inflation.

Linde `82, Albrecht and Steinhardt `82

Guth `81, Sato `80, Starobinsky `80, Kazanas `80, Brout, Englert, Gunzig, `79

Fluctuations of volume

Distortion of space in a volume-conserving way

Scalar mode

Inflaton’s quantum fluctuations induce fluctuations in time and volume.

Super-horizon modes do not evolve.

: gravitational potential

Φ

Ψ

: curvature perturbations

ds2 = −(1 + Φ)dt2 + a(t)2(1 + 2Ψ)dx2

Tensor mode

Tensor mode perturbations are fluctuations of graviton itself.

ds2 = −dt2 + a(t)2 (δij + hij) dxidxj hij : traceless, divergent-free tensor = graviton.

hij ∼ Hinf MP

Observation vs Theory

Scalar mode Tensor mode V : the inflaton potential

φ

During inflation

After inflation

The inflaton excursion exceeds the Planck scale for r > O(10-3).

Lyth 1997

• Inflaton field excursion
• Inflation energy scale

Lyth bound:

Vinf ' (2 ⇥ 1016 GeV)4 ⇣ r 0.1 ⌘

Planck 2015 results XX

Predicted values of (ns, r)

Quadratic chaotic infl

SM Higgs inflation

The SM Higgs potential needs to be modified at large field values for successful inflation

h

SM Higgs inflation

The SM Higgs potential needs to be modified at large field values for successful inflation

h

(1)Non-canonical kinetic term (2)Non-minimal coupling to gravity

Higgs inflation with running kinetic term

The transition is at h = O(1013)GeV.

Nakayama and FT, 1008.2956,1008.4467, Hertzberg, 1110.5650

If a kinetic term grows at large field values, the potential gets flatter in terms of the canonically normalized field.

The quadratic chaotic inflation is possible, but it is now disfavored by Planck.

e.g.) L = 1

2

• 1 + ξh2

(∂h)2 − λ 4

• h2 − v22

FT 1006.2801,

ˆ h ⇠    h for h ⌧ 1/pξ pξh2 for h 1/pξ

hc ∼ 1/ p ξ

h4

ˆ h2

V (ˆ h) ⇠    λˆ h4 for h ⌧ 1/pξ

λ ξ ˆ

h2 for h 1/pξ

Needs some extension e.g. polynomial chaotic inflation.

Higgs inflation with running kinetic term

The transition is at h = O(1013)GeV.

Nakayama and FT, 1008.2956,1008.4467, Hertzberg, 1110.5650

If a kinetic term grows at large field values, the potential gets flatter in terms of the canonically normalized field.

The quadratic chaotic inflation is possible, but it is now disfavored by Planck.

e.g.) L = 1

2

• 1 + ξh2

(∂h)2 − λ 4

• h2 − v22

FT 1006.2801,

ˆ h ⇠    h for h ⌧ 1/pξ pξh2 for h 1/pξ

hc ∼ 1/ p ξ

h4

ˆ h2

V (ˆ h) ⇠    λˆ h4 for h ⌧ 1/pξ

λ ξ ˆ

h2 for h 1/pξ

Needs some extension e.g. polynomial chaotic inflation.

Nakayama, FT, Yanagida, 1303.7315

Salopek, Bond, Bardeen, `89, Bezrukov and Shaposhnikov `07

The potential for a canonically normalized scalar in the Einstein frame is where

V (φ) = 1 Ω4 λ 4

• h(φ) v22 ' λM 4

P

4ξ2 ✓ 1 2e−p

2 3 φ MP

◆

h MP / p ξ

Higgs inflation w/ non-minimal coupling

Salopek, Bond, Bardeen, `89, Bezrukov and Shaposhnikov `07

V (φ) = 1 Ω4 λ 4

• h(φ) v22 ' λM 4

P

4ξ2 ✓ 1 2e−p

2 3 φ MP

◆

Higgs inflation w/ non-minimal coupling

Potential becomes flatter at h & MP /

p ξ

h ∼ MP √ξ ∼ 1016 GeV

ξ ' 1.7 ⇥ 104 ✓ λ 0.13 ◆1/2 ✓ N 60 ◆

• Large coupling required by the COBE normalization.
• Higher dim. operators assumed to be negligible.

Caveats:

Unitarity is OK during inflation, but it matters at high E in the EW vacuum.

Strengths:

• Minimal particle content
• Reheating takes place naturally
• Consistent with the Planck data
• Quartic coupling runs, and it is sensitive to mt

SM Higgs inflation

ns ' 0.967, r ' ⇢ 0.13 running kinetic term 3 ⇥ 10−3 nonminimal coupling

Case of non-minimal coupling:

The SM near-criticality

The SM vacua is at the border between stability and meta-stability. Why??

Andreassen, Frost, Schwartz, 1408.0292

Hamada, Oda, Kawai, Park, 1408.4864

At the border, there is another minimum at around the Planck scale, which has the same energy as the EW vacuum.

The SM near-criticality

See 1212.5716 for arguments based on non-locality and various apps.

• cf. “Multiple point principle”
• There should be several degenerate vacua in energy.

Bennett, Nielsen `94 Froggatt, Nielsen `96

Topological Higgs Inflation

Hamada, Oda, FT 1408.5556

• Domain walls connecting the EW and Planck scale vacua.

h

vPlanck vEW

V

x

V

h ≈ 0

h ≈ vP lanck

Domain wall

Topological Higgs Inflation

Hamada, Oda, FT 1408.5556

• Domain walls connecting the EW and Planck scale vacua.

h

vPlanck vEW

V

x

V

h ≈ 0

h ≈ vP lanck

Domain wall w & H−1

Topological Higgs Inflation

Hamada, Oda, FT 1408.5556

• Domain walls connecting the EW and Planck scale vacua.

h

vPlanck vEW

V

x

V

h ≈ 0

h ≈ vP lanck

Domain wall w & H−1

The SM criticality may be related to the topological Higgs inflation.

The non-minimal coupling to gravity helps to satisfy this bound.

Inflation occurs inside domain walls if they are sufficiently thick:

vP lanck & a few MP

N.B. Another inflation needed to generate δ ∼ 10−5

Uplifting by new physics

• Negative effective potential may be lifted by new physics

effects above a certain scale.

h

Veff

New physics

h6 Λ2

NP

Domain walls in the Higgs potential

• Domain walls can be formed if the two vacua are

(quasi)-degenerate.

1 2 3 4 5 6 7 8 0.5 1 1.5 2 2.5 VH/1028GeV4 ϕ/108GeV 173.28 173.29 173.30

• Unstable domain walls annihilate, generating GWs.

Position of the false vacuum B i a s e n e r g y d e n s i t y

Domain walls in the Higgs potential

10-3 10-2 1012 1013 (Vf/Vmax)1/4 ϕf/GeV aLIGO ET D W d

• m

i n a t i

• n

early decay

Kitajima, FT, 1502.03725

TR = 3 × 108 GeV

• Unstable domain walls annihilate, generating GWs.

Position of the false vacuum B i a s e n e r g y d e n s i t y

Domain walls in the Higgs potential

TR = 104 GeV

10-5 10-4 10-3 108 109 1010 1011 1012 (Vf/Vmax)1/4 ϕf/GeV LISA DECIGO DW domination early decay

Kitajima, FT, 1502.03725

Higgs new inflation

GUT Higgs new inflation was extensively studied in the early 80s.

V

• Hawking `82, Starobinsky `82, Guth and Pi `82

It was, however, soon abandoned because CW corrections lead to too large density perturbations.

• 1. SUSY
• 2. Cancellations between gauge and Yukawa

couplings.

• 3. Very small gauge and Yukawa couplings
• 4. Extra damping mechanism
• 5. Gauge singlet inflaton

Known solutions

Hawking `82, Ellis, Nanopoulos, Olive, Tamvakis `82

Hawking `82, Starobinsky `82, Guth and Pi `82

Kolb, Turner Starobinsky `82, Baremboim, Chun, Lee, 1309.1695

Nakayama, FT 1108.0070,1203.0323

Shafi, Vilenkin `84, Pi `84

The last solution became popular since then. Now let us revisit the first solution using SUSY.

SUSY B-L Higgs new inflation

V

• δφ = H

2π

hφi ⇠ 1015 GeV

Senoguz and Shafi, `04, cf. Asaka et al `99

In SUSY, two Higgs are required for anomaly cancellation.

Φ(+2), ¯ Φ(−2) , Inflaton: φ2 =

• Φ¯

Φ

• The B-L breaking scale (inflaton VEV)

is fixed by COBE normalization.

vB−L = hφi ⇠ 1015 GeV

W = χ ⇣ v2

• Φ¯

Φ 2⌘ V (φ) ' v4 kv4φ2 v2φ4 + φ8 · · ·

MP = 1

Planck units adopted

The CW potential is partially cancelled between B-L gauge boson and gaugino contributions, Requiring that the curvature of the potential be smaller than O(0.1)Hinf, we obtain

Mλ . Hinf

• K. Nakayama and FT 1108.0070,

1203.0323

VCW (φ) ' g2

B−L

32π2 M 2

λφ2

✓ 1 3 ln φ2 φ2

∗

◆

N.B. The upper bound on SUSY breaking was overestimated in the literature.

Soft SUSY breaking mass

• f the B-L gaugino

A similar bound holds for the soft mass of RH sneutrino

Inflation scale Hinf

SUSY B-L Higgs inflation implies O(100)TeV SUSY!

Nakayama, FT 1203.0323

10-4 10-3 10-2 10-1 104 105 106 107

k Hinf [GeV]

Hinf ∼ 800TeV

Mλ, m ˜

N . O(100) TeV

Summary

• SUSY B-L Higgs inflation implies SUSY breaking
• f O(100)TeV.

r << 10-3

δ ⇠ 10−5, MP ' 2.4 ⇥ 1018 GeV ) vB−L ⇠ 1015 GeV, mSUSY ⇠ O(100)TeV consistent with mH, mν

• The SM Higgs can drive inflation if the potential is

modified to be flatter at large field values.

• Non-canonical kinetic term
• Running kinetic inflation
• Non-minimal coupling to gravity.
• is needed in the minimal set-up.
• The SM criticality may cause topological inflation.
• Domain walls annihilate producing GWs.

r ~ 10-3 r ~ 0.1

mt ∼ 171 GeV