On the Vainshtein Mechanism - KICP Workshops · 2015-10-26 · KICP – Oct. 2015 On the Vainshtein...
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On the Vainshtein Mechanism
Gustavo Niz
University of Guanajuato
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University of Guanajuato
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University of Guanajuato
Leon
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Content● Motivation
● The Vainshtein Mechanism
– Basics
– Exploring solutions and stability (perts)
– Relaxing symmetry and strong gravity
● Toy model (without gravity)
● Conclusions
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Why?
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Why?
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Why?
Screening
Mechanism
*Cosmological modifications
of order 1
*Strong gravity regime may
also show somethingBaker et al, 2014
PPN
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Why?
2nd. Laboratory
– Derivative interactions arise from UV physics
– Strongly coupled regime
– Dualities & UV completion? (e.g. Keltner & Tolley, 1502.05706)
– Is it helpful for condensed matter or particle physics?
Strongly coupled field
Vainshteinradius
Weakly coupled field
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Vainshtein Mechanism (Review)
Start with
Spherically symmetric ansatz
In massive gravity by Vainshtein, 1972 (see Babichev and Deffayet, 2013)
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Scalar equation could be integrated once (Nicolis et al)
with solution
Around flat space (test field) for large
FromKinetic
FromGalileon
~ Mass
Vainshtein Mechanism (Review)
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
1) Suggests 1/sqrt(coupling) expansion
2) Should recover GR (Schwarzschild) at short scales.
3) Consistent construction with this expansion
New Vainshtein radius
(larger than in Minkowski)
(Gabadadze el al, Padilla et al)
Vainshtein Mechanism (Review)
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
“Vainshtein” effective theory
Description that captures the Vainshtein effect from Horndeski's Lagriangian
Truncate the theory so that
1) It is an expansion around flat space
2) Leading order in and
3) Keep all second order derivatives of
with an associated scale
(Koyama, Niz, Tasinato)
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
“Vainshtein” effective theory
Remarks
● It is equivalent to demand the Galilean symmetry(c.f. Nicolis et al)
● Reduces to (limits of) well know theories:
dRGT massive gravity, DGP , (restricted) Galileons, etc.
● Does not include other models from Horndeski which (may) present the Vainshtein mechanism,
eg. the Fab Fouror k-mouflage
(de Rham et al) (Berezhiani et al, Nicolis et al)(Dvali et al)
(Charmousis al, Kaloper et al)
(Babichev et al)
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
“Vainshtein” effective theory
Under this decoupling limit
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
“Vainshtein” effective theory
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
“Vainshtein” effective theory
Field redefinition New couplings
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Spherically symmetric solutions
Spherically symmetric ansatz imply the equations:
Expect many more solutions than before!
1
2
“Mass” inside a given radius
Metric perts
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Two important behaviours within the Vainshtein radius
Koyama et al, Sbisa et al, Chkareuli et al, Sjors et al, Kaloper et al, Kimura et al, Berezhiani et al, Babichev et al, Li et al, Narikawa et al, Hiramatsu et al, de Rham et al, Renaux-Petel, ...
Weak (usual) screening Strong screening
A B
Spherically symmetric solutions
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Construct phase space of how inner-outer solns connect
For dRGT
(Sbisa et al)
How A and B connect to asymptotic solutions
Spherically symmetric solutions
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Stability
Scalar perturbations around weak screening soln. A
Where all the are functions of the effective theory parameters, particularly of
which tune the terms
Koyama et al
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Stability
Original Galileon, studied by Nicolis et al
Superluminal propagation in radial modes
Extremely subluminal in radial piece!
Disformal coupling
Leads to Restricted Galileon (Berezhiani et al)
has a ghost mode
There are no asymptotically flat Vainshtein solutions
1
2
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Inside the Vainshtein radius and outside the source, the leading terms are
Speed of fluctuations is always superluminal, and unstable.
● The instability can be avoided inside the source
● Need to look beyond static & spherical symmetry!
3
StabilityKoyama et al
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Beyond Vanilla...
Play with the matter sector
TOV
Scalarisation
(see Teruaki's talk)
Polytropic EOS
Chagoya, Koyama, Niz & Tasinato
Found that:small corrections
avoids it
mechanism works better for higher densities
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Beyond Vanilla...
Play with the matter sector
Polytropic EOS. Only issue in strong gravity regime
Chagoya, Koyama, Niz & Tasinato
-T (gr/cm3)
density
Critical Densityabove knownNeutron star's densities
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Beyond Vanilla...
Away from spherical symmetry
Slow rotation shows no big corrections
Filaments (cylindrical) solutions present suppressed Vainshtein effect
Pancakes (planar) solutions do not exhibit screening
Chagoya, Koyama, Niz & Tasinato
Gabadadze et al, Bloomfield et al, Falck et al.
Brax et al, Bloomfield et al, Falck et al.
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Are these solutions unique to gravitational systems?
Let us rewind a bit and consider a simple toy model
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Toy Model
Simple Bi-galileon
EOM (two integration constants)
Chagoya, Niz, Tasinato(preliminary)
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Toy Model
1/r singularity removal (strong screening)
Existence cond.
1
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Toy Model
Other field & Perturbations
No Ghost
1
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Toy Model
Superluminality inside the Vainshtein radius?
Not straightforward to calculate velocities because fields are coupled, but found solutions, for
1
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Toy Model
With there is one further solution where both fields are regular near zero.
Always a Ghost
1
Other operators may avoid Derrick's theorem
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Toy Model
Confinement
Existence cond.
2
Perturbations are always unstable
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Toy Model
Other/higher operators
1) Change the exponent
near r=0
2) Improve stability
of perturbations
Is this solution relevant for confinement?
2
Strassler Notes On Confinementand Duality
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Toy Model - Richness
Inner Outer
1
2
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On the Vainshtein MechanismKICP – Oct. 2015 G. Niz
Conclusions
● Models with derivative interactions (of Galileon type) have rich space of solutions
● Are solutions tied to instabilities?
– Some may go away by adding other operators or when calculating the relevant observables (group vs front velocity, see Keltner and Tolley)
● May have interesting applications beyond modified gravity