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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
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
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
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]
CMB
天体スケール
宇宙論スケール
重力波
銀河
いろいろな環境における
現在の宇宙
一般相対論でOK
OK…? 不確定要素多し
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]
CMB
天体スケール
宇宙論スケール
重力波
銀河
いろいろな環境における
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
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
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
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
0 = �(x� ct)<latexit sha1_base64="T+tRP1QI8CTeERV7nqa/7/eWjG8=">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</latexit><latexit sha1_base64="T+tRP1QI8CTeERV7nqa/7/eWjG8=">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</latexit><latexit sha1_base64="T+tRP1QI8CTeERV7nqa/7/eWjG8=">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</latexit><latexit sha1_base64="T+tRP1QI8CTeERV7nqa/7/eWjG8=">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</latexit>
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]
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
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
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
aµ,Kµ⌫ ⇠ rµn⌫ ! rµr⌫�<latexit sha1_base64="iVQ53Ji+MFHGxs/Oc3DR46QhK3o=">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</latexit><latexit sha1_base64="iVQ53Ji+MFHGxs/Oc3DR46QhK3o=">AAACrXichVFNT9VAFD1UEHh+8JQNiZvGF4wL87wlJBhXRDckbvh6QEKxmdbhMaGdNu30Jfjy/oB/wAUrSIwxJv4JN/4AWbDAvXGJiRsX3PaVIBDhNp05c+49d87M+EmoMkN0OGDdGBy6OTwyWrt1+87dsfq9+ytZnKeBbAVxGKdrvshkqLRsGWVCuZakUkR+KFf97ZdFfrUj00zFetnsJHIjEm2tNlUgDFNefU54XTfKe0/sVyVwdd6z3UxFtquFHwqPOVt7TNuuif8lT2GRSbaUV29Qk8qwLwOnAg1UMR/XP8LFG8QIkCOChIZhHEIg428dDggJcxvoMpcyUmVeoocaa3OuklwhmN3msc2r9YrVvC56ZqU64F1C/lNW2pikA/pEx/SNPtNP+vvfXt2yR+Flh2e/r5WJN/ZuYunPtaqIZ4OtM9WVng028az0qth7UjLFKYK+vvP2/fHS88XJ7iPap1/sf48O6SufQHd+Bx8W5OIuavwAzsXrvgxWppoONZ2F6cbsi+opRvAAD/GY73sGs5jDPFq87xd8xxF+WE+tluVar/ul1kClGce5sNonAHOmLA==</latexit><latexit sha1_base64="iVQ53Ji+MFHGxs/Oc3DR46QhK3o=">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</latexit><latexit sha1_base64="iVQ53Ji+MFHGxs/Oc3DR46QhK3o=">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</latexit>
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
X ⌘ (r�)2<latexit sha1_base64="jFxb1+/vUff2GtfJmT80jM9rL3o=">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</latexit><latexit sha1_base64="jFxb1+/vUff2GtfJmT80jM9rL3o=">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</latexit><latexit sha1_base64="jFxb1+/vUff2GtfJmT80jM9rL3o=">AAACfXichVHLSsNAFD2N7/qquhHcBEtFQcqtCIor0Y1LX62FtpYkjnYwTWKSFrToB/gDLlwpiojoT7jxB1z0E8SlghtBb9OiqKh3mJkzZ+65c2ZGd0zp+UTVkNLU3NLa1t4R7uzq7umN9PWnPLvkGiJp2KbtpnXNE6a0RNKXvinSjiu0om6KNX17vra/VhauJ21r1d91RK6obVlyUxqaz1Q+MphWs2KnJMvqaNbSdFNTs05Bjq1P5CNRilMQ6gdIfAdRNGLRjlwgiw3YMFBCEQIWfMYmNHjcMkiA4DCXQ4U5l5EM9gX2EWZtibMEZ2jMbvO4xatMg7V4XavpBWqDTzG5u6xUEaN7uqQnuqMreqDXX2tVgho1L7s863WtcPK9h4MrL/+qijz7KHyq/vTsYxPTgVfJ3p2Aqd3CqOvLe0dPKzPLscoIndIj+z+hKt3yDazys3G+JJaPEeYP+PHcP0FqIp6geGJpMjo71/iKdgxhGKP83lOYxQIWkeRzD3CGa9yE3pSYMq7E66lKqKEZwJdQpt4BeVSSrg==</latexit><latexit sha1_base64="jFxb1+/vUff2GtfJmT80jM9rL3o=">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</latexit>
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 ]
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、
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
�µ⌫ ⌘ rµr⌫�<latexit sha1_base64="DhsLCyMGzrhOIGupylbdHc8w74o=">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</latexit><latexit sha1_base64="DhsLCyMGzrhOIGupylbdHc8w74o=">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</latexit><latexit sha1_base64="DhsLCyMGzrhOIGupylbdHc8w74o=">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</latexit><latexit sha1_base64="DhsLCyMGzrhOIGupylbdHc8w74o=">AAAClHichVFNSxtBGH6y1RpjbWKFIngJBktP8U0pKNKDKIWexCRNIrgSdtdJMmR3dt2PQBr8A72XHnqyUErpT/CoQv9AD/6E4lHBi4e+uwlKK63vMDPPPPM+7zwzY3q2DEKis5T2YGz84UR6MjP1aPpxNjfzpB64kW+JmuXarr9tGoGwpRK1UIa22PZ8YTimLRpmdyPeb/SEH0hXvQ37nth1jLaSLWkZIVPN3JLudWRzoDuRrqKDvC72I9nL68owbaPJ7A1UDOPUXIGKlET+BpT+BgWMYsvNfYWOPbiwEMGBgELI2IaBgNsOSiB4zO1iwJzPSCb7AgfIsDbiLMEZBrNdHtu82hmxitdxzSBRW3yKzd1nZR6L9JO+0QX9oO/0i67/WWuQ1Ii99Hk2h1rhNbPv56pX96ocnkN0blX/9RyihZXEq2TvXsLEt7CG+t67jxfV1cri4Bl9pnP2f0hndMw3UL1L60tZVD4hwx9w57nvgvqLYomKpfLLwtr66CvSmMcCnvN7L2MNb7CFGp/7AUc4wan2VHulbWivh6laaqSZxR+hbf4G2Sqcgg==</latexit>
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>
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 Horndeski
GLPV
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、
Class I Class II
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 Horndeski
GLPV
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、
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=">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</latexit>
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
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
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
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
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�3⇥ 10�15 <cGW � cEM
cEM< 7⇥ 10�16
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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
�µ⌫ ⌘ rµr⌫�<latexit sha1_base64="DhsLCyMGzrhOIGupylbdHc8w74o=">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</latexit><latexit sha1_base64="DhsLCyMGzrhOIGupylbdHc8w74o=">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</latexit><latexit sha1_base64="DhsLCyMGzrhOIGupylbdHc8w74o=">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</latexit><latexit sha1_base64="DhsLCyMGzrhOIGupylbdHc8w74o=">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</latexit>
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
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
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
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
= 4⇡Gs⇢<latexit sha1_base64="RpZ3OHNws4VDH/0QZSzTuHxKBzE=">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</latexit><latexit sha1_base64="RpZ3OHNws4VDH/0QZSzTuHxKBzE=">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</latexit><latexit sha1_base64="RpZ3OHNws4VDH/0QZSzTuHxKBzE=">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</latexit><latexit sha1_base64="RpZ3OHNws4VDH/0QZSzTuHxKBzE=">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</latexit>
⇤�1 ⇠ H�10 ⇠ 1Gpc
<latexit sha1_base64="zGzVFMh9a2p/kWQem8Dz0FG48WE=">AAACkHicSyrIySwuMTC4ycjEzMLKxs7BycXNw8vHLyAoFFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKxQtox/gAFackxlXrGtYqxBRn5ip4xBsg8QwVqmOKchXcC5Jr4wWUDfUMwEDBAIMBk1JmgIKAfIHlDDEMKQz5DMkMpQy5DKkMeQwlQHYOQyJDMRBGMxgyGDAUAMViGaqBYkVAViZYPpWhloELqLcUqCoVqCIRKJoNJNOBvGioaB6QDzKzGKw7GWhLDhAXAXUqMKgaXDVYafDZ4ITBaoOXBn9wmlUNNgPklkognQTRm1oQz98lEfydoK5cIF3CkIHQhdfNJQxpDBZgt2YC3V4AFgH5Ihmiv6xq+udgqyDVajWDRQavge5faHDT4DDQB3llX5KXBqYGzWbgQo4A3IwwIz1DAz3DQBNlBydoVHAwSDMoMWgAw9ucwYHBgyGAIRRo70SG7QwHGA4yCTFZMNkzOUKUMjFC9QgzoAAmLwCOLpi7</latexit><latexit sha1_base64="zGzVFMh9a2p/kWQem8Dz0FG48WE=">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</latexit><latexit sha1_base64="zGzVFMh9a2p/kWQem8Dz0FG48WE=">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</latexit><latexit sha1_base64="zGzVFMh9a2p/kWQem8Dz0FG48WE=">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</latexit>
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
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。
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
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。
弱重力場(ニュートン則)
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
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。
弱重力場(ニュートン則)
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=">AAACe3ichVHLSsNAFD2N7/qqCiK4KRZFRMuNKIor0Y3LVq0WrJQkTnUwTWKSFrT6A/6AC1cWRKT+hRt/wIWfIC4V3Ch4mwZERb3DzJw5c8+dMzO6Y0rPJ3qIKE3NLa1t7R3Rzq7unt5YX/+GZ5dcQ2QM27TdrK55wpSWyPjSN0XWcYVW1E2xqe8v1/c3y8L1pG2t+4eO2C5qu5YsSEPzmcrHBnPC8aRpW/GcOCjJcnwql5V5NR9LUJKCiP8EaggSCCNlx66Qww5sGCihCAELPmMTGjxuW1BBcJjbRoU5l5EM9gVOEGVtibMEZ2jM7vO4y6utkLV4Xa/pBWqDTzG5u6yMY5Tu6Zqe6Y5q9Ehvv9aqBDXqXg551hta4eR7T4fWXv9VFXn2sfep+tOzjwLmA6+SvTsBU7+F0dCXj86e1xZWRytjVKUn9n9BD3TLN7DKL8ZlWqyeI8ofoH5/7p9gYzqpUlJNzyQWl8KvaMcwRjDO7z2HRawghQyfe4wqariJvCsJZUKZbKQqkVAzgC+hzH4A5i2SeQ==</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=">AAACm3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8vHLyAoFFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKxQuYaVjEFGQquMf7acZV6xrWKsSkFpZmlinAhKtjinIV3MNrIbIahtoxEZnxBprxAsoGegZgoIDJMIQylBmgICBfYDlDDEMKQz5DMkMpQy5DKkMeQwmQncOQyFAMhNEMhgwGDAVAsViGaqBYEZCVCZZPZahl4ALqLQWqSgWqSASKZgPJdCAvGiqaB+SDzCwG604G2pIDxEVAnQoMqgZXDVYafDY4YbDa4KXBH5xmVYPNALmlEkgnQfSmFsTzd0kEfyeoKxdIlzBkIHThdXMJQxqDBditmUC3F4BFQL5Ihugvq5r+OdgqSLVazWCRwWug+xca3DQ4DPRBXtmX5KWBqUGzGbiAEWCIHtyYjDAjPUMDPcNAE2UHJ2hUcDBIMygxaADD25zBgcGDIYAhFGjvHIZDDKcZzjDJMjkzeTH5QJQyMUL1CDOgAKZQAJHVm5I=</latexit><latexit sha1_base64="SEdktDQDBhzl9aSdwUFdI0gs2Hw=">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</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=">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</latexit><latexit sha1_base64="SEdktDQDBhzl9aSdwUFdI0gs2Hw=">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</latexit><latexit sha1_base64="SEdktDQDBhzl9aSdwUFdI0gs2Hw=">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</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=">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</latexit><latexit sha1_base64="efXkZ+NuGtCjDuAHYDfqrYNjvrM=">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</latexit>
⌅1 > �0.14<latexit sha1_base64="BFDuOhErBwWFZrLUlEs2MNMTXzs=">AAACcHichVFNLwNRFD0d3/VVbJpYKA0RieaONCEWImwsFaUJTTMzXnnpdGbMTJvQ+AP+QBc2SETEz7DxByz6E8QOiY2F22lDENzJvHfeeffcd967umNKzyeqhZSW1rb2js6ucHdPb19/ZGBw07NLriHShm3abkbXPGFKS6R96Zsi47hCK+qm2NILy/X9rbJwPWlbG/6hI7JFbc+SeWloPlPZnYzMqbGF2DQl1GQuEqcEBRH7AOp3EEczVu3IFXawCxsGSihCwILP2IQGj79tqCA4zGVRYc5lJIN9gWOEWVviLMEZGrMFHvd4td1kLV7Xa3qB2uBTTP5dVsYwTvd0Tc90Rzf0QG+/1qoENepeDnnWG1rh5PpPouuv/6qKPPvY/1T96dlHHnOBV8nenYCp38Jo6MtH1ef1+bXxygRd0CP7P6ca3fINrPKLcZkSa6cIcwN+PPdPsDmTULldqWR8canZik4MYwyT/N6zWMQKVpHmcw9QxRnOQ09KVBlRRhupSqipGcKXUKbeARWIjRQ=</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:
|↵H |, |�1| < O(0.1)<latexit sha1_base64="krTMEG5+TWF1uk828W54euGsFns=">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</latexit><latexit sha1_base64="krTMEG5+TWF1uk828W54euGsFns=">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</latexit><latexit sha1_base64="krTMEG5+TWF1uk828W54euGsFns=">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</latexit><latexit sha1_base64="krTMEG5+TWF1uk828W54euGsFns=">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</latexit>
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=">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</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
<latexit sha1_base64="uBZW4q8jQRvAOEplAyeOH3NFZvc=">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</latexit><latexit sha1_base64="uBZW4q8jQRvAOEplAyeOH3NFZvc=">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</latexit><latexit sha1_base64="uBZW4q8jQRvAOEplAyeOH3NFZvc=">AAACi3ichVG7SsRAFD3G9/patRFsFhdFEJcbH/hAQRTBRvC1KvgISRw1mE1Ckl3QsD8g9hZWCiJiZ6udjT9g4SeIpYKNhTfZgKioN2TumTP33Dkzozmm4flEj2VSeUVlVXVNbaKuvqGxKdncsuzZeVcXWd02bXdVUz1hGpbI+oZvilXHFWpOM8WKtjcVrq8UhOsZtrXk7ztiI6fuWMa2oas+U0qya101nV1VCWapmBpP9VKG5MHNoCfMI0UliIihopJMM4gi9RPIMUgjjjk7eYF1bMGGjjxyELDgMzahwuNvDTIIDnMbCJhzGRnRukARCdbmuUpwhcrsHo87PFuLWYvnYU8vUuu8i8m/y8oUOumBLumF7umKnuj9115B1CP0ss9ZK2mFozQdti2+/avKcfax+6n607OPbQxHXg327kRMeAq9pC8cHL8sji50Bl10Rs/s/5Qe6Y5PYBVe9fN5sXCCBD+A/P26f4LlvoxMGXl+ID0xGT9FDdrRgW6+7yFMYAZzyPK+R7jGDW6lBqlfGpXGSqVSWaxpxZeQpj8AObeU6w==</latexit><latexit sha1_base64="uBZW4q8jQRvAOEplAyeOH3NFZvc=">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</latexit>
(= ↵M0a�)
<latexit sha1_base64="psXjuIq7PkTimKgoWdidJdrwKW0=">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</latexit><latexit sha1_base64="psXjuIq7PkTimKgoWdidJdrwKW0=">AAACfXichVHBSiNBEH0ZddWom6xeBC+DIaIgQ0VcFGFB1osXwUSjgtHQM7Y6ZDIzzHQCbtAP2B/Yw54URUT0J7z4Ax78BPGo4EXQyiQiImo13VX9ul7V627Td+xQEV3HtJbWtm/tHZ3xru6e74nkj96l0KsElsxbnuMFK6YIpWO7Mq9s5cgVP5CibDpy2SzN1M+XqzIIbc9dVDu+XCuLLdfetC2hGCom+4f1X3pBOP62KNbmaFesF0yphD5STKbIGPtJbPr7IGNQZCk0bd5LHqOADXiwUEEZEi4Uxw4EQh6ryIDgM7aGGmMBR3Z0LrGLOHMrnCU5QzBa4nWLd6tN1OV9vWYYsS3u4vAMmKkjTVd0Qnd0Sad0Q48f1qpFNepadtibDa70i4m//QsPX7LK7BW2X1mfalbYxGSk1WbtfoTUb2E1+NU//+4WpnLp2hAd0C3r36druuAbuNV76ygrc/8R5w94eWX942BpzMiQkcmOp6Z/N7+iAwMYxDC/9wSmMYt55LnvHg5xhvPYk5bWRjWjkarFmpw+vDFt4hkiUpKH</latexit><latexit sha1_base64="psXjuIq7PkTimKgoWdidJdrwKW0=">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</latexit><latexit sha1_base64="psXjuIq7PkTimKgoWdidJdrwKW0=">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</latexit>
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