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Synergizing Screening Mechanisms on Different Scales
Jeremy Sakstein University of Pennsylvania
Probing the dark sector and general relativity at all scales
CERN 17th August 2017
Or…. What should astrophysical tests of gravity mean to you?
Jeremy Sakstein University of Pennsylvania
Probing the dark sector and general relativity at all scales
CERN 17th August 2017
Two views of MG
• Want UV modifications of gravity
• Higher-order operators
• Typically satisfy SS bounds
• Look for deviations from GR in strong field regime
1) Strong field:
Two views of MG
• Want IR modifications of gravity
• Relevant for cosmology but ruled out by SS bounds
• Use screening mechanisms to hide modifications in SS
• Natural suppression of deviations
• Don’t need to tune parameters
2) Cosmologists:
Screening mechanisms
Non-linear effects decouple cosmological scales from the solar system
solar system astrophysics cosmology
screened partially screened unscreened
Some inconvenient truths about screening mechanisms
• Highly-non-linear field equations
Can’t use PPN Well-posedness? Do we care (EFT)? Two-body/low symmetry systems?
• Need novel tests
Complex modelling for laboratory tests Novel astrophysical probes
Astrophysical probes - mildly screened regime
Cepheid stars Dwarf stars Galaxy clusters
White dwarf stars Neutron starsBlack holes
The problem with MGNewtonian limit of GR:
r2�N = 4⇡G⇢ FN = r�N
Modified gravity — new scalar graviton:
F5 = ↵r�
F5
FN= 2↵2
r2� = 8⇡↵G⇢
solar system: 2↵2 < 10�5
(Shapiro time-delay effect, Cassini)
Screening mechanisms
Two options:
Non-Poisson kinetic terms Vainshtein screening
Kill off the source no scalar gradient
chameleon/symmetron/f(R)
r2�+ F (@�, @2�, . . .) = 8⇡↵G⇢+ V 0(�)
Chameleon screening
Add a scalar potential:
r2� = 8⇡↵G⇢+ V (�),�
Get these to cancel out dynamically
r2� = 0
r2� = 8⇡↵G⇢
rs
R
Chameleon/Symmetron/f(R)
Chameleon/Symmetron/f(R)
r2� = 0
r2� = 8⇡↵G⇢
rs
R
Vainshtein screening
Change kinetic terms — e.g. cubic galileon:
1
r2d
dr2
r2�0 +
2r2c3
r�02�= 8⇡↵G⇢
Poisson termGalileon term
(crossover scale )rc
Coupling to matter
Vainshtein MechanismWe can integrate this once:
- Vainshtein radius
Vainshtein screening
Vainshtein screening is generic• DGP braneworld gravity
• Covariant galileons
• Massive gravity
• Massive bi-gravity
• Horndeski
• Beyond Horndeski — breaks down inside objects
VERY generic scalar-tensor theories
with three D.O.F
Screened
Unscreened
(�PPN = 1)
Vainshtein breaking in beyond Horndeski
Fgrav =GM(r)
r2+⌥1G
4
d2M(r)
dr2
Inside objects:
E.g. for the simplest case (one new scalar d.o.f):
T H E A L P H A PA R A M E T E R S
↵B(t) `braiding’ — mixing of scalar + metric kinetic terms.:
kinetic term of scalar field.↵K(t) :
speed of gravitational waves, . ↵T (t) : c2T = 1 + ↵T
running of effective Planck mass.:↵M (t) =1
H
d ln M2(t)
dt
↵H(t) disformal symmetries of the metric.:
VERY important parameter
Credit: Tessa Baker
VERY important parameter
5 functions that control linear cosmology (EFT of DE)
NR probes combinations of three of them:
⌥1 =4↵2
H
c2T (1 + ↵B)� ↵H � 1
Constraining these constrains cosmology!
Outline of this talk
• Chameleon/symmetron/f(R) — Cepheid stars
• Vainshtein/galileons — supermassive black holes
• Beyond Horndeski — dwarf + neutron stars
- strength of fifth-force
- self-screening parameter
object is unscreened if
(fully unscreened)
Chameleon/symmetron/f(R)Two parameters:
(fR0 = 2�0/3)
r2� = 8⇡↵G⇢
rs
Astrophysical screening
main-sequence post-MS dwarf galaxy
Need void dwarfs due to environmental screening
Complication: environmental screening
Can only use unscreened dwarf galaxies in voids!
Screening map of SDSS data: Cabre et al. 2012
Chameleon stars — MESA
A new and powerful tool to compare with observations
2↵2 = 1/3
Testing chameleons using starsParameters probed using distance indicators
Need a formula to relate observational data to distances
Test using distance indicators
Main idea:
• Distances measurements assume theory of gravity
• Different methods should agree
• Compare distances to unscreened galaxies
d2L =L
4⇡FE.g. Luminosity distance:
CepheidsPeriod-luminosity relation
Cares about gravity:
�d
d= �0.3
�G
G
T / G�1/2
Tip of the red giant branch
• Peak luminosity is fixed - standard candle • Set by nuclear physics - independent of gravity
Distance indicators
New constraints
Excluded
Jain, Vikram, JS (2012)
f(R)
The big pictureBurrage, JS ‘16
↵ = � =MPl
M
Astrophysics can’t do better than thisn = 1
Ve↵ =⇤4+n
�n+
↵�⇢
Mpl
Negative n is also a chameleon!
F (R) lives here
⇤ = 2.4⇥ 10�3 eV
Chameleon relevant for cosmology
Advertisement: living review
Symmetron/Chameleon/f(R)/photon coupling
Astrophysics
AtomInterferometry
Eo..t-Wash
0 5 10 15 20-100
-80
-60
-40
-20
0
Ve↵ = �µ2
2
✓1� ⇢
µ2M2s
◆+
�
4�4
µ = 2.4⇥ 10�3eV
Galileons• Self-acceleration (DE but does not solve CC)
• Nice UV properties
• Massive gravity
• Braneworld models
• Hard to test due to Vainshtein screening
No hair theorem
No galileon charge Q so BH does not feel galileon force
Hui & Nicolis ‘12
Black holes described by mass and spin only!
Q = MMatter has
Matter and BH fall at different rates
Violation of the strong equivalence principle
Hui & Nicolis ‘12
Eötvös experiments with black holes
Galaxy clusters: nature’s leaning towers
BH
Virgo Cluster
● Newtonian
● Galileon (rc = 500 Mpc)
● Galileon (rc = 6000 Mpc)
-- RMS Cosmological
0.5 1 5 10
50100
5001000
5000104
(km/s)2/kpc
rVnDGP
self-accelerating
NFW, c=5M = 1015M�
Offset
● ρ = 0.05M☉ pc-3, M200 = 1015M☉
● ρ = 0.1M☉ pc-3, M200 = 1015M☉
-- ρ = 0.1M☉ pc-3, M200 = 2x1014M☉
0.5 1 5 10 Mpc
0.05
0.10
0.50
1
Offsetkpc
M 87
M 87
LLR
7.9 5. 3.8
/Mpc
/(1000 km)-1self-acceleration
⇤3 =�6Mp/r
2c
�1/3
JS, Jain, Heyl, Hui APJL ‘17
Future tests
• More galaxies — SDSS, DES, Euclid + X-ray/Radio
• Morphological distortions
• Missing SMBHs!
This is one galaxy!
Screened
Unscreened
Tests of beyond Horndeski
Tests of beyond Horndeski
Fgrav =GM(r)
r2+⌥1G
4
d2M(r)
dr2
�2
3< ⌥1 < 1
No stable stellar configurations Saito et al. 2015
Gravity weaker than GR!
Dwarf stars - a new test of gravity
Red dwarf
Dwarf stars - a new test of gravity
Perfect tests:
• Chemically and structurally homogeneous
• Equation of state is well-known
• Lots of interest in low mass objects (KEPLER, GAIA)
Low mass M-R
Brown dwarf
Red dwarf
MMHB
Gravity weaker
Core cooler and less dense at fixed mass
Higher MMHB
Red dwarfs — MMHBHydrogen burning when core is hot and dense enough
Red dwarfs — MMHB
LHB = Le↵
Stable burning when production balances loss
EOS + theory of gravity Proton burning
:
MMMHB = 0.08�(⌥1)
�(⌥1 = 0)M�
New constraintLowest mass star is Gl 886 C
M = 0.0930± 0.0008M�
) ⌥1 < 0.027
JS, PRL (2015)
Neutron stars
Mass — Sun
Radius — few km
Relativistic: v/c ⇠ 1
Mass, spin, charge, quadrupole moment,…, hair!
Testing GR with neutron stars
• No rotation — mass-radius relation
• O( ) — moment of inertia
• O( ) — tidal Love number/quadrupole moment
!Angular velocity
!
!2
Can we test Vainshtein with this?
Most massive NS observed
Larger maximum mass
Larger radii
Devil is in the detail
Babichev, …, JS ‘16
Equation of state is unknown!
Need EOS-independent testsBreu, Rezzolla ‘16
Moment of inertia
We can do this for BH
Modifications are larger than the scatter
This measurement is 10 years away!Need specific systems to decouple spin-orbit coupling
Complication: rotation effects scalar at O( ) but not O( ). Lose integrability.!!2
Credit: Alessandra Bounanno
Summary — novel astrophysical probes
• Chameleons/symmetrons/f(R):
Test using distance indicators Astrophysical region nearly saturated
• Vainshtein:
SMBHs — normal branch in trouble Can push to self-accelerating with future surveys
• Beyond Horndeski:Directly constrains cosmology Dwarf and neutron stars promising probes
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