Phenomenology of beyond Horndeski theories Kazuya Koyama University of Portsmouth.
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Transcript of Phenomenology of beyond Horndeski theories Kazuya Koyama University of Portsmouth.
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Phenomenology of beyond Horndeski theories
Kazuya Koyama University of Portsmouth
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Job opening at University of Portsmouth Dennis Sciama fellowship (three years)
Three year postdoc position on “Cosmological tests of Gravity”
Deadline 18 December 2015 Contact me [email protected] for details Visit http://www.icg.port.ac.uk/
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Recent progress Horndeski theory the most general 2nd order scalar-tensor theory
Deffayet, Gao, Steer and Zahariade ’11; Kobayashi, Yamaguchi and Yokoyama ‘11
Horndeski ‘74
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Unitary gauge
This terms is problematic as this includes
Horndeski in the unitary gauge
𝑛𝜇=−𝜕𝜇𝜙
√−𝑋�� h 𝑖𝑗
𝐿4𝐻=𝐺4 (𝜙 ,𝑋 ) 𝑅−2𝐺4 𝑋 (𝜙 , 𝑋 ) [(𝛻2𝜙 )2− (𝜕𝜇𝜕𝜈𝜙 ) (𝜕𝜇𝜕𝜈 𝜙 ) ]
Gleyzes, Langlois, Piazza, Vernizzi ‘14
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Counter term Horndeski
Beyond Horndeski
𝐿4𝐻=𝐺4 (𝜙 , 𝑋 )𝑅−2𝐺4 𝑋(𝜙 ,𝑋 )[ (𝛻2𝜙 )2− (𝜕𝜇𝜕𝜈𝜙 ) (𝜕𝜇𝜕𝜈𝜙 )]
2𝑋 2 (𝜕𝜇𝜙𝜕𝜈 𝜙𝛻𝜇𝜕𝜈 𝜙𝛻2𝜙−𝜕𝜇𝜙𝛻𝜇𝜕𝜈𝜙𝜕𝜆𝜙𝛻𝜆𝜕𝜈𝜙 )=− (𝛻𝜇 𝑋 ) (𝐾 𝑛𝜇−��𝜇 )
𝑋
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Beyond Horndeski
Remarks Away from unitary gauge e.o.m contain higher derivatives however, it has been shown that this does not lead to a ghost Decoupling limit in the Minkowski
the same as Horndeski – differences appears around cosmological backgrounds
(𝜕𝑖𝜙 )2 𝑑𝑑𝑡 [( ��𝑁 )
2] h𝑖𝑗
Gleyzes, Langlois, Piazza, Vernizzi ‘14
Deffayet, Esposito-Farese, Steer 1506.01974
KK, Niz, Tasinato ‘14
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Covariant v Covariantised Galileon Unitary gauge
Horndeski covariant Galileon
Beyond Horndeski covariantised Galileon
𝐿4=𝐴4 (𝑡 ,𝑁 ) (𝐾 2−𝐾 𝑖𝑗𝐾𝑖𝑗 )+𝐵4 (𝑡 ,𝑁 ) 𝑅(3 )
𝐴4=−B4+2 X B4 X
𝐴4=−𝑀𝑝𝑙
2
2−3𝑐44𝑀 6 𝑋
2 ,𝐵4=−𝑀𝑝𝑙
2
2−
𝑐44𝑀 6 𝑋
2
𝐴4=−𝑀𝑝𝑙
2
2−3𝑐44𝑀 6 𝑋
2 ,𝐵4=−𝑀𝑝𝑙
2
2
Deffayet, Epsosito-Farese, Vikram ‘09, Deffayet, Deser, Epsosito-Farese ‘09
Gleyzes, Langlois, Piazza, Vernizzi ‘14
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Toy model Quitessece in beyond Horndeski
Background exactly the same as GR
Perturbations tensor sound speed scalar sound speed
𝐿=−12𝑋+𝑉 (𝜙 )+𝐿4+𝐿𝑚𝐿4=𝐴4 (𝐾 2−𝐾 𝑖𝑗𝐾
𝑖𝑗 )+𝐵4𝑅(3 )
𝐴4=−12𝑀𝑝𝑙
2 ,𝐵4=12𝑀𝑝𝑙
2 𝐹 (𝜙 )
𝑐𝑡2=−
𝐵4
𝐴4
𝑐𝑠2=1−2 (1−𝑐𝑡
2 )− 2𝑀𝑝𝑙2 𝐻 2
��2 [ (1−𝑐𝑡2 ) ��𝐻2 −
2𝑐𝑡𝑐𝑡
𝐻 ]
De Felice, KK, Tsujikawa, 1503.06539
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Tensor sound speed and anisotropic stress Horndeski matter domination no restriction in beyond Horndeski
𝐴4=−B4+2 X B4 X
It is possible to suppress the growth Tsujikawa, 1505.02459
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Non-linear interactions Covariantised Galileon
Around cosmological background
≫
Kobayashi, Watanabe and Yamauchi, 1411.4130
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Equations of motion
Spherically symmetric solutions
Equations of motion Kobayashi, Watanabe and Yamauchi, 1411.4130KK, Sakstein 1502.06872
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Breaking of Vainshtein mechanism Second order equation
Vainshtein solutions
Vainshtein mechanism is broken inside matter source
1/3
3,
8V Vpl
Mr r r
M
Kobayashi, Watanabe and Yamauchi, 1411.4130KK, Sakstein 1502.06872
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Stellar structure Hydrostatic equation
It is possible to weaken gravity
𝑃=𝑃𝑔𝑎𝑠+𝑃𝑟𝑎𝑑=(1−𝛽 )𝑃𝑟𝑎𝑑
KK, Sakstein 1502.06872Saito, Yamauchi, Mizuno, Gleyzes, Langlois 1503.01448
1 solar mass 0.3
0.2
0.1
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HR diagram
GR
1 solar mass star
KK, Sakstein 1502.06872
modified MESA code
Weak gravity raises the minimal mass for hydrogen burning . The observations of low mass M-dwarf stars could give a very strong constraint
Sakstein in preparation
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Dark matter halos NFW profile Milyway-like dark matter halo
Rotation curve
KK, Sakstein 1502.06872
GR0.3,0.5
0.10.3
0.5
Lensing potential/ gravitational potential
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Cosmology Covariant galileon
Planck 2015 (+BAO+CMB lensing)
requires massive neutrinos ISW cross correlation can excludes the models
Time dependent Newton constant For quartic/qunitc Galileon, the Vainshtein mechanism fails to suppress time dependent Newton constant
Covariantised galileon quintic galileon is unstable during MD era Kase and Tsujikawa 1407.0794
Barreira et.al. 1406.0485
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Some remarks Non-linear structure formation
The Vainshtein mechanism is broken inside matter distribution Relativistic stars
Neutron stars Non-ghost
Connection between Horndeski and beyond Horndeski
the problematic term can be removed by a re-definition of variable 2
4ij ij X i j
dh h
dt N
4 4[ ] [ ]H BHL g L g
Gleyzes, Langlois, Piazza, Vernizzi ‘14