宇宙を支配する重力法則は何か？¤の学校_ryo... · 2018-07-25 ·...

宇宙を支配する重力法則は何か？ 2018年7月22日第48回天文天体物理若手夏の学校

山口大学創成科学研究科理論宇宙物理学研究室齊藤　遼

今日は

について、お話しします。

修正重力理論

今日は

について、お話しします。

修正重力理論一般相対論

今日の話の流れ

1.  なぜ一般相対論の修正を試みるか？

2.  加速膨張の統一理論 ‒ 高階微分スカラーテンソル理論

Koyama, arXiv:1504.04623 Joyce+, arXiv:1407.0059 Heisenberg, arXiv:1807.01725

レビュー論文

2.1 統一理論の理論的整合性

2.2 統一理論の観測的検証重力波と第５の力

重力とは時空（時間＋空間）の歪み（曲がり）であり、モノの質量によって、時空の歪みが生み出される。

重いモノの周りでは、時間が遅れたり、モノが縮んだりする。

一般相対性原理と等価原理からの理論的帰結！

一般相対論 Einstein（1916）

重力とは時空（時間＋空間）の歪み（曲がり）であり、モノの質量によって、時空の歪みが生み出される。

重いモノの周りでは、時間が遅れたり、モノが縮んだりする。

一般相対性原理と等価原理からの理論的帰結！

一般相対論 Einstein（1916）

観測的にどこまで正しいのだろうか？

一般相対論の検証曲率 or 密度

重力ポテンシャル ICG研究所HPより [Baker+ 15]

重力波

CMB 銀河

現在の宇宙

（連星パルサー）

（地球）

いろいろな環境における



CMB

天体スケール

宇宙論スケール

重力波

銀河


現在の宇宙

一般相対論でOK

OK…？不確定要素多し



CMB

天体スケール

宇宙論スケール

重力波

銀河


現在の宇宙

一般相対論でOK

OK…？不確定要素多し

非常に大きな外挿

修正の必要性：宇宙の加速膨張何かしらの

　現在の宇宙は，加速膨張している．その説明には，何かしらの未検証の物理を導入する必要がある．我々の基礎物理への理解が未だ不十分であることのサイン

宇宙の組成比

？

たくさんの候補

未知の負の圧力を持つ物質が存在 ?

暗黒エネルギー

宇宙論的なスケールでは、一般相対論が破綻？

修正重力理論

現在の標準宇宙項

イメージ

いずれも加速膨張を説明可能 & “自然な”導入法は知られておらず

理論・観測の両面で多角的な研究が必要

修正重力理論研究の目的 1.  様々な加速膨張モデルをどう区別するか？

2.  整合性のチェック

一般相対論を修正すると何が起こるか？

着眼すべき観測量は何か？できれば、新しい現象の発見と検証法の提案例）ニュートン重力 → 一般相対論：宇宙膨張、重力波、時間の遅れ、、、

一般相対論を修正すると何かマズいことはないか？

例えば宇宙膨張解や天体解の存在・安定性

高密度環境（太陽系など）でのテストとの整合性

高エネルギー領域への拡張性




Koyama, arXiv:1504.04623 Joyce+, arXiv:1407.0059 Heisenberg, arXiv:1807.01725

レビュー論文



Einstein方程式は、計量の高々2回微分までで書かれた、4次元の

局所的・共変的な作用から導かれる唯一の運動方程式である。

以上の何かしらの仮定を破る必要がある

一般相対論をどう修正するか？

Lovelockの定理（Einstein方程式の唯一性）

CLASSIFICATION

➤ Lovelock’s theorem (1971):“The only second-order, local gravitational field equations derivable from an action containing solely the 4D metric tensor (plus related tensors) are the Einstein field equations with a cosmological constant.”

✦ > 2nd-order time derivatives.✦ Non-local action ⇒ things like .⇤�2

✦ Introduce new fields.✦ Posit extra dimensions.✦ Don’t derive field equations from an action.

UK Dark Energy Strategy 20201.Classification.

Modified Gravity

Add new field content

Higher dimensions Non-local

Scalar

Vector

Tensor

f

✓R

⇤

◆

Some! degravitation

scenarios

Scalar-tensor & Brans-Dicke

GalileonsGhost condensates

the Fab Four

Coupled Quintessencef(T)

Einstein-Cartan-Sciama-Kibble

Chern-Simons

Cuscuton

Chaplygin gases

Einstein-Aether

Massive gravityBigravity

EBI

Bimetric MOND

Horndeski theories Torsion theories

KGB

TeVeS

General RμνRμν, ☐R,etc.f (R)

Hořava-Lifschitz

f (G)

Conformal gravity

Strings & Branes

Generalisations of SEH

Cascading gravity

Lovelock gravity

Einstein-Dilaton-Gauss-Bonnet

Gauss-Bonnet

Randall-Sundrum Ⅰ & Ⅱ DGP

Kaluza-Klein

Lorentz violation

Lorentz violation

Emergent Approaches

Padmanabhan thermo.

2T gravity

Rµ⌫⇤�1Rµ⌫

Higher-order

CDT

Tessa Baker

Lovelock’s theorem

Non-action Approaches

Entanglement entropy ht

tp://

users

.ox.ac

.uk/~

lady2

729

by

修正重力理論余分な自由度を導入

計量の高階微分を導入

非局所理論高次元理論

CLASSIFICATION

➤ Lovelock’s theorem (1971):“The only second-order, local gravitational field equations derivable from an action containing solely the 4D metric tensor (plus related tensors) are the Einstein field equations with a cosmological constant.”

✦ > 2nd-order time derivatives.✦ Non-local action ⇒ things like .⇤�2

✦ Introduce new fields.✦ Posit extra dimensions.✦ Don’t derive field equations from an action.

UK Dark Energy Strategy 20201.Classification.

Modified Gravity

Add new field content

Higher dimensions Non-local

Scalar

Vector

Tensor

f

✓R

⇤

◆

Some! degravitation

scenarios

Scalar-tensor & Brans-Dicke

GalileonsGhost condensates

the Fab Four

Coupled Quintessencef(T)

Einstein-Cartan-Sciama-Kibble

Chern-Simons

Cuscuton

Chaplygin gases

Einstein-Aether

Massive gravityBigravity

EBI

Bimetric MOND

Horndeski theories Torsion theories

KGB

TeVeS

General RμνRμν, ☐R,etc.f (R)

Hořava-Lifschitz

f (G)

Conformal gravity

Strings & Branes

Generalisations of SEH

Cascading gravity

Lovelock gravity

Einstein-Dilaton-Gauss-Bonnet

Gauss-Bonnet

Randall-Sundrum Ⅰ & Ⅱ DGP

Kaluza-Klein

Lorentz violation

Lorentz violation

Emergent Approaches

Padmanabhan thermo.

2T gravity

Rµ⌫⇤�1Rµ⌫

Higher-order

CDT

Tessa Baker

Lovelock’s theorem

Non-action Approaches

Entanglement entropy ht

tp://

users

.ox.ac

.uk/~

lady2

729

by

修正重力理論余分な自由度を導入

計量の高階微分を導入

非局所理論高次元理論

もっと系統的に加速膨張モデル（のエッセンス）を解析できないか？

一般相対性原理と等価原理からの理論的帰結！特別な観測者（座標系）は存在しない

　一般相対論の原理のうち、宇宙論的スケールで

正しくない可能性のあるものは何か、、、？

加速膨張の統一理論のアプローチ

特別な観測者

銀河の地図 [SDSS project]

宇宙マイクロ波背景放射（CMB） [Planck衛星]

�T

T= O(10�5)

宇宙が一様等方に見える観測者が存在する（CMB静止系）

特別な観測者

実際に観測される宇宙マイクロ波背景放射（右） [COBE衛星]

�T

T= O(10�3)

�T

T= O(10�5)

地球はCMB静止系に対して370km/sで運動している。

加速膨張の統一理論のアイデア

特別な観測者（座標系）は存在しない

１. 特別な観測者（座標系）がある２. ただし、理論が幾何学量（計量）で書けることは保つ

この一般化の下で加速膨張を起こす整合的な理論はあるか？

膨張宇宙の幾何学 t

0 = �(t� vx/c

2) , x

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ｔ’ 一定：非一様等方

ｔ一定面：一様等方

時間 t 方向

時間 t’ 方向

膨張宇宙の幾何学

ｔ一定面：一様等方

時間 t 方向

nµ 加速/外的曲率

(3)Rµ⌫⇢�内的曲率

Nラプス関数

aµ,Kµ⌫ ⇠ rµn⌫<latexit sha1_base64="GsrroZXFcD2x0UF4XUhS1ahhjZg=">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</latexit><latexit sha1_base64="GsrroZXFcD2x0UF4XUhS1ahhjZg=">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</latexit><latexit sha1_base64="GsrroZXFcD2x0UF4XUhS1ahhjZg=">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</latexit><latexit sha1_base64="GsrroZXFcD2x0UF4XUhS1ahhjZg=">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</latexit>

3+1分解

[ Gleyzes+ 13, 15 ]

1.  特別な“時間方向”がある（“空間”座標変換不変性は保つ） 2.  理論は幾何学量で書ける

外部曲率内部曲率

A unifying action of dark energy (DE)

ラプス

＊専門家への注 f(R)も含む。しかし、Massive gravityは条件１を満たさないため，入っていない．

S =

�d4x

��gL[N, aµ, Kµ� ,(3)Rµ��; t]

加速

加速膨張（DE）の統一理論

多くの加速膨張モデルがこの理論で記述できる

加速膨張（DE）の有効理論膨張時空まわりで作用を展開

Zd3xdta3

M2

2

⇢�Kij�K

ij � (1 + ↵L) �K2 +H2↵K�N2

+ 4H↵B�K�N + (1 + ↵H)R�N + 4�1�K�N + · · ·�

<latexit sha1_base64="S1CJMckYFoQi/rsMN7YQP4ySiLY=">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</latexit><latexit sha1_base64="S1CJMckYFoQi/rsMN7YQP4ySiLY=">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</latexit><latexit sha1_base64="S1CJMckYFoQi/rsMN7YQP4ySiLY=">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</latexit><latexit sha1_base64="S1CJMckYFoQi/rsMN7YQP4ySiLY=">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</latexit>

SEFT =<latexit sha1_base64="klET/Jm6vgxpm/XVMj7LjoMPmP4=">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</latexit><latexit sha1_base64="klET/Jm6vgxpm/XVMj7LjoMPmP4=">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</latexit><latexit sha1_base64="klET/Jm6vgxpm/XVMj7LjoMPmP4=">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</latexit><latexit sha1_base64="klET/Jm6vgxpm/XVMj7LjoMPmP4=">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</latexit>

[Gleyzes+ 13; Gubitosi + 13]

多くの加速膨張モデルの“宇宙論”を統一的に解析できる

CMB計算コード：EFTCAMB [Hu+ 14; Raveri+ 14]

理論的整合性（安定性）

観測・実験と比較する前に、理論は以下の整合性（安定性）の条件を満たす必要がある。

ハミルトニアンが下に有界基底状態がある

下に有界でないハミルトニアンを持つ系は量子力学的に不安定

宇宙の時計 - 理論の書き換え nµ

時間一定面を定めるスカラー関数が存在する：

Clock場

nµ / rµ�N�2 ! (r�)2

�(t,x) = 一定

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高階スカラーテンソル理論 DEの統一理論は2階微分を含んだスカラーテンソル理論に等価：

S =

Zd4x

p�gL

⇥�,r�,r2

�

⇤

Ostrogradskyゴーストの問題

　作用が高階微分（場の2階微分以上）を含むと余分な自由度が現れる。この余分な自由度のハミルトニアンは下に有界でなく不安定性をもたらす。

初期条件

Ostrogradsky （1850）

DHOST (Degenerate Higher-Order ST)

Horndeski

EOMが2階微分まで GLPV

自由度が＋１のみ（高階微分に起因する余計な自由度がない） [ Langlois & Noui 15 ]

[ Horndeski 74 ]

[ Gleyzes+ 14 ]

加速膨張の統一理論

整合的な高階スカラーテンソル理論ラグランジアンの関数形をうまく選べば、２階微分を含んでも、余分な自由度を含まないようにできる

[ Horndeski 74] [Creminelli+ 05] [Deffayet+ 09, Kobayashi+ 11] Horndeski理論

L2 = G2(�, X),

L3 = �G3(�, X)��,

L4 = G4(�, X)R + G4X

�(��)2 � (�µ��)2

�,

L5 = G5(�, X)Gµ��µ�� 1

6G5X

�(��)3 � 3��(�µ��)2 + 2(�µ��)3

�.

ラグランジアンを運動方程式が２階微分方程式になるように選ぶ

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X微分

最初の非自明な理論

高階微分によって余分な自由度（初期条件）は生じない Ostrogradskyゴースト

[ Horndeski 74] [Creminelli+ 05] [Deffayet+ 09, Kobayashi+ 11] Horndeski理論

L2 = G2(�, X),

L3 = �G3(�, X)��,

L4 = G4(�, X)R + G4X

�(��)2 � (�µ��)2

�,

L5 = G5(�, X)Gµ��µ�� 1

6G5X

�(��)3 � 3��(�µ��)2 + 2(�µ��)3

�.

ラグランジアンを運動方程式が２階微分方程式になるように選ぶ

実はさらなる一般化が可能 Beyond Horndeski

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X微分

最初の非自明な理論

高階微分によって余分な自由度（初期条件）は生じない

しかし、 Ostrogradskyゴースト

２階微分を含んでも、余分な自由度を含まないようにできる

DHOST (Degenerate Higher-Order ST)

Horndeski

EOMが2階微分まで GLPV

自由度が＋１のみ（高階微分に起因する余計な自由度がない） [ Langlois & Noui 15 ]

[ Horndeski 74 ]

[ Gleyzes+ 14 ]


整合的な高階スカラーテンソル理論ラグランジアンの関数形をうまく選べば、

Beyond Horndeski

DHOST理論 Langlois & Noui 15 ]

DHOST = Degenerate Higher-Order Scalar-Tensor theories

４階の運動方程式, しかし加速度項の係数行列が縮退している：

det

✓@2L

@Qm@Qn

◆= 0

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* { Qn }はスカラー場や計量

縮退条件

for any background

高階微分によって余分な自由度（初期条件）は生じない Ostrogradskyゴースト

これでも

縮退した高階スカラーテンソル理論

２次のDHOST理論 Langlois & Noui 15 ]

L = P +Q⇤�+ FR+5X

I=1

AILI

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縮退条件関数に３つの条件 2つのクラス: Class I & Class II

理論は５つの関数パラメータを持つ: P ,Q , F ,A1 , A3

* 3 [Achour+ 16]

２次のDHOST理論 Langlois & Noui 15 ]

L = P +Q⇤�+ FR+5X

I=1

AILI


縮退条件関数に３つの条件 2つのクラス: Class I & Class II

理論は５つの関数パラメータを持つ: P ,Q , F ,A1 , A3

* 3 [Achour+ 16]

Horndeski ( Class I )

P = G2, Q = �G3, F = G4

A1 = �A2 = 2G4X (Others 0)<latexit sha1_base64="ZkuLJbJJgU6iouxmWWxUgcZVj/Q=">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</latexit><latexit sha1_base64="ZkuLJbJJgU6iouxmWWxUgcZVj/Q=">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</latexit><latexit sha1_base64="ZkuLJbJJgU6iouxmWWxUgcZVj/Q=">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</latexit><latexit sha1_base64="ZkuLJbJJgU6iouxmWWxUgcZVj/Q=">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</latexit>

⇢<latexit sha1_base64="NUWsDJQMUuNz4hqZlqIiJi+Wi8U=">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</latexit><latexit sha1_base64="NUWsDJQMUuNz4hqZlqIiJi+Wi8U=">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</latexit><latexit sha1_base64="NUWsDJQMUuNz4hqZlqIiJi+Wi8U=">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</latexit><latexit sha1_base64="NUWsDJQMUuNz4hqZlqIiJi+Wi8U=">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</latexit>


DHOST Horndeski

GLPV



Class I Class II


DHOST Horndeski

GLPV



Class I Class II

安定な宇宙論解なし [Langlois+ 17]

ここまでのまとめ 1.  なぜ一般相対論の修正を試みるか？

2.  加速膨張の統一理論

-  宇宙論スケールでの一般相対論の検証

-  加速膨張の原因？

-  特別な座標系の存在に基づくアプローチ

-  理論の整合性 DHOST = 縮退したスカラーテンソル理論

Class I ( Horndeski )

Class II 安定な宇宙論解なし ⇢<latexit sha1_base64="NUWsDJQMUuNz4hqZlqIiJi+Wi8U=">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</latexit> <latexit sha1_base64="NUWsDJQMUuNz4hqZlqIiJi+Wi8U=">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</latexit> <latexit sha1_base64="NUWsDJQMUuNz4hqZlqIiJi+Wi8U=">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</latexit> <latexit sha1_base64="NUWsDJQMUuNz4hqZlqIiJi+Wi8U=">AAACanichVG7SgNBFD1Z3/GRqI2SRowRq3BXBMVKtLH0FSOYEHbXUZfsi91JQIM/YGclaKUgIn6GjT9gkU8Q7RRsLLy7WRAV9Q4zc+bMPXfOzOieZQaSqJlQ2to7Oru6e5K9ff0DqfTg0Gbg1nxDFAzXcv0tXQuEZTqiIE1piS3PF5qtW6KoV5fC/WJd+IHpOhvywBNlW9tzzF3T0CRTxVJQ0wMhK+ks5SmKsZ9AjUEWcay46WuUsAMXBmqwIeBAMragIeC2DRUEj7kyGsz5jMxoX+AISdbWOEtwhsZslcc9Xm3HrMPrsGYQqQ0+xeLus3IMOXqgG3qhe7qlR3r/tVYjqhF6OeBZb2mFV0kdj6y//auyeZbY/1T96VliF3ORV5O9exET3sJo6euHpy/r82u5xiRd0hP7v6Am3fENnPqrcbUq1s6R5A9Qvz/3T7A5nVcpr67OZBcW46/oRgbjmOL3nsUClrGCQuTuBGc4TzwrQ8qokmmlKolYM4wvoUx8ANOwjK4=</latexit>

重力波と電磁波の同時検出

重力波

電磁波中性子星連星

�tarrival = O(1) sec

[LIGO/VIRGO collaboration 17]

DL = 40+8�14Mpc

<latexit sha1_base64="O873pystaPRW8XAi0RR6YYf788Y=">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</latexit><latexit sha1_base64="O873pystaPRW8XAi0RR6YYf788Y=">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</latexit><latexit sha1_base64="O873pystaPRW8XAi0RR6YYf788Y=">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</latexit><latexit sha1_base64="O873pystaPRW8XAi0RR6YYf788Y=">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</latexit>

�3⇥ 10�15 <cGW � cEM

cEM< 7⇥ 10�16

<latexit sha1_base64="LnuQ1lVqn/1xZ3iBrn2IQA8v2Wo=">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</latexit><latexit sha1_base64="LnuQ1lVqn/1xZ3iBrn2IQA8v2Wo=">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</latexit><latexit sha1_base64="LnuQ1lVqn/1xZ3iBrn2IQA8v2Wo=">AAACv3ichVHNahRBEP4yiSauP1n1IuTSuES87FKTRCPBQ2IQvQj5cbPBbFxmOr1rk/ljpndhM8wL+AIePCmIBF9C8JIXyCEvIIgHhQhePFg7O6AxqNV011df11dd3e1Gnk4M0dGINTp25uz4xLnS+QsXL02WL1/ZSMJuLFVdhl4Yb7pOojwdqLrRxlObUawc3/VUw91dHuw3eipOdBg8Nv1IbftOJ9BtLR3DVKv8pDormkb7KhE2PU2r9q1M3BXNduzING3GvpBZK/cPGpmoCjkM7j/KsvQ3zJL5k2VuZ6JVrlCNchOngV2ACgpbCctv0cQOQkh04UMhgGHswUHCYws2CBFz20iZixnpfF8hQ4m1Xc5SnOEwu8trh6Otgg04HtRMcrXkUzyeMSsFpumQ9umYDugdfaIff62V5jUGvfTZu0OtilqTz6+tf/+vymdv8OyX6p89G7RxJ+9Vc+9RzgxuIYf63t6L4/WFten0Br2mz9z/KzqiD3yDoPdNvllVay9R4g+w/3zu02BjpmZTzV6dqyzeK75iAlO4jpv83vNYxEOsoM7nvsdHfMFXa8nqWIEVDVOtkUJzFSfM6v8EhNKplQ==</latexit><latexit sha1_base64="LnuQ1lVqn/1xZ3iBrn2IQA8v2Wo=">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</latexit>

重力波と電磁波の速さの一致：

GW170817 and GRB170817A

重力波の速さ

[ Creminelli & Vernizzi 17, Ezquiaga & M. Zumalacarregui 17, Baker+ 17]

[ Crisostomi & Koyama 17, Langlois, RS, Yamauchi, & Noui 17 ]

理論の関数パラメータ

スカラー場（Clock場）によってローレンツ対称性が破れている：

A1 ' 0理論への制限

c2GW = c2EM

1� �2

c

✓A1

F

◆�

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４つの関数パラメータ: P ,Q , F ,A1 , A3

L = P +Q⇤�+ FR+5X

I=1

AILI


Horndeski:�P = G2, Q = �G3, F = G4

A1 = �A2 = 2G4X (Others 0)<latexit sha1_base64="ZkuLJbJJgU6iouxmWWxUgcZVj/Q=">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</latexit><latexit sha1_base64="ZkuLJbJJgU6iouxmWWxUgcZVj/Q=">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</latexit><latexit sha1_base64="ZkuLJbJJgU6iouxmWWxUgcZVj/Q=">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</latexit><latexit sha1_base64="ZkuLJbJJgU6iouxmWWxUgcZVj/Q=">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</latexit>

G4X = 0<latexit sha1_base64="ZZLO3QgpQak6GZHJTJ6k4hMw8OU=">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</latexit><latexit sha1_base64="ZZLO3QgpQak6GZHJTJ6k4hMw8OU=">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</latexit><latexit sha1_base64="ZZLO3QgpQak6GZHJTJ6k4hMw8OU=">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</latexit><latexit sha1_base64="ZZLO3QgpQak6GZHJTJ6k4hMw8OU=">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</latexit>

高階微分の高次の項なし (A terms)

高次のHorndeskiは棄却され、Beyond Horndeski のみ残る

“Viable” DHOST理論

スカラー場（Clock場）は、物質間に新たな力を媒介する：

r2� + · · · = 4⇡Gs⇢

第５の力高密度環境の重力法則にも影響（近傍の実験や観測にも）

意外と近くに加速膨張の起源に迫るヒントがあるかも？？

しかし、その振る舞いは通常の重力場に比べて，豊かで複雑

遮蔽機構：スカラー場の自己相互作用による第５の力の遮蔽

例）カメレオン機構、K-Mouflage（kinetic screening）機構、Vainshtein機構ポテンシャル項１階微分項高階微分項

第５の力

Vainshtein機構 Schwarzschild半径より大きなスケールで、第５の力は高階微分項の非線形効果が重要になる。

r2� +r2�

✓r2�

⇤2

◆2

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⇤�1 ⇠ H�10 ⇠ 1Gpc

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加速膨張のスケール

線形近似解　　　　　　　は、以下のスケールで破綻： �L = GM/r<latexit sha1_base64="H5eNH10ZtrJZOoTBN55w6vWUSfs=">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</latexit><latexit sha1_base64="H5eNH10ZtrJZOoTBN55w6vWUSfs=">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</latexit><latexit sha1_base64="H5eNH10ZtrJZOoTBN55w6vWUSfs=">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</latexit><latexit sha1_base64="H5eNH10ZtrJZOoTBN55w6vWUSfs=">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</latexit>

r2�L/⇤2 ⌘ (rV /r)

3 � 1<latexit sha1_base64="szSlXzjdN3ACFwKVQqYuvY/epjA=">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</latexit><latexit sha1_base64="szSlXzjdN3ACFwKVQqYuvY/epjA=">AAAClXicSyrIySwuMTC4ycjEzMLKxs7BycXNw8vHLyAoFFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKxQsYxOQlJuUkxhkpxBRkZMb76Mf4ADWngAVSC0szyxQ0iuLD9Is044wVYtLTFQzjBZQN9AzAQAGTYQhlKDNAQUC+wHKGGIYUhnyGZIZShlyGVIY8hhIgO4chkaEYCKMZDBkMGAqAYrEM1UCxIiArEyyfylDLwAXUWwpUlQpUkQgUzQaS6UBeNFQ0D8gHmVkM1p0MtCUHiIuAOhUYVA2uGqw0+GxwwmC1wUuDPzjNqgabAXJLJZBOguhNLYjn75II/k5QVy6QLmHIQOjC6+YShjQGC7BbM4FuLwCLgHyRDNFfVjX9c7BVkGq1msEig9dA9y80uGlwGOiDvLIvyUsDU4NmM3ABI8AQPbgxGWFGeoYGeoaBJsoOTtCo4GCQZlBi0ACGtzmDA4MHQwBDKNDeaQx7GI4yHGMSZ7JlcmFygyhlYoTqEWZAAUz+AEeDmkE=</latexit><latexit sha1_base64="szSlXzjdN3ACFwKVQqYuvY/epjA=">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</latexit><latexit sha1_base64="szSlXzjdN3ACFwKVQqYuvY/epjA=">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</latexit>

; rV ⇠ (rS/H20 )

1/3<latexit sha1_base64="HqtxHnmndIR+dcivlWD0oc4asYg=">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</latexit><latexit sha1_base64="HqtxHnmndIR+dcivlWD0oc4asYg=">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</latexit><latexit sha1_base64="HqtxHnmndIR+dcivlWD0oc4asYg=">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</latexit><latexit sha1_base64="HqtxHnmndIR+dcivlWD0oc4asYg=">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</latexit>

Vainshtein半径


弱重力場（ニュートン則）

rV � 107AU

Vainshtein半径

加速膨張一般相対論

1AU



rV � 107AU

Vainshtein半径

加速膨張一般相対論 Horndeski理論では遮蔽が起こる

Kimura+ 12, Narikawa & RS+ 13, Koyama+ 13,…]

1AU



rV � 107AU

Vainshtein半径

加速膨張一般相対論 Horndeski理論では遮蔽が起こる

Kimura+ 12, Narikawa & RS+ 13, Koyama+ 13,…]

1AU

　しかし、（高次の）Horndeski理論は、重力波の制限から棄却されていた．．．

Vainshtein機構の破れ Beyond Horndeskiでは

Vainshtein機構が有限密度領域で働かなくなる

[ Kobayashi+ 15 ] (for GLPV理論)

モデルパラメータ Horndeski理論ではゼロ

[ Crisostomi & Koyama 17 ]

[ Langlois, RS, Yamauchi, & Noui 17 ]

[ Dima & Vernizzi 18 ]

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d�

dr= GN

✓M

r2+ ⌅1

d2M

dr2

◆

d

dr= GN

✓M

r2+ ⌅2

dM

dr+ ⌅3

d2M

dr2

◆

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1AU

Vainshtein

M�� = 0 M�� 0

rV � 107AU

天体の内部でのみ重力が修正される

Vainshtein機構の破れ

例）天体構造の変化：ポリトロープ

Ε = -0.5 (orange), -0.3, -0.1, 0, 0.1,

0.15 (blue), 0.3, 0.5, 1 (red)

0 1 2 3 4 5 60.0

0.2

0.4

0.6

0.8

1.0

1.2

Ξ

Χ!Ξ"�

� 半径

密度

n=3

✏ ⌘ �⌅1<latexit sha1_base64="NAymI3Juemg5bFm5C+D2N0Xht8w=">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</latexit><latexit sha1_base64="NAymI3Juemg5bFm5C+D2N0Xht8w=">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</latexit><latexit sha1_base64="NAymI3Juemg5bFm5C+D2N0Xht8w=">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</latexit><latexit sha1_base64="NAymI3Juemg5bFm5C+D2N0Xht8w=">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</latexit>

天体の状態方程式をポリトロープ（　　　　　）で近似して解析 P � �1+ 1n

[ RS+ 15, Koyama & Sakstein 15 ]

J. Sakstein (2015) 水素燃焼する最小質量 < 観測されている赤色矮星の最小質量

R. K. Jain+ (2015) 白色矮星のチャンドラセカール質量 & 質量半径関係

RS+ (2015) 星の存在条件

⌅1 > �1/6

⌅1 < 7⇥ 10�3

J. Sakstein+ (2016)

⌅1 = 0.028+0.23�0.17

(相対論効果の再検討の必要あり) Babichev, RS+ (2016)

⌅2 = 0.28+1.49�1.53

弱重力レンズ効果 & 銀河団のX-ray mass

Ξ パラメータへの制限

�6⇥ 10�2 < ⌅1 < 4⇥ 10�2

天体を観測することで、DHOSTを検証可能加速膨張の原因？

•  重力定数が、重力波と重力ポテンシャルとで異なる：

•  ４パラメータのうち, 独立なのは２つだけ：

⌅0 = �↵H � 3�1 , ⌅1 = � (↵H + �1)2

2(↵H + 2�1)<latexit sha1_base64="Tf3gIb41+Ii8uWy6TiXCk2U5mvw=">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</latexit><latexit sha1_base64="Tf3gIb41+Ii8uWy6TiXCk2U5mvw=">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</latexit><latexit sha1_base64="Tf3gIb41+Ii8uWy6TiXCk2U5mvw=">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</latexit><latexit sha1_base64="iVLU9HNA3QAQiBrG+aKcm8Cw9WY=">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</latexit>

⌅2 = ↵H , ⌅3 = ��1(↵H + �1)

2(↵H + 2�1)<latexit sha1_base64="imDiffraPj1cte6Sz2OPZiYcnXk=">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</latexit><latexit sha1_base64="imDiffraPj1cte6Sz2OPZiYcnXk=">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</latexit><latexit sha1_base64="imDiffraPj1cte6Sz2OPZiYcnXk=">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</latexit><latexit sha1_base64="imDiffraPj1cte6Sz2OPZiYcnXk=">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</latexit>

[ Cf. Dima & Vernizzi 18 ]

(8⇡GN )�1 ⌘ (8⇡GGW)�1(1 + ⌅0)<latexit sha1_base64="SEdktDQDBhzl9aSdwUFdI0gs2Hw=">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</latexit><latexit sha1_base64="SEdktDQDBhzl9aSdwUFdI0gs2Hw=">AAACm3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8vHLyAoFFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKxQuYaVjEFGQquMf7acZV6xrWKsSkFpZmlinAhKtjinIV3MNrIbIahtoxEZnxBprxAsoGegZgoIDJMIQylBmgICBfYDlDDEMKQz5DMkMpQy5DKkMeQwmQncOQyFAMhNEMhgwGDAVAsViGaqBYEZCVCZZPZahl4ALqLQWqSgWqSASKZgPJdCAvGiqaB+SDzCwG604G2pIDxEVAnQoMqgZXDVYafDY4YbDa4KXBH5xmVYPNALmlEkgnQfSmFsTzd0kEfyeoKxdIlzBkIHThdXMJQxqDBditmUC3F4BFQL5Ihugvq5r+OdgqSLVazWCRwWug+xca3DQ4DPRBXtmX5KWBqUGzGbiAEWCIHtyYjDAjPUMDPcNAE2UHJ2hUcDBIMygxaADD25zBgcGDIYAhFGjvHIZDDKcZzjDJMjkzeTH5QJQyMUL1CDOgAKZQAJHVm5I=</latexit><latexit sha1_base64="SEdktDQDBhzl9aSdwUFdI0gs2Hw=">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</latexit><latexit sha1_base64="SEdktDQDBhzl9aSdwUFdI0gs2Hw=">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</latexit>

↵H ⌘ 2FX �2c/F ,�1 ⌘ (A3�

2c � 4FX)�2

c/4F<latexit sha1_base64="h01KZOdgT778EylqY2rLN0pwXcE=">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</latexit><latexit sha1_base64="h01KZOdgT778EylqY2rLN0pwXcE=">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</latexit><latexit sha1_base64="h01KZOdgT778EylqY2rLN0pwXcE=">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</latexit><latexit sha1_base64="h01KZOdgT778EylqY2rLN0pwXcE=">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</latexit>

“Viable” DHOST理論の予言

２つ制限すれば棄却できる

⌅0 = �↵H � 3�1 , ⌅1 = � (↵H + �1)2

2(↵H + 2�1)<latexit sha1_base64="Tf3gIb41+Ii8uWy6TiXCk2U5mvw=">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</latexit><latexit sha1_base64="Tf3gIb41+Ii8uWy6TiXCk2U5mvw=">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</latexit><latexit sha1_base64="Tf3gIb41+Ii8uWy6TiXCk2U5mvw=">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</latexit><latexit sha1_base64="iVLU9HNA3QAQiBrG+aKcm8Cw9WY=">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</latexit>

⌅2 = ↵H , ⌅3 = ��1(↵H + �1)

2(↵H + 2�1)<latexit sha1_base64="imDiffraPj1cte6Sz2OPZiYcnXk=">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</latexit><latexit sha1_base64="imDiffraPj1cte6Sz2OPZiYcnXk=">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</latexit><latexit sha1_base64="imDiffraPj1cte6Sz2OPZiYcnXk=">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</latexit><latexit sha1_base64="imDiffraPj1cte6Sz2OPZiYcnXk=">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</latexit>

[ Cf. Dima & Vernizzi 18 ]

↵H ⌘ 2FX �2c/F ,�1 ⌘ (A3�

2c � 4FX)�2

c/4F<latexit sha1_base64="h01KZOdgT778EylqY2rLN0pwXcE=">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</latexit><latexit sha1_base64="h01KZOdgT778EylqY2rLN0pwXcE=">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</latexit><latexit sha1_base64="h01KZOdgT778EylqY2rLN0pwXcE=">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</latexit><latexit sha1_base64="h01KZOdgT778EylqY2rLN0pwXcE=">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</latexit>

“Viable” DHOST理論の予言

２つ制限すれば棄却できる

現在、最も厳しい制限

•  重力定数が、重力波と重力ポテンシャルとで異なる：

•  ４パラメータのうち, 独立なのは２つだけ：

(8⇡GN )�1 ⌘ (8⇡GGW)�1(1 + ⌅0)<latexit sha1_base64="SEdktDQDBhzl9aSdwUFdI0gs2Hw=">AAACm3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8vHLyAoFFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKxQuYaVjEFGQquMf7acZV6xrWKsSkFpZmlinAhKtjinIV3MNrIbIahtoxEZnxBprxAsoGegZgoIDJMIQylBmgICBfYDlDDEMKQz5DMkMpQy5DKkMeQwmQncOQyFAMhNEMhgwGDAVAsViGaqBYEZCVCZZPZahl4ALqLQWqSgWqSASKZgPJdCAvGiqaB+SDzCwG604G2pIDxEVAnQoMqgZXDVYafDY4YbDa4KXBH5xmVYPNALmlEkgnQfSmFsTzd0kEfyeoKxdIlzBkIHThdXMJQxqDBditmUC3F4BFQL5Ihugvq5r+OdgqSLVazWCRwWug+xca3DQ4DPRBXtmX5KWBqUGzGbiAEWCIHtyYjDAjPUMDPcNAE2UHJ2hUcDBIMygxaADD25zBgcGDIYAhFGjvHIZDDKcZzjDJMjkzeTH5QJQyMUL1CDOgAKZQAJHVm5I=</latexit><latexit sha1_base64="SEdktDQDBhzl9aSdwUFdI0gs2Hw=">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</latexit><latexit sha1_base64="SEdktDQDBhzl9aSdwUFdI0gs2Hw=">AAACm3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8vHLyAoFFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKxQuYaVjEFGQquMf7acZV6xrWKsSkFpZmlinAhKtjinIV3MNrIbIahtoxEZnxBprxAsoGegZgoIDJMIQylBmgICBfYDlDDEMKQz5DMkMpQy5DKkMeQwmQncOQyFAMhNEMhgwGDAVAsViGaqBYEZCVCZZPZahl4ALqLQWqSgWqSASKZgPJdCAvGiqaB+SDzCwG604G2pIDxEVAnQoMqgZXDVYafDY4YbDa4KXBH5xmVYPNALmlEkgnQfSmFsTzd0kEfyeoKxdIlzBkIHThdXMJQxqDBditmUC3F4BFQL5Ihugvq5r+OdgqSLVazWCRwWug+xca3DQ4DPRBXtmX5KWBqUGzGbiAEWCIHtyYjDAjPUMDPcNAE2UHJ2hUcDBIMygxaADD25zBgcGDIYAhFGjvHIZDDKcZzjDJMjkzeTH5QJQyMUL1CDOgAKZQAJHVm5I=</latexit><latexit sha1_base64="SEdktDQDBhzl9aSdwUFdI0gs2Hw=">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</latexit>

!0.4 !0.2 0.0 0.2 0.4

!0.4

!0.2

0.0

0.2

0.4

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�1<latexit sha1_base64="efXkZ+NuGtCjDuAHYDfqrYNjvrM=">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</latexit><latexit sha1_base64="efXkZ+NuGtCjDuAHYDfqrYNjvrM=">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</latexit><latexit sha1_base64="efXkZ+NuGtCjDuAHYDfqrYNjvrM=">AAACanichVG7SgNBFD1ZXzE+EmOjpBGjYhXuiqBYBW0s4yOJoBJ211GXbHaX3UkgBn/AzkowlYKI+Bk2/oCFnyDaRbCx8GazICrqHWbmzJl77pyZ0V3L9CXRY0Tp6u7p7Yv2xwYGh4bjiZFkwXeqniHyhmM53pau+cIybZGXprTElusJraJboqiXV9r7xZrwfNOxN2XdFbsV7cA2901Dk0wVd3QhtZJaSqQpQ0FM/ARqCNIII+ckrrGDPTgwUEUFAjYkYwsafG7bUEFwmdtFgzmPkRnsCxwjxtoqZwnO0Jgt83jAq+2QtXndrukHaoNPsbh7rJzAND3QDbXonm7pid5/rdUIarS91HnWO1rhluInYxtv/6oqPEscfqr+9Cyxj8XAq8ne3YBp38Lo6GtHZ62NpfXpxgxd0jP7v6BHuuMb2LVX42pNrDcR4w9Qvz/3T1CYy6iUUdfm09nl8CuiSGESs/zeC8hiFTnkA3enOEcz8qIklXEl1UlVIqFmFF9CmfoA/xiMRA==</latexit><latexit sha1_base64="efXkZ+NuGtCjDuAHYDfqrYNjvrM=">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</latexit>

⌅1 > �0.14<latexit sha1_base64="BFDuOhErBwWFZrLUlEs2MNMTXzs=">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</latexit><latexit sha1_base64="BFDuOhErBwWFZrLUlEs2MNMTXzs=">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</latexit><latexit sha1_base64="BFDuOhErBwWFZrLUlEs2MNMTXzs=">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</latexit><latexit sha1_base64="BFDuOhErBwWFZrLUlEs2MNMTXzs=">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</latexit>

⌅1 < 7⇥ 10�3<latexit sha1_base64="4vN0qYaEdRYsTsuuBPzSi90hRUk=">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</latexit><latexit sha1_base64="4vN0qYaEdRYsTsuuBPzSi90hRUk=">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</latexit><latexit sha1_base64="4vN0qYaEdRYsTsuuBPzSi90hRUk=">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</latexit><latexit sha1_base64="4vN0qYaEdRYsTsuuBPzSi90hRUk=">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</latexit>

赤線: Hulse-Taylorパルサー（連星中性子星の公転周期変化）

�7.5⇥ 10�3 <GN

GGW� 1 < 2.5⇥ 10�3

<latexit sha1_base64="3iZ2L4gU0AAJ+C6z2Ff+Wq12WNc=">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</latexit><latexit sha1_base64="3iZ2L4gU0AAJ+C6z2Ff+Wq12WNc=">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</latexit><latexit sha1_base64="3iZ2L4gU0AAJ+C6z2Ff+Wq12WNc=">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</latexit><latexit sha1_base64="3iZ2L4gU0AAJ+C6z2Ff+Wq12WNc=">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</latexit>

現在の制限：

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Ξパラメータへの制限

赤色矮星の質量

天体解の存在条件

Ξ1へのより厳しい制限が必要（天体内部の重力）

もし全てのΞパラメータがゼロだった場合、

FX = 0 , A3 = 0

Viable DHOST理論:

LDHOSTviable = P +Q⇤�+ F (�)R

３次のHorndeski理論 + 共形結合

Viable DHOST理論：どこまで狭まるか？

さらなる制限宇宙論からのテスト、より一般の環境でのVainshtein機構、など

宇宙論によるテスト -  積分Sachs-Wolfe効果

20 40 60 80 100`

�0.3

�0.2

�0.1

0.0

0.1

0.2

`(`+

1)C

Tg

`/2

⇡[µ

K]

⇤CDM

⌫Gal3

⌫Gal4

⌫Gal5

WISE Data

from Ref. [30]

単純なモデルを7.5σで棄却

Q⇤� / (r�)2⇤�<latexit sha1_base64="d+/rF3Ft+4mLNGZabviviO75SbU=">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</latexit><latexit sha1_base64="d+/rF3Ft+4mLNGZabviviO75SbU=">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</latexit><latexit sha1_base64="d+/rF3Ft+4mLNGZabviviO75SbU=">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</latexit><latexit sha1_base64="d+/rF3Ft+4mLNGZabviviO75SbU=">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</latexit>

CMBの赤方偏移効果

[ Renk+ 17 ]

-  Planck2018 VI

; ↵M ⌘ F /HF<latexit sha1_base64="G7yRB6ajs28q3ZViMGaxtrPqhpI=">AAACgXichVHLLgRBFD3ae7wGGwmLiQlhM26LhLARErGReA0SI5PuVqjo6W7dNZMwYWHpByysSASx4hds/ICFTxBLEhsLd3o6EQS3UlWnTt1z61SV6dkyUESPFVplVXVNbV19rKGxqbkl3tq2FLh53xJpy7Vdf8U0AmFLR6SVVLZY8Xxh5ExbLJvbk6X95YLwA+k6i2rXE2s5Y9ORG9IyFFPZeNfYQcawvS0jO5PIiJ28LCQy664qTu0PTE9l40lKURiJn0CPQBJRzLrxC2SwDhcW8shBwIFibMNAwG0VOggec2soMuczkuG+wD5irM1zluAMg9ltHjd5tRqxDq9LNYNQbfEpNneflQn00ANd0Qvd0zU90fuvtYphjZKXXZ7NslZ42ZajjoW3f1U5nhW2PlV/elbYwEjoVbJ3L2RKt7DK+sLe8cvC6HxPsZfO6Jn9n9Ij3fENnMKrdT4n5k8Q4w/Qvz/3T7A0mNIppc8NJccnoq+oQye60cfvPYxxTGMWaT73EJe4wa1WqfVrpA2WU7WKSNOOL6GNfQA+9pPr</latexit><latexit sha1_base64="G7yRB6ajs28q3ZViMGaxtrPqhpI=">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</latexit><latexit sha1_base64="G7yRB6ajs28q3ZViMGaxtrPqhpI=">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</latexit><latexit sha1_base64="G7yRB6ajs28q3ZViMGaxtrPqhpI=">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</latexit>

[ Planck collaboration 18 ]

↵M0 = �0.015+0.019�0.017

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(= ↵M0a�)

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まとめ

-  一般相対論の予言は悉く実験・観測で確かめられてきたが、宇宙の加速膨張は未だ説明できない：

-  特別な座標系の存在 → 加速膨張の統一理論

-  さまざまな理論的・観測的制約．Viable DHOST理論：

宇宙論的スケールでの一般相対性理論の破綻？

一般相対論の広範な有効性 & 残される加速膨張の謎

LDHOSTviable = P +Q⇤�+ F (�)R

宇宙を支配する重力法則は何か？¤の学校_ryo... · 2018-07-25 ·...

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