phenomenology of beyond horndeski theories kazuya koyama university of portsmouth
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Phenomenology of beyond Horndeski theories
Kazuya Koyama University of Portsmouth
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/
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
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
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
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
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
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
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
Non-linear interactions Covariantised Galileon
Around cosmological background
≫
Kobayashi, Watanabe and Yamauchi, 1411.4130
Equations of motion
Spherically symmetric solutions
Equations of motion Kobayashi, Watanabe and Yamauchi, 1411.4130KK, Sakstein 1502.06872
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
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
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
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
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
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