Post on 25-Apr-2018
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Outline
1 Cosmic acceleration
Deviations from cosmological constantMatter couplings from modifiedgravityChameleon scalars and screening
2 Experimental probes
Eot-Wash torsion pendulumexperimentChameleons in Eot-Wash
3 Quantum-stable chameleons
Chameleon models with smallquantum correctionsApproximate Eot-Wash constraintsForecasts
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments
Eot-W
ash φ
4
0.01 0.1 1 10 100 1000matter coupling β
0.0001
0.001
0.01
0.1
mas
s m
φ(ρ l
ab) [
eV]
excluded by Eot-Wash
large quantum corrections
Eot-W
ash φ
4
0.01 0.1 1 10 100 1000matter coupling β
0.0001
0.001
0.01
0.1
mas
s m
φ(ρ l
ab) [
eV]
excluded by Eot-Wash
large quantum corrections
Types of dark energy
Dynamical explanations of the cosmic acceleration can differ froma cosmological constant in two ways: evolution and coupling.
Dark energy evolves
V (φ)
H(z) evolves with φ
Constrain using
Dark energy couples
New effects:
fifth forcesnew particle
Screening mechanism
chameleon (mass)Vainshtein (kinetic)
Constrain using:
532nmNd:YAG
laser
HamamatsuH7422P−40
PMT
(BK7 glass) (BK7 glass)
(BK7 glass)lens
vacuum pump
window
magnetic field region
entrance
(B = 5 Tesla)
exit window
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments
Types of dark energy
Dynamical explanations of the cosmic acceleration can differ froma cosmological constant in two ways: evolution and coupling.
Dark energy evolves
V (φ)
H(z) evolves with φ
Constrain using
Dark energy couples
New effects:
fifth forcesnew particle
Screening mechanism
chameleon (mass)Vainshtein (kinetic)
Constrain using:
532nmNd:YAG
laser
HamamatsuH7422P−40
PMT
(BK7 glass) (BK7 glass)
(BK7 glass)lens
vacuum pump
window
magnetic field region
entrance
(B = 5 Tesla)
exit window
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments
Types of dark energy
Dynamical explanations of the cosmic acceleration can differ froma cosmological constant in two ways: evolution and coupling.
Dark energy evolves
V (φ)
H(z) evolves with φ
Constrain using
Dark energy couples
New effects:
fifth forcesnew particle
Screening mechanism
chameleon (mass)Vainshtein (kinetic)
Constrain using:
532nmNd:YAG
laser
HamamatsuH7422P−40
PMT
(BK7 glass) (BK7 glass)
(BK7 glass)lens
vacuum pump
window
magnetic field region
entrance
(B = 5 Tesla)
exit window
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments
Modified gravity and coupled scalar fields
The simplest modified gravity models reduce at low energies to4-D matter-coupled scalar field theories.
Modified gravity
f (R) gravity:action S =∫ d4x
√−g
16πGNf (R)
DGP, etc.:non-compactextra dimension
Kaluza-Klein,etc.: compactextra dimension
Effective scalar
Conformaltransformation⇒ chameleon
Decoupling limit(weak gravity)⇒ Galileon
Small extradimension limit⇒ radion
New physics
matter coupling,self-interactionV (φ)
matter coupling,non-canonicalkinetic term
matter coupling,photon (gaugefield) coupling
A matter coupling implies a fifth force which must be screened.
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments
Modified gravity and coupled scalar fields
The simplest modified gravity models reduce at low energies to4-D matter-coupled scalar field theories.
Modified gravity
f (R) gravity:action S =∫ d4x
√−g
16πGNf (R)
DGP, etc.:non-compactextra dimension
Kaluza-Klein,etc.: compactextra dimension
Effective scalar
Conformaltransformation⇒ chameleon
Decoupling limit(weak gravity)⇒ Galileon
Small extradimension limit⇒ radion
New physics
matter coupling,self-interactionV (φ)
matter coupling,non-canonicalkinetic term
matter coupling,photon (gaugefield) coupling
A matter coupling implies a fifth force which must be screened.
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments
Modified gravity and coupled scalar fields
The simplest modified gravity models reduce at low energies to4-D matter-coupled scalar field theories.
Modified gravity
f (R) gravity:action S =∫ d4x
√−g
16πGNf (R)
DGP, etc.:non-compactextra dimension
Kaluza-Klein,etc.: compactextra dimension
Effective scalar
Conformaltransformation⇒ chameleon
Decoupling limit(weak gravity)⇒ Galileon
Small extradimension limit⇒ radion
New physics
matter coupling,self-interactionV (φ)
matter coupling,non-canonicalkinetic term
matter coupling,photon (gaugefield) coupling
A matter coupling implies a fifth force which must be screened.
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments
Modified gravity and coupled scalar fields
The simplest modified gravity models reduce at low energies to4-D matter-coupled scalar field theories.
Modified gravity
f (R) gravity:action S =∫ d4x
√−g
16πGNf (R)
DGP, etc.:non-compactextra dimension
Kaluza-Klein,etc.: compactextra dimension
Effective scalar
Conformaltransformation⇒ chameleon
Decoupling limit(weak gravity)⇒ Galileon
Small extradimension limit⇒ radion
New physics
matter coupling,self-interactionV (φ)
matter coupling,non-canonicalkinetic term
matter coupling,photon (gaugefield) coupling
A matter coupling implies a fifth force which must be screened.
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments
Chameleon effect
Veff(φ) = V (φ) + βMPl
(−Tµµ )φ ≈ V (φ) + βρ
MPlφ
V(φ)
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments
Chameleon effect
Veff(φ) = V (φ) + βMPl
(−Tµµ )φ ≈ V (φ) + βρ
MPlφ
Vint = βmat ρmat φ / MPl
V(φ)
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments
Chameleon effect
Veff(φ) = V (φ) + βMPl
(−Tµµ )φ ≈ V (φ) + βρ
MPlφ
φmin(ρlow)
(meff2 = V’’ is small)
V(φ)Veff(φ,ρlow)
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments
Chameleon effect
Veff(φ) = V (φ) + βMPl
(−Tµµ )φ ≈ V (φ) + βρ
MPlφ
φmin(ρlow)
(meff2 = V’’ is small)
φmin(ρhigh)
(meff2 is large)
V(φ)Veff(φ,ρlow)
Veff(φ,ρhigh)
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments
Fifth-force constraints from a torsion pendulum
Eot-Wash Experiment
http://www.npl.washington.edu/eotwash
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments
φ4 chameleon field in Eot-Wash pendulum
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments
-6 -4 -2 0 2 4 6
-0.6-0.4
-0.2 0
0.2 0.4
0.6 0.8 1
1.2
0
5
10
15
20
25
φ [mm-1]
20 15 10 5
x [mm]
z [mm]
φ [mm-1]
AU, S. Gubser, J. Khoury, PRD 74 104024 (2006)Adelberger, Heckel, Hoedl, Hoyle, Kapner, AU, PRL 98 131104 (2007)
Chameleons with small quantum corrections
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments
∆V1−loop(φ) = meff(φ)4
64π2 log(meff(φ)2
µ2
)⇒ meff , φ change
Eot-W
ash φ
4
0.01 0.1 1 10 100 1000matter coupling β
0.0001
0.001
0.01
0.1
mas
s m
φ(ρ l
ab) [
eV]
excluded by Eot-Wash
large quantum corrections
Eot-W
ash φ
4
0.01 0.1 1 10 100 1000matter coupling β
0.0001
0.001
0.01
0.1
mas
s m
φ(ρ l
ab) [
eV]
excluded by Eot-Wash
large quantum corrections
AU, W. Hu, J. Khoury, PRL 109 041301 (2012)
1-D plane-parallel approximation to Eot-Wash constraints
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments
self-
coup
ling
λ
0.001 0.01 0.1 1 10 100 1000matter coupling β
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
linear
Eot-Wash
1Dpp approx.
large quantum corrections
self-
coup
ling
λ
0.001 0.01 0.1 1 10 100 1000matter coupling β
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
linear
Eot-Wash
1Dpp approx.
large quantum corrections
AU, arXiv:1209:0211, submitted to PRD (2012)
V (φ) = λ4!φ
4
Next-generation Eot-Wash: Forecasts
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments
self-
coup
ling
λ
0.01 0.1 1 10 100 1000 10000matter coupling β
10-4
10-3
10-2
10-1
100
101
102
103
104
linea
r
Eot
-Was
h cu
rren
t
Eot-Washnext-generation(1Dpp approx.)
large quantum corrections
self-
coup
ling
λ
0.01 0.1 1 10 100 1000 10000matter coupling β
10-4
10-3
10-2
10-1
100
101
102
103
104
linea
r
Eot
-Was
h cu
rren
t
Eot-Washnext-generation(1Dpp approx.)
large quantum corrections
self-
coup
ling
γ
0.01 0.1 1 10 100 1000matter coupling β
10-3
10-2
10-1
100
101
102
103
104
linear Eot-Washnext-generation(1Dpp approx.)
large quantum correctionsself-
coup
ling
γ
0.01 0.1 1 10 100 1000matter coupling β
10-3
10-2
10-1
100
101
102
103
104
linear Eot-Washnext-generation(1Dpp approx.)
large quantum corrections
0.01 0.1 1 10 100 1000matter coupling β
4
6
8
10
12
14
16
18
20
pow
er la
w in
dex
n
linea
r
Eot-Washnext-generation (1Dpp approx.)
largequantumcorrections
0.01 0.1 1 10 100 1000matter coupling β
4
6
8
10
12
14
16
18
20
pow
er la
w in
dex
n
linea
r
Eot-Washnext-generation (1Dpp approx.)
largequantumcorrections
0.01 0.1 1 10 100matter coupling β
-30
-25
-20
-15
-10
-5
-1
pow
er la
w in
dex
n
linea
r
Eot-Washnext-generation(1Dpp approx.)
largequantumcorrections
0.01 0.1 1 10 100matter coupling β
-30
-25
-20
-15
-10
-5
-1
pow
er la
w in
dex
n
linea
r
Eot-Washnext-generation(1Dpp approx.)
largequantumcorrections
AU, arXiv:1209:0211, submitted to PRD (2012)
V (φ) = λ4!φ4 V (φ) = γM5
Λ/φ
V (φ) = γM4−nΛ
φn V (φ) = γM4−nΛ
φn
Conclusions
1 Modified gravity could be responsible for the cosmicacceleration.
2 Scalar-mediated fifth forces from modified gravity must bescreened in order to evade constraints from tests of gravity.
3 Chameleon-screened models with small quantum correctionsand gravitation-strength couplings extend just beyond currentexperimental bounds in parameter space.
4 The next-generation Eot-Wash torsion pendulum experimentwill exclude a large range of quantum-stable chameleonmodels.
Amol Upadhye Dark energy fifth forces in torsion pendulum experiments