Universal predictions of
screened modified gravity
in galaxy cluster
David F. Mota
Universal predictions of
screened modified gravity
in galaxy cluster
Mass of clusters
inferred via lensing, kinematics and thermal observations
are different!
David F. Mota
Scalar-Tensor Theories
with Chameleon or Symmetron screening mechanisms
Chameleon f(R)-gravity
•
Effective potential (Einstein frame)
•
Free parameters
fR0 , n
Hu & Sawicki (2007)
Hinterbichler & Khoury (2010)
The Symmetron
S=
•
Z
d4 x
p
g

R
16⇡G
1
(@')2
2
V (') + Sm (g̃µ⌫ , )
Effective potential
•
Free parameters
•
Range
•
Symmetry breaking
•
Coupling strength
Lensing Mass
measured via gravitational lensing
Lensing Mass
measured via gravitational lensing
Conformal Invariance: photons not affected by Modified Gravity
Lensing Mass
measured via gravitational lensing
Conformal Invariance: photons not affected by Modified Gravity
Lensing Mass in (conformal) Modified Gravity same as GR
Kinematical Mass: from velocity dispersions
Kinematical Mass: from velocity dispersions
<V2 >
Mkinematic
= FN
R
Kinematical Mass: from velocity dispersions
<V2 >
Mkinematic
= FN + F
R
Kinematical Mass: from velocity dispersions
<V2 >
Mkinematic
= FN + F
R
Modified Gravity enhances kinematical mass
Modified Gravity with Screening Mechanisms:
Fifth force depends on environmental density
Screened
Kinematic mass is same in GR
Unscreened
Kinematic mass differs from GR
Modified Gravity with Screening Mechanisms:
Fifth force depends on environmental density
Screened
Kinematic mass is same in GR
Unscreened
Kinematic mass differs from GR
Kinematic Mass depends on location in a
high/low dense environment (size of cluster)
Smoking gun for Screening Mechanisms
Lensing Mass vs. Environmental dependent Kinematic Mass
Lensing Mass same as in GR
M
MD
⌘
ML
1
Kinematic Mass depends
on environment
Smoking gun for Screening Mechanisms
Lensing Mass vs. Environmental dependent Kinematic Mass
Lensing Mass same as in GR
Kinematic Mass depends
on environment
GR :
M
MD
⌘
ML
1
F (R) :
Chameleon/Symmetron :
=0
1
M 2 [0, ]
3
2
2
[0,
2
]
M
M
Smoking gun for Screening Mechanisms
Lensing Mass vs. Kinematic Mass
0.6
0.5
Mkinetic /Mlens
1.0
0.4
0.3
LCDM200
LCDM256
FofR04
FofR05
FofR06
0.2
0.1
0.0
0.1
0.2 13
10
1014
Mlens (M h 1 )
1015
fofr4~24 Mpc
fofr5~7 Mpc
fofr6~2 Mpc
Smoking gun for Screening Mechanisms
Lensing Mass vs. Kinematic Mass
Unscreened Modified Gravity
0.6
0.5
Mkinetic /Mlens
1.0
0.4
0.3
LCDM200
LCDM256
FofR04
FofR05
FofR06
0.2
0.1
0.0
0.1
0.2 13
10
1014
Mlens (M h 1 )
1015
fofr4~24 Mpc
fofr5~7 Mpc
fofr6~2 Mpc
Smoking gun for Screening Mechanisms
Lensing Mass vs. Kinematic Mass
Unscreened Modified Gravity
0.6
0.5
Mkinetic /Mlens
1.0
0.4
0.3
LCDM200
LCDM256
FofR04
FofR05
FofR06
0.2
0.1
0.0
0.1
0.2 13
10
1014
Mlens (M h 1 )
Screened Modified Gravity
1015
fofr4~24 Mpc
fofr5~7 Mpc
fofr6~2 Mpc
Smoking gun for Screening Mechanisms
Lensing Mass vs. Kinematic Mass
Unscreened Modified Gravity
0.6
1.2
0.5
1.0
LCDM200
LCDM256
FofR04
FofR05
FofR06
0.2
0.1
0.0
1.0
0.3
Mkinetic /Mlens
Mkinetic /Mlens
1.0
0.4
0.8
A
B
C
D
0.6
0.4
0.2
0.0
0.1
0.2 13
10
LCDM200
LCDM256
Symmetron
Symmetron
Symmetron
Symmetron
1014
Mlens (M h 1 )
Screened Modified Gravity
1015
fofr4~24 Mpc
fofr5~7 Mpc
fofr6~2 Mpc
0.2 13
10
1014
Mlens (M h 1 )
1015
Smoking gun for Screening Mechanisms
Lensing Mass vs. Kinematic Mass
Large coupling/small scale screening
Unscreened Modified Gravity
0.6
1.2
0.5
1.0
LCDM200
LCDM256
FofR04
FofR05
FofR06
0.2
0.1
0.0
1.0
0.3
Mkinetic /Mlens
Mkinetic /Mlens
1.0
0.4
0.8
A
B
C
D
0.6
0.4
0.2
0.0
0.1
0.2 13
10
LCDM200
LCDM256
Symmetron
Symmetron
Symmetron
Symmetron
1014
Mlens (M h 1 )
Screened Modified Gravity
1015
fofr4~24 Mpc
fofr5~7 Mpc
fofr6~2 Mpc
0.2 13
10
1014
Mlens (M h 1 )
1015
Smoking gun for Screening Mechanisms
Lensing Mass vs. Kinematic Mass
Large coupling/small scale screening
Unscreened Modified Gravity
0.6
1.2
0.5
1.0
LCDM200
LCDM256
FofR04
FofR05
FofR06
0.2
0.1
0.0
1.0
0.3
Mkinetic /Mlens
Mkinetic /Mlens
1.0
0.4
0.8
A
B
C
D
0.6
0.4
0.2
0.0
0.1
0.2 13
10
LCDM200
LCDM256
Symmetron
Symmetron
Symmetron
Symmetron
1014
Mlens (M h 1 )
Screened Modified Gravity
1015
fofr4~24 Mpc
fofr5~7 Mpc
fofr6~2 Mpc
0.2 13
10
1014
Mlens (M h 1 )
small coupling/large scale screening
1015
Thermal Mass: from x-ray measurements of
temperature and density profiles of baryons
Umetsu et al., ApJ 755, 56 (2012)
Thermal Mass: from x-ray measurements of
temperature and density profiles of baryons
Umetsu et al., ApJ 755, 56 (2012)
dP
Mass holds hydrostatic equilibrium:
=
dr
GM (r)⇢(r)
r2
Thermal Mass: from x-ray measurements of
temperature and density profiles of baryons
Umetsu et al., ApJ 755, 56 (2012)
dP
Mass holds hydrostatic equilibrium:
=
dr
GM (r)⇢(r)
+F
r2
Thermal Mass: from x-ray measurements of
temperature and density profiles of baryons
Umetsu et al., ApJ 755, 56 (2012)
dP
Mass holds hydrostatic equilibrium:
=
dr
GM (r)⇢(r)
+F
r2
Thermal mass in Modified Gravity depends on the fifth
force (which is environmental dependent!)
Smoking gun for Screening Mechanisms
Lensing Mass vs. Environmental dependent Thermal Mass
0.5
⇤CDM
FofR04
FofR05
FofR06
0.4
MThermal
MLens
1
0.3
0.2
0.1
0.0
0.1
1013
1014
1015
MLens (M h0 1 )
fofr4~24 Mpc
fofr5~7 Mpc
fofr6~2 Mpc
Smoking gun for Screening Mechanisms
Lensing Mass vs. Environmental dependent Thermal Mass
Unscreened Modified Gravity
0.5
⇤CDM
FofR04
FofR05
FofR06
0.4
MThermal
MLens
1
0.3
0.2
0.1
0.0
0.1
1013
1014
1015
MLens (M h0 1 )
fofr4~24 Mpc
fofr5~7 Mpc
fofr6~2 Mpc
Smoking gun for Screening Mechanisms
Lensing Mass vs. Environmental dependent Thermal Mass
Unscreened Modified Gravity
0.5
⇤CDM
FofR04
FofR05
FofR06
0.4
MThermal
MLens
1
0.3
0.2
0.1
0.0
0.1
1013
1014
1015
MLens (M h0 1 )
Screened Modified Gravity
fofr4~24 Mpc
fofr5~7 Mpc
fofr6~2 Mpc
Smoking gun for Screening Mechanisms
Lensing Mass vs. Environmental dependent Thermal Mass
Unscreened Modified Gravity
0.5
1.6
⇤CDM
FofR04
FofR05
FofR06
0.4
1.2
MThermal
MLens
1
1.0
1
0.3
MThermal
MLens
⇤CDM
Symmetron A
Symmetron B
Symmetron C
Symmetron D
1.4
0.2
0.1
0.8
0.6
0.4
0.2
0.0
0.0
0.1
1013
10
14
10
MLens (M h0 1 )
Screened Modified Gravity
fofr4~24 Mpc
fofr5~7 Mpc
fofr6~2 Mpc
15
0.2
1013
1014
MLens (M h0 1 )
1015
Smoking gun for Screening Mechanisms
Lensing Mass vs. Environmental dependent Thermal Mass
Large coupling/small scale screening
Unscreened Modified Gravity
0.5
1.6
⇤CDM
FofR04
FofR05
FofR06
0.4
1.2
MThermal
MLens
1
1.0
1
0.3
MThermal
MLens
⇤CDM
Symmetron A
Symmetron B
Symmetron C
Symmetron D
1.4
0.2
0.1
0.8
0.6
0.4
0.2
0.0
0.0
0.1
1013
10
14
10
MLens (M h0 1 )
Screened Modified Gravity
fofr4~24 Mpc
fofr5~7 Mpc
fofr6~2 Mpc
15
0.2
1013
1014
MLens (M h0 1 )
1015
Smoking gun for Screening Mechanisms
Lensing Mass vs. Environmental dependent Thermal Mass
Large coupling/small scale screening
Unscreened Modified Gravity
0.5
1.6
⇤CDM
FofR04
FofR05
FofR06
0.4
1.2
MThermal
MLens
1
1.0
1
0.3
MThermal
MLens
⇤CDM
Symmetron A
Symmetron B
Symmetron C
Symmetron D
1.4
0.2
0.1
0.8
0.6
0.4
0.2
0.0
0.0
0.1
1013
10
14
10
MLens (M h0 1 )
Screened Modified Gravity
fofr4~24 Mpc
fofr5~7 Mpc
fofr6~2 Mpc
15
0.2
1013
1014
MLens (M h0 1 )
small coupling/large scale screening
1015
Thermal + Lense+Kinematic Mass
Probe for non-universal couplings
0.8
LCDM200
LCDM256
DM1G1
DM1G0.1
DM0.1G1
Mkinetic /Mlens
1.0
0.6
0.4
0.2
0.0
0.2 13
10
1014
Mlens (M h 1 )
1015
Thermal + Lense+Kinematic Mass
Probe for non-universal couplings
Kinematic mass strongly
affected by coupling to DM
0.8
LCDM200
LCDM256
DM1G1
DM1G0.1
DM0.1G1
Mkinetic /Mlens
1.0
0.6
0.4
0.2
0.0
0.2 13
10
1014
Mlens (M h 1 )
1015
Thermal + Lense+Kinematic Mass
Probe for non-universal couplings
Kinematic mass strongly
affected by coupling to DM
0.8
LCDM200
LCDM256
DM1G1
DM1G0.1
DM0.1G1
Mkinetic /Mlens
1.0
0.6
0.4
0.2
0.0
0.2 13
10
1014
Mlens (M h 1 )
Kinematic mass weakly affected
by coupling to baryons
1015
Thermal + Lense+Kinematic Mass
Probe for non-universal couplings
Kinematic mass strongly
affected by coupling to DM
0.8
LCDM200
LCDM256
DM1G1
DM1G0.1
DM0.1G1
Mkinetic /Mlens
1.0
0.6
0.4
0.2
0.0
0.2 13
10
1014
Mlens (M h 1 )
1015
Kinematic mass weakly affected
by coupling to baryons
Kinematic Mass probes couplings to dark matter
Thermal + Lense+Kinematic Mass
Probe for non-universal couplings
Kinematic mass strongly
affected by coupling to DM
0.8
⇤CDM
DM1G0.1
DM0.1G1
DM1G1
1.0
0.8
1
1.0
0.6
0.4
0.6
MThermal
MLens
Mkinetic /Mlens
1.2
LCDM200
LCDM256
DM1G1
DM1G0.1
DM0.1G1
0.2
0.4
0.2
0.0
0.2 13
10
0.0
1014
Mlens (M h 1 )
1015
0.2
1013
1014
MLens (M h0 1 )
Kinematic mass weakly affected
by coupling to baryons
Kinematic Mass probes couplings to dark matter
1015
Thermal + Lense+Kinematic Mass
Probe for non-universal couplings
Kinematic mass strongly
affected by coupling to DM
0.8
⇤CDM
DM1G0.1
DM0.1G1
DM1G1
1.0
0.8
1
1.0
0.6
0.4
0.6
MThermal
MLens
Mkinetic /Mlens
1.2
LCDM200
LCDM256
DM1G1
DM1G0.1
DM0.1G1
0.2
0.4
0.2
0.0
0.2 13
10
0.0
1014
Mlens (M h 1 )
Kinematic mass weakly affected
by coupling to baryons
1015
0.2
1013
1014
MLens (M h0 1 )
Thermal mass weakly affected
by coupling to dark matter
Kinematic Mass probes couplings to dark matter
1015
Thermal + Lense+Kinematic Mass
Probe for non-universal couplings
Kinematic mass strongly
affected by coupling to DM
Thermal mass strongly affected
by coupling to baryons
0.8
⇤CDM
DM1G0.1
DM0.1G1
DM1G1
1.0
0.8
1
1.0
0.6
0.4
0.6
MThermal
MLens
Mkinetic /Mlens
1.2
LCDM200
LCDM256
DM1G1
DM1G0.1
DM0.1G1
0.2
0.4
0.2
0.0
0.2 13
10
0.0
1014
Mlens (M h 1 )
Kinematic mass weakly affected
by coupling to baryons
1015
0.2
1013
1014
MLens (M h0 1 )
Thermal mass weakly affected
by coupling to dark matter
Kinematic Mass probes couplings to dark matter
1015
Thermal + Lense+Kinematic Mass
Probe for non-universal couplings
Kinematic mass strongly
affected by coupling to DM
Thermal mass strongly affected
by coupling to baryons
0.8
⇤CDM
DM1G0.1
DM0.1G1
DM1G1
1.0
0.8
1
1.0
0.6
0.4
0.6
MThermal
MLens
Mkinetic /Mlens
1.2
LCDM200
LCDM256
DM1G1
DM1G0.1
DM0.1G1
0.2
0.4
0.2
0.0
0.2 13
10
0.0
1014
Mlens (M h 1 )
Kinematic mass weakly affected
by coupling to baryons
1015
0.2
1013
1014
MLens (M h0 1 )
Thermal mass weakly affected
by coupling to dark matter
Kinematic Mass probes couplings to dark matter
Thermal Mass probes couplings to baryons
1015
Probing for non-universal couplings
Observational Constraints
Summary
}
The measured mass of galaxy clusters can probe equivalence
principle violations
} In screened modified gravity the mass inferred via lensing
diferes from the mass inferred via kinematical methods
and thermal methods
} The differences between the observed masses are
environmental dependent
}
Non-universally coupled models can be differentiated by
combining lensing, kinematic and thermal mass
} Lensing mass probes gravity
} Kinematic mass probes coupling to dark matter
} Thermal mass probes coupling to baryons