Dark energy fifth forces in torsion pendulum experiments · matter coupling b 0.1 0.01 0.001 0.0001 mass m ... Types of dark energy Dynamical explanations of the cosmic acceleration

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


0.0001

0.001

0.01

0.1

mas

s m

φ(ρ l

ab) [

eV]



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




Dark energy evolves

V (φ)


Constrain using

Dark energy couples

New effects:


Screening mechanism


Constrain using:

532nmNd:YAG

laser


PMT


(BK7 glass)lens

vacuum pump

window


entrance

(B = 5 Tesla)

exit window




Dark energy evolves

V (φ)


Constrain using

Dark energy couples

New effects:


Screening mechanism


Constrain using:

532nmNd:YAG

laser


PMT


(BK7 glass)lens

vacuum pump

window


entrance

(B = 5 Tesla)

exit window


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.




Modified gravity


√−g

16πGNf (R)



Effective scalar




New physics








Modified gravity


√−g

16πGNf (R)



Effective scalar




New physics








Modified gravity


√−g

16πGNf (R)



Effective scalar




New physics






Chameleon effect

Veff(φ) = V (φ) + βMPl

(−Tµµ )φ ≈ V (φ) + βρ

MPlφ

V(φ)


Chameleon effect


(−Tµµ )φ ≈ V (φ) + βρ

MPlφ

Vint = βmat ρmat φ / MPl

V(φ)


Chameleon effect


(−Tµµ )φ ≈ V (φ) + βρ

MPlφ

φmin(ρlow)

(meff2 = V’’ is small)

V(φ)Veff(φ,ρlow)


Chameleon effect


(−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)


Fifth-force constraints from a torsion pendulum

Eot-Wash Experiment

http://www.npl.washington.edu/eotwash


φ4 chameleon field in Eot-Wash pendulum


-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


∆V1−loop(φ) = meff(φ)4

64π2 log(meff(φ)2

µ2

)⇒ meff , φ change

Eot-W

ash φ

4


0.0001

0.001

0.01

0.1

mas

s m

φ(ρ l

ab) [

eV]



Eot-W

ash φ

4


0.0001

0.001

0.01

0.1

mas

s m

φ(ρ l

ab) [

eV]



AU, W. Hu, J. Khoury, PRL 109 041301 (2012)

1-D plane-parallel approximation to Eot-Wash constraints


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.


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.


AU, arXiv:1209:0211, submitted to PRD (2012)

V (φ) = λ4!φ

4

Next-generation Eot-Wash: Forecasts


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.)


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



self-

coup

ling

γ


10-3

10-2

10-1

100

101

102

103

104

linear Eot-Washnext-generation(1Dpp approx.)

large quantum correctionsself-

coup

ling

γ


10-3

10-2

10-1

100

101

102

103

104

linear Eot-Washnext-generation(1Dpp approx.)



4

6

8

10

12

14

16

18

20

pow

er la

w in

dex

n

linea

r

Eot-Washnext-generation (1Dpp approx.)

largequantumcorrections


4

6

8

10

12

14

16

18

20

pow

er la

w in

dex

n

linea

r

Eot-Washnext-generation (1Dpp approx.)


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



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



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.


Documents

Dark energy fifth forces in torsion pendulum experiments · matter coupling b 0.1 0.01 0.001 0.0001 mass m ... Types of dark energy Dynamical explanations of the cosmic acceleration