Hillclimbing
Higgs inﬂation
Kin-ya Oda(Osaka)with

Ryusuke Jinno (IBS)&

Kunio Kaneta (IBS→Minnesota)

標準模型大勝利!!
mF
mVκ F v or κ V v（良く⾔えば）
1t

ATLAS and CMS
LHC Run 1

WZ

10−1

τ

−2

10

10−3

b

ATLAS+CMS
SM Higgs bosonµ[M, ε] fit
68% CL
95% CL

−4

10

10−1

1

10

102

Particle mass [GeV]ATLAS & CMS (2016)

picture from web

8 TeV

13 TeV

BSM死屍累々

LQ1(ej) x2
LQ1(ej)+LQ1(νj) β=0.5
LQ2(μj) x2
LQ2(μj)+LQ2(νj) β=0.5
LQ3(τb) x2
LQ3(νb) x2
LQ3(τt) x2
LQ3(vt) x2
Single LQ1 (λ=1)
Single LQ2 (λ=1)

coloron(jj) x2

MultijetResonancescoloron(4j) x2

Leptoquarks

gluino(3j) x2

gluino(jjb) x2
01（悪く⾔えば）

2

3

4

TeV

RS Gravitons

RS1(jj), k=0.1

0RS1(ee,μμ), k=0.1

NR BH, nED=6, MD=4 TeV

2

3

4

QBH (jj), nED=4, MD=4 TeV
ADD (j+MET), nED=4, MD

Large Extra
Dimensions

ADD (ee,μμ), nED=4, MS

Heavy Gauge
BosonsSSM Z'(jj)TeV

4String Scale (jj)TeV

CMS Preliminary
SSM Z'(ττ)

3

ADD (jj), nED=4, MS
QBH, nED=6, MD=4 TeV

12

ADD (γ+MET), nED=4, MD

RS1(γγ), k=0.1
01

ADD (γγ), nED=4, MS
Jet Extinction Scale0

SSM Z'(ee)+Z'(µµ)

1

2

3

4

5

6

7

8

9

10

TeV

TeVまでにはなんにもなかった
SSM W'(jj)dijets, Λ+ LL/RR

SSM W'(lv)dijets, Λ- LL/RR

SSM Z'(bb)dimuons, Λ+ LLIM

0

1

2

3

4

TeV

5

dielectrons, Λ+ LLIM

ExcitedFermionse* (M=Λ)μ* (M=Λ)q* (qg)q* (qγ) f=1
b*

dimuons, Λ- LLIM
dielectrons, Λ- LLIM
single e, Λ HnCM
single μ, Λ HnCM

Compositenessinclusive jets, Λ+
inclusive jets, Λ0

1

2

3

4

5

6

TeV

CMS Exotica Physics Group Summary – ICHEP, 2016!

TeV
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21

今そこにあるBSM新物理✦ なんもなさ、を直接あつかう★ 漸近安全性→ ⼭⽥くんのトーク（昨⽇）✦ いやなんもなくないし派★ 暗⿊物質、ニュートリノ質量→ 中⻄さんのポスター（今⽇）★ インフレーション！

→ このトークのテーマ（実は、なんもなさ、とのハイブリッド）

前提

神は我々をキワキワに置いた（観測事実）

Our Universe

プランクスケールで３重のゼロ：４点結合、そのβ関数、裸の質量。
[Hamada, Kawai, KO, 2012]
picture from web

Plan
1. 宇宙ヤバイ
2. 多重臨界原理はヒッグス質量を予⾔していた
3. 登⼭ヒッグス・インフレーション

宇宙ヤバイ

http://dic.nicovideo.jp/a/宇宙ヤバイ

16

Planck Collaboration: Constraints on inflation

rom the 2015 maps using similar sky coverage to the 2013F(CY) likelihood (but greater sky coverage at 217 GHz and di↵eren
point source masks, as discussed in the text). The column labelled 2015F(CHM) (Plik) lists parameters for the Plik cross-half
mission likelihood that uses identical sky coverage to the CamSpec likelihood. The 2015 temperature likelihoods are combinedwith the Planck lowP likelihood to constrain ⌧. The last two columns list the deviations of the Plik parameters from those ohe nominal-mission and the CamSpec 2015(CHM) likelihoods. To help refer to specific columns, we have numbered the first six
explicitly.

宇宙論が精密科学になってしまった[1] Parameter[2] 2013N(DS)[3] 2013F(DS)[4] 2013F(CY)[5] 2015F(CHM)[6] 2015F(CHM) (Plik)

100✓MC . . . . . . . . .
⌦ b h2 . . . . . . . . . . .
⌦ c h2 . . . . . . . . . . .
H0 . . . . . . . . . . . .
ns . . . . . . . . . . . .
⌦m . . . . . . . . . . . .
8 . . . . . . . . . . . .
⌧ . . . . . . . . . . . . .
109 As e 2⌧ . . . . . . . .

1.04131 ± 0.00063
0.02205 ± 0.00028
0.1199 ± 0.0027
67.3 ± 1.2
0.9603 ± 0.0073
0.315 ± 0.017
0.829 ± 0.012
0.089 ± 0.013
1.836 ± 0.013

1.04126 ± 0.00047
0.02234 ± 0.00023
0.1189 ± 0.0022
67.8 ± 1.0
0.9665 ± 0.0062
0.308 ± 0.013
0.831 ± 0.011
0.096 ± 0.013
1.833 ± 0.011

1.04121 ± 0.00048
0.02230 ± 0.00023
0.1188 ± 0.0022
67.8 ± 1.0
0.9655 ± 0.0062
0.308 ± 0.013
0.828 ± 0.012
0.094 ± 0.013
1.831 ± 0.011

1.04094 ± 0.00048
0.02225 ± 0.00023
0.1194 ± 0.0022
67.48 ± 0.98
0.9682 ± 0.0062
0.313 ± 0.013
0.829 ± 0.015
0.079 ± 0.019
1.875 ± 0.014

1.04086 ± 0.00048
0.02222 ± 0.00023
0.1199 ± 0.0022
67.26 ± 0.98
0.9652 ± 0.0062
0.316 ± 0.014
0.830 ± 0.015
0.078 ± 0.019
1.881 ± 0.014([2][6])/ [6]
0.71
0.61
0.00
0.03
0.67
0.06
0.08
0.85
3.46

([5]

[6])/ [5]
0.17
0.13
0.23
0.22
0.48
0.23
0.07
0.05
0.42

直にインフレーション由来

Fig. 11. Marginalized joint 68 % and 95 % CL regions for (✏1 , ✏2 , ✏3 ) (top panels) and (✏V , ⌘V , ⇠V2 ) (bottom panels) for Planck
TT+lowP (red contours), Planck TT,TE,EE+lowP (blue contours), and compared with the Planck 2013 results (grey contours).

pixel-based likelihood that extends up to multipoles ` = 29. Useof the polarization information in this likelihood is denoted as“lowP” in this paper The optical depth inferred from the lowP
ikelihood combined with the Planck T T likelihood is typically⌧ ⇡ 0.07, and is about 1 lower than the typical values of⌧ ⇡ 0.09 inferred from the WMAP polarization likelihood (seeSect. 3.4) used in the 2013 papers. As discussed in Sect. 3.4
and in more detail in Planck Collaboration XI 2015) the LFI
70 GHz and WMAP polarization maps are consistent when bothare cleaned with the HFI 353 GHz polarization maps.7

3) In the 2013 papers, the Planck temperature likelihood wasquadruplets of PSBs. For example, at 217 GHz we produce fou
temperature and two temperature+polarization maps. We refeto these maps as detectors-set maps (or “DetSets” for short)
note that the DetSet maps can also be produced for any arbitrary
time period. The high multipole likelihood used in the 2013 pa
pers was computed by cross-correlating HFI DetSet maps fo
the “nominal” Planck mission extending over 15.5 months.8 Fo
the 2015 papers we use the full-mission Planck data extending
over 29 months for the HFI and 48 months for the LFI. In the
Planck 2015 analysis, we have produced cross-year and crosshalf-mission likelihoods in addition to a DetSet likelihood. The
baseline 2015 Planck temperature-polarization likelihood is also
a hybrid, matching the high multipole likelihood at ` = 30 to the
Planck pixel-based likelihood at lower multipoles.

a hybrid: over the multipole range ` = 2–49, the likelihood
was based on the Commander algorithm applied to 94 % ofhe sky computed using a Blackwell-Rao estimator. The like12. Marginalized was
joint 68 constructed% and 95 % CL regions
for n and r
Planck in combination with other data sets, comparedihood at higher multipoles (`Fig.
=50–2500)
from(4)fromThesky coverage used in the 2013 CamSpec likelihood wasto the theoretical predictions of selected inflationary models.
cross-spectra over the frequency range 100–217 GHz using the

Planck (2015)
s

0.002

今後の進展が期待できる✦ 宇宙背景重⼒⼦輻射が熱い（⽐喩的に）★ r から間接的に✤ CMB B-mode が受かれば即（明⽇にでも;Recall BICEP2）★ 直接観測は？
✤ (Ultimate) DECIGO で⾏けるかfrom DECIGO website

（参考）こんなかんじらしい
GW from Inflation

Primordial GW

GW energy density ratio Ωgw

Earlier universe Æ Smaller horizon scale Æ High GW freq.
Original Figure by
S. Kuroyanagi (2011)

KAGRA

DECIGO

GW from Inflation

Frequency [Hz]Energy density ∝ Tensor-Scalar Ratio (𝑟).
Power spectrum : Evolution history of the Universe.
DECIGO Correlation

・Spectrum Power.
Æ Energy scaleof inflation
・Cut-off freq.
ÆEnergy scaleof Reheating
Nakayama+,
Journal of Cosmology
and Astroparticle Physics
06 (2008) 020.

RESCEU APCosPA Summer School on Cosmology and Particle Astrophysics (August 3rd, 2014, Matsumoto)RESCEU APCosPA Summer School on Cosmology and Particle Astrophysics (August 3rd, 2014, Matsumoto)

安東さんのスライドから (2014)

もうすぐプランクスケール（重力×量子論）が
直接見える

Plan
1. 宇宙ヤバイ
2. 多重臨界原理はヒッグス質量を予⾔していた
3. 登⼭ヒッグス・インフレーション

ヒッグス質量は予言されていたStandard model criticality prediction top mass 173 IL 5 GeV
and Higgs mass 135 III 9 GeV
C.D. Froggatt a, H.B. Nielsen b

Phys. Lett. (1996)(2012)

MPP？なにそれ

nd
Nielsenofargue
that moreformulationof the[36,
QFT
may
n
n valuethe Higgs
fieldfundamental
is ThearoundthePlanck
scale
37,
38].
quantumfield
theory(QFT)
isformulated b
us to the micro-canonical ensemble, in which rather the average field
Howeverin theisstatisticalmechanics,
the most
is the microeld theory(QFT)
formulatedby thepathfundamental
integral conceptZ
ed whilecanonicalthe coupling
constants are determined dynamically. Let us
ensemble:S({ })['
Z
Z({
})
=
[d']
e
r argument step by step.
S({ })['] XAs =an illustration,
considerand vaporZ({ })[d']elet us ⌦(E),a system(Hofn co-existingE) . water(182)
onical ensemble
becomes
equivalent
to =themicro-canonicalone
in(180)thewithFrogatt&
Nielsen(1996)
a fixed pressure in a piston, placed inna room temperature. We add heat into
where the{ }1partition
thedependencethe[Review
in Hamada,
Kawai,
KO,
1501.04455]
amic (large volume)
limit:
Given(181),
weon
canthe piston.
The temperatureindenotes
the pistonfunction
rises
to
the
boiling point.
Even
if couplin
Froggattand Nielsen
argue
more
fundamental
formulationofthe
QFT may
we further
continueto coupling
addthatthe heat,isused to makethe water
into
thecolvapor,lectively.
Theitconstants
partitionfunction(180)
is analogous
multiplicity
se thedependence
on
the
(and
mass)
be analogous
to the micro-canonicalensemble,ratherthe average
field
without changing
the temperature. Thisway, forina whichlarge range
of energy,
theensembleinthestatisticalmechanics:
tition function(180)
analogous
to theonetodeterminedincanonical
temperature
is is
tuned
to
be the boilingpoint aredue
the thetwo co-existing
phases. Let us
正準
⼩正準
value is
fixed
while
the
coupling
constants
dynamically.
!
X
In
QFT
language,
this
will
be
translatedtothestatement
that
even
if
NatureZ
Z
Z
atisticalreview
mechanics:
Hntheir argument step by step.
X
Z(
)
=
e
.
changesthe field value in the micro-canonical version of theE(E QFT,E) the couplingE) := d The
e constantZ( ) (mass)
=X
d
dE
(H
E)to ethe micro-canonical one in the
canonical
ensemble
becomes equivalentis tuned to the value thatnallows two co-existing vacua.17

小正準版・場の理論（式で）

n
H
n
ple
point
principle
thermodynamic(largevolume)limit:
the partition
function(181),
we cann the Given
統計⼒学
Z(
)
=
e
.
(181)
The
ordinary
QFT
startsfrom
path
integral(180).
Letus
illustratetheZ
Z the multiplicity in the micro-canonic
V ! compute
1, we
will
recoverthe multiplicity
situation
by a simple
toy model:in the statisticalmechanics, the most fundan However(E E)= thed MPP
dE⌦(E)
e thatZ that⇣⌘original argument Z
forsays
the SM parameters
✓
◆
✓
Z
Z
canonical
ensemble:
熱⼒学（⼤体積）極限
R dD x Z|@'| 2+Z ⇤ + m |'| + |'| + · ·!
S
⇤,
m
,
,
.
.
.
[']
=
· micro.
(185)
Z
Z
Z
tisticalmechanics,
themostfundamental
concept
istheed so that our SM vacuum isE degeneratewithanother
one
whose
XD
X(E E) D
d S(E)x (@')(E
E),ation
I
,
I
,
.
.
.
)
!
[d']
e
d
x
I
d
x
|
2
4
0
⌦(E)
:=
d
e
Z(
)
=
d
dE
(H
E)
e
=
d
dE
e
,
(183)
n
⌦(E)
=
(H
E)
.
:
n
value of the Higgs field is around the Planck scale [36, 37, 38].
2

2

D

2

2

4

The partition function reads

n
n
Z
Z
Z
Xis formulated
m field theory (QFT)
by
the
path
integralS(⇤,m2 , ,... )[']
2
(E. E)Z ,⌦(E);⇤,m,E), . ,.noting. ... ) =[d']e ⌦(E)=ddE
eused the entropy
ln
that
S(E),
E,
and E(182)are(186)⌦(E)=⌦(IZ:=(H=:S(E),II.
0 Froggatt
2n 4
andNielsen
argue
that
more
fundamental
Z the
Zintegral overariables, intheV thermodynamic
limit,and E is
limit
!
1,
the
multiplicity
inthemicro-canonicalensem
nwe will recover
S({
})[']
場の理論 Z({
analogous
micro-canonicalensemble,(183)in w}) = [d'](180)
The counterpart
ofbe
Eq.e
(183) should ,betothethe
following:
S(E)
(E E)
=
d
dE
e
,
by the strong peak at their stationary values; byof✓ taking variations
◆ ✓
◆

ZZ
Z coupling constantsZ✓◆
Zis fixed
Z
R
value
while
the
are
dete
“entropy”
is
given
by
en
argue
that
more
fundamental
formulation
of
the
QFT
may
2
d x (@')
DD
e get dS/dE = and E = E:2D2

⇤I0 +m2 I2 + I4 +···

2
⌦(I
,
I
,
I
,
.
.
.
)
=
d⇤
dm
d
·
·
·
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Z
⇤,
m
, , .d. . x |'|
⌦(I
,
I
,
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.
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)
!
[d']
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d
x
I
I2
0
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0
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reviewS(E)their:=argument
step bystep.
where we used the entropyln ⌦(E); noting
that
S(E), E, and E arenotes
the dependenceensemble,
on ✓thecoupling
constants(andaveragemass) cole micro-canonicalrather
the
field
◆
Z
Zin which
Z
Z
S(E)extensive
variables,inthethermodynamic
limit,
over
isth
S
2
⇤Ione
+m Iin+theIthe+···integral(⇤,m , ,... and)['] EThe
canonical
ensemble
becomes
equivalenttopartitionfunction(180)
isanalogoustothecanonical
⌦(E)
!
e
=
⌦(E).
(184)
=
d⇤
dm
d
·
·
·
e
[d']
e
=: 0⌦(IS(I,areI02,,Idetermined
I2 ,4I,4 ,.... . )). = ln⌦(I0 , I2 , I4Let, . . .us) .
e the coupling constants
dynamically.
limit V ! 1, we will recover the multiplicity in the micro-canonical ensemble: 18
✓Z
◆ ✓Z
Z
2 ◆ ✓Z2RD
02d2
x (@')2 4
D
D⌦(I0 , I2 , I4 , . . . ) ! [d'] e
d x I0d x |'|I2
dD x |'|4◆I4 · · ·小正準版・場の理論（言葉で）Frogatt & Nielsen (1996)[Review in Hamada, Kawai, KO, 1501.04455]✦ 統計⼒学では⼩正準形式が本質★ 決まったエネルギー E の状態を⾜し上げて状態数Ωを勘定。
★ 全部の状態を⾜し上げる正準形式は、熱⼒学極限で状態数Ωが⼩正準形

式と⼀致することで正当化される。
✦ 場の理論だとどうなる？
★ 神はまず⼩正準的に場の空間積分値 I

n

を決める。

★ 全部の場の配位を⾜し上げる従前の経路積分から、結合定数（や宇宙項、質量、…）を⾜し上げて熱⼒学極限を取ると状態数Ωが得られる。
✦ Q: どんな結合定数（や宇宙項、質量、…）が配位を dominate するのか？

多重臨界原理
Frogatt & Nielsen (1996)[Review in Hamada, Kawai, KO, 1501.04455]✦ ⼩正準の神は場の空間積分値を好きに取りたい。
✦ 熱⼒学（⼤体積）極限において⾜し上げられる結合定数（や宇宙項、質量、…）はその値を挟む複数の真空が縮退するように⾃動的に tune される。

F(750), We Miss You!

Holger F. Bech Nielsen

F(750), We Miss You!

Veff (|Φ|)

Holger F. Bech Nielsen

micro canonical³ > dM @ G H >M @  E
Our VacuumΦmin 1

New VacuumΦmin 2246 GeV

10 GeV
18

MPlanck|Φ|

canonical
 ³ > dM @ exp  H >M @ / T

The total energy is given first, and the temperatu
多相共存は広いE に対してis determined
as a result.
Example: Water molecules in a cylinder with a
同じ T* を選ぶ。
fixed pressure.

Figure 4: Two different minima in the effective potential for the Higgs field.

the Planck energy scale is the “fundamental physics scale” for both energy and Higgs fields; they
have the same dimension.
Figure 6: Vapour, water and ice equilibrium in a bottle.
Two of the vacua, which we discuss today have for some reason exceptionally small, say,
Higgs field, while the “high field” vacuum has the “normal” order of unity in Planck3.1units
value
Model
Reasons
for its Higgs expectation value. So we rather ask the question:
It should be stressed that in specific model-pictures one can also derive the “Multiple (CritWhy do the two vacua, “present vacuum” and “condensate vacuum”, not have Planck scale,icality) Point Principle” supposedly though it is only possible in models allowing the couplingsay, Higgs fields? (Let me for the moment postpone a discussion of the fact that indeed
we haveconstants
to depend on the future too. Ninomiya and one of us (HBN) “derived” it in the imagian explanation[26, 27] from the “multiple point principle”, that these two vacua have exceptionallynary action type of theory, and somewhat similarly in a nonlocal theory by Stillits [71, 72] and it
was done in babyuniverse theory, see works by Kawana et al. [15, 16, 17, 18].
small Higgs expectation values scale.)

From Nielsen et al. (2017)

3. Reason

4. The Difficulty of the Bound State

When we - as we now do - want to check if the “multiple point principle” is a true/valid law
But Why should we believe in the postulate of the Multiple Point Principle ? of nature, we have the difficulty that an important role is played by a bound state with which thevacuum, which we call “condensate vacuum”, is filled.

p
vapor
water

T
T*

vapor
water + vapor
water

E

一般化された多重臨界原理
Nielsen (2012)✦ 熱⼒学極限で、なんかある量を extremize しようと思ったら複数の allowed region の端に来る。
F(750), We Miss You!

Holger F. Bech Nielsen

11
10

8

6
4
2
0

From Nielsen
et al.
(2017)
Figure 5: Contour
curves.

もういっこ臨界だと尚良い✦ プランクスケールで３重のゼロ：★ ４点結合、そのβ関数、裸の質量。

Hamada, Kawai, KO (2013)✦ 同時に R の係数 も臨界になってるかも！？

→今⽇の話

Plan
1. 宇宙ヤバイ
2. 多重臨界原理はヒッグス質量を予⾔していた
3. 登⼭ヒッグス・インフレーション

余談：Hillclimbing
ぐぐる翻訳よりぐぐる画像検索より

Higgs inﬂation16✦ ナイスである：

Planck Collaboration: Constraints on inflation

Salopek, Bond, Bardeen (1989)
Bezrukov, Shaposhnikov (2008)★ ⼈類が今まで⾒た唯⼀の素スカラー場★ CMB の bests ﬁt modelFig. 11. Marginalized joint 68 % and 95 % CL regions for (✏1 , ✏2 , ✏3 ) (top panels) and (✏V , ⌘V , ⇠V2 ) (bottom panels) for Planck
TT+lowP (red contours), Planck TT,TE,EE+lowP (blue contours), and compared with the Planck 2013 results (grey contours).

Planck (2015)

Fig. 12. Marginalized joint 68 % and 95 % CL regions for ns and r0.002 from Planck in combination with other data sets, comparedto the theoretical predictions of selected inflationary models.

extrapolation of the eﬀective potential Vef f ( h ) using purely Standard Model would leadto a negative eﬀective potential. Various other discussion of the Higgs and Fermion masses
from cosmological restriction are found in [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22, 23, 24, 25, 26, 27, 28, 29, 30].
Also Shaposnikov et al [31] have predited the Higgs mass using it as inflaton, It may
be explainable that our predictions and Shaposnikovs et al.’s are close by both having
Standard Model high up in energy.
p
In Michael Scherer’s dissertation[32] one finds a Higgs mass 6.845v (where v is the
Higgs field vacuum expectation value).
Sylwester Kornowski rather postdict [33] the Higgs mass.
A bit depending on the temperature in the cosmological eras to be passed a suﬃciently
low Higgs mass would lead to the next minimum in the eﬀective potential being so lowthat the vacuum we live in would have decayed.

MPP と両立できる?
✦ 【鑑賞】天才の描いた絵→

Nielsen (2012)For higher mass than about the 129.4 GeV the eﬀective potential will be positive allover.

✦ 途中で⼭があると inﬂation には使えない？

Hamada, Kawai, KO (2014)★ 上から勢いよく落とせば通り越せる。

→ 中⻄さんのポスター（今⽇）★ R も臨界になってたらいんじゃね？

→ このはなし

登山インフレーション
Z

S⇠

h

Jinno, Kaneta (2017)

p
2
4
d x
g F ( )R + (@ ) + V ( )2✦ Einstein frame potential 〜 V/F★ V(φ)=0 の点で F(φ)=0 なら持ち上がる。
✦ Einstein frame の canonical 場は⼤体 ln F
2

★ V/F

が F の多項式なら exponentially ﬂat.

iModel 2 corresponds n = 2 in Eq. (7). In this figure thevertical axes is arbitrary, and we take M = 0.1MP .

登山ヒッグス・インフレーション✦ やったこと

where β2 ≃ 2 × 10−5 =: β2SM in the SM [25]. The
and where
higherβ orderterms
loop-suppressed, β , · · ·−5 areSM=: β2 in the SM [25]. The3 cubic
2 ≃ 2 × 10
and andwillhigher
be neglectedorder termshereafter.
are loop-suppressed, β3 , · · · ≪ β2
Inandthewillfollowing
weKaneta,
set λmin =KO
0 so(2017)that thebeJinno,neglected
hereafter.
In the following
λmin
0 soassumingthat the potential becomeszero atweφset
M= by
the
J =
tial becomeszerois atrealized
φJ = Mwith
by assuming
MPP
In theSM, thisthe topthequark
In the SM, this is realized with the top quark massmt ≃171.4 GeV for the strong
strongcoupling
coupling
αs0.1185≃ 0
mt ≃ 171.4 GeV for the
α
≃
s
18
18
leadingto toMM≃≃44××10
GeV[17].
[17].However,
However,the pleading
10 GeVthe precise
valuesof theβ2β2andthatrealize
realize
λmin
are avaluesof theand M
M thatλmin= 0=are0alteredby extraparticlessuch
such asright-handed
neutrinby extraparticles
as thetheheavy
heavy
right-handed
Higgs-portal dark
see seee.g. e.g.
Refs.Ref[30–
nos nos
andandthetheHiggs-portal
darkmatter;matter;34]. Therefore we take them as free parameters hereafter
34]. Therefore
we take
as freeher
Also, we consider
thethemfollowingformsparameters
for the conforma
2 Letter:the following forms for the con
Also,
factorwe
in consider
this3
factor in this Letter:
⎧
% &2
φJ
⎪
⎪
⎧⎨1 − % &2 (Model 1),
M
φJ&4
%
Ω =⎪
(13)
⎪
1
−
(Model1),⎨⎪φJ⎪⎩1 − M(Model 2).
&
%
Ω
=
M
F ⎪
4
φ
J
⎪
⎩1 −
(Modelthis2).
setup, theWe summarize the setup M
in Fig. 1. Given★ 4点結合を minimum のまわりで展開★ λ(φ) 〜 β2 [ln (φ/M)]

Einstein-frame potential is expanded as⎧
We summarize
thesetup in Fig. 1. Given this setu
4
⎪
β
M
⎪
⎨ 2 potential(1 − FΩ − ·is· · )expanded(Model
Einstein-frameas 1),
16
%
&
V =
(14)
4
β
M
1
⎪
2
⎧⎪
22
1− Ω
− ···
(Model 2).
⎩ 4
F
⎪
12
⎪ β2 M64⎨(1 − Ω − · · · )(Model 1),

結果✦ r （宇宙背景重⼒⼦

放射の効果）がもうすぐみえる。
✦ 普通の Higgs

inﬂation と区別がつく。

Jinno, Kaneta, KO (2017)

まとめ
1. 宇宙ヤバイ
2. 多重臨界原理はヒッグス質量を予⾔していた
3. 登⼭ヒッグス・インフレーション•

多重臨界原理と整合的•

普通の Higgs inﬂation と区別可能

Thank you!