[PPT] - Cosmic acceleration Evolution with time Coupling to known particles PowerPoint Presentation

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Cosmic acceleration

Amol Upadhye High-intensity searches for dark energy and modified gravity 2

Evolution with time Coupling to known particles

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Outline

1 Introduction

Motivation: DE scale MΛ = 2.4 × 10−3 eV Dark energy: a phenomenological tool box Example: Chameleon screening

2 Fifth forces

Quantum-stable chameleons E¨

t-Wash constraints and forecasts

Neutron experiments

3 New particles

Production through photon coupling GammeV-CHASE afterglow experiment Upcoming experiments

Amol Upadhye High-intensity searches for dark energy and modified gravity 3

532nm Nd:YAG laser Hamamatsu H7422P−40 PMT (BK7 glass) (BK7 glass) (BK7 glass) lens vacuum pump window magnetic field region entrance (B = 5 Tesla) exit window

SLIDE 4

Coupled dark energy from modified gravity

Modified gravity Effective scalar New physics 4-D modified action: R → f (R) Conformal trans.: ⇒ chameleon matter coupling, effective m(ρ)

Amol Upadhye High-intensity searches for dark energy and modified gravity 4

A phenomenological toolbox:

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Coupled dark energy from modified gravity

Modified gravity Effective scalar New physics 4-D modified action: R → f (R) Conformal trans.: ⇒ chameleon matter coupling, effective m(ρ) 4-D modified action: φ → −φ symmetry Conformal trans.: ⇒ symmetron matter coupling, uncoupled phase

Amol Upadhye High-intensity searches for dark energy and modified gravity 4

A phenomenological toolbox:

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Coupled dark energy from modified gravity

Modified gravity Effective scalar New physics 4-D modified action: R → f (R) Conformal trans.: ⇒ chameleon matter coupling, effective m(ρ) 4-D modified action: φ → −φ symmetry Conformal trans.: ⇒ symmetron matter coupling, uncoupled phase DGP, etc.: non-compact extra dimension Decoupling limit (weak gravity) ⇒ Galileon matter coupling, non-canonical kinetic term

Amol Upadhye High-intensity searches for dark energy and modified gravity 4

A phenomenological toolbox:

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Coupled dark energy from modified gravity

Modified gravity Effective scalar New physics 4-D modified action: R → f (R) Conformal trans.: ⇒ chameleon matter coupling, effective m(ρ) 4-D modified action: φ → −φ symmetry Conformal trans.: ⇒ symmetron matter coupling, uncoupled phase DGP, etc.: non-compact extra dimension Decoupling limit (weak gravity) ⇒ Galileon matter coupling, non-canonical kinetic term Kaluza-Klein, etc.: compact extra dim. Small extra dim. ⇒ radion matter coupling, photon coupling At low energies, dark energy can have a matter coupling, whose fifth force must be screened locally. Dark energy can also have a photon coupling, allowing the production of dark energy particles.

Amol Upadhye High-intensity searches for dark energy and modified gravity 4

A phenomenological toolbox:

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Chameleon mechanism

Amol Upadhye High-intensity searches for dark energy and modified gravity 5

effective potential: Veff(φ, ρ) = V (φ) + βρφ/MPl

V(φ)

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Chameleon mechanism

Amol Upadhye High-intensity searches for dark energy and modified gravity 5

effective potential: Veff(φ, ρ) = V (φ) + βρφ/MPl

Vint = βmat ρmat φ / MPl V(φ)

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Chameleon mechanism

Amol Upadhye High-intensity searches for dark energy and modified gravity 5

effective potential: Veff(φ, ρ) = V (φ) + βρφ/MPl

φmin(ρlow) (meff

2 = V’’ is small)

V(φ) Veff(φ,ρlow)

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Chameleon mechanism

Amol Upadhye High-intensity searches for dark energy and modified gravity 5

effective potential: Veff(φ, ρ) = V (φ) + βρφ/MPl

φmin(ρlow) (meff

2 = V’’ is small)

φmin(ρhigh) (meff

2 is large)

V(φ) Veff(φ,ρlow) Veff(φ,ρhigh)

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At which scale should we probe each model?

Amol Upadhye High-intensity searches for dark energy and modified gravity 6

V (φ) ∝ φn + const. ⇒ meff ∝ ρ

n−2 2n−2 (use lab for n − 1

2, n > 2)

1e-50 1e-40 1e-30 1e-20 1e-10 1 1e-30 1e-20 1e-10 1 meff ∝ ρ(n-2)/(2n-2) [eV] density ρ [g/cm3] V(φ) ∝ φn n=-1 n=1/2 n=2/3 n=4 laboratory cosmology

AU, PRD 86:102003(2012)[arXiv:1209.0211]

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Part II: Fifth forces

Amol Upadhye High-intensity searches for dark energy and modified gravity 7

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Laboratory benchmark: “quantum-stable” chameleons

Amol Upadhye High-intensity searches for dark energy and modified gravity 8

∆V1−loop(φ) = meff(φ)4

64π2

log

meff(φ)2

µ2

< Vtree

⇒ meff ≤

48π2β2ρ2

M2

Pl

1/6 = 0.0073

βρ

10g/cm3

1/6 eV

Eot-Wash φ4

0.01 0.1 1 10 100 1000 matter coupling β 0.0001 0.001 0.01 0.1 mass mφ(ρlab) [eV] excluded by Eot-Wash large quantum corrections

Eot-Wash φ4

0.01 0.1 1 10 100 1000 matter coupling β 0.0001 0.001 0.01 0.1 mass mφ(ρlab) [eV] excluded by Eot-Wash large quantum corrections AU, Hu, Khoury, PRL 109:041301(2012)[arXiv:1204.3906]

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Fifth-force tests using a torsion pendulum

E¨

t-Wash Experiment

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

Amol Upadhye High-intensity searches for dark energy and modified gravity 9

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E¨

t-Wash constraints on chameleons

Amol Upadhye High-intensity searches for dark energy and modified gravity 10

V (φ) = λ

4!φ4

self-coupling λ 0.001 0.01 0.1 1 10 100 1000 matter 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-coupling λ 0.001 0.01 0.1 1 10 100 1000 matter 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

E¨

t-Wash: Adelberger, Heckel, Hoedl, Hoyle, Kapner, AU. PRL 98 131104 (2007)

1Dpp: AU, PRD 86 102003 (2012) [arXiv:1209.0211] V (φ) = λ

4!φ4

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Next-generation E¨

t-Wash: chameleon forecasts

Amol Upadhye High-intensity searches for dark energy and modified gravity 11 V (φ) = λ

4! φ4

V (φ) = γM5

Λ/φ

V (φ) = M4−n

Λ

φn V (φ) = M4−n

Λ

φn

self-coupling λ 0.01 0.1 1 10 100 1000 10000 matter coupling β 10-4 10-3 10-2 10-1 100 101 102 103 104 linear Eot-Wash current Eot-Wash next-generation (1Dpp approx.) large quantum corrections self-coupling λ 0.01 0.1 1 10 100 1000 10000 matter coupling β 10-4 10-3 10-2 10-1 100 101 102 103 104 linear Eot-Wash current Eot-Wash next-generation (1Dpp approx.) large quantum corrections self-coupling γ 0.01 0.1 1 10 100 1000 matter coupling β 10-3 10-2 10-1 100 101 102 103 104 linear Eot-Wash next-generation (1Dpp approx.) large quantum corrections self-coupling γ 0.01 0.1 1 10 100 1000 matter coupling β 10-3 10-2 10-1 100 101 102 103 104 linear Eot-Wash next-generation (1Dpp approx.) large quantum corrections 0.01 0.1 1 10 100 1000 matter coupling β 4 6 8 10 12 14 16 18 20 power law index n linear Eot-Wash next-generation (1Dpp approx.) large quantum corrections 0.01 0.1 1 10 100 1000 matter coupling β 4 6 8 10 12 14 16 18 20 power law index n linear Eot-Wash next-generation (1Dpp approx.) large quantum corrections 0.01 0.1 1 10 100 matter coupling β

30
25
20
15
10
5
1

power law index n linear Eot-Wash next-generation (1Dpp approx.) large quantum corrections 0.01 0.1 1 10 100 matter coupling β

30
25
20
15
10
5
1

power law index n linear Eot-Wash next-generation (1Dpp approx.) large quantum corrections

AU, PRD 86:102003(2012)[arXiv:1209.0211]

V (φ) = λ

4! φ4

V (φ) = γM5

Λ/φ

V (φ) = M4−n

Λ

φn V (φ) = M4−n

Λ

φn

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Estimated (1Dpp) E¨

t-Wash constraints on symmetrons

Amol Upadhye High-intensity searches for dark energy and modified gravity 12 10-8 10-6 10-4 10-2 100 102 0.1 1 10 torque [fN·m] disk separation ∆zS-T [mm] µ=10-2eV µ=3×10-3eV µ=10-3eV µ=3×10-4eV µ=10-4eV

101 102 103 104 matter coupling energy M [GeV] 10-10 10-8 10-6 10-4 10-2 100 102 self-coupling λ unscreened fifth forces excluded for µ = 10-3eV µ = 3×10-4eV µ = 3 × 1

3

e V µ = 10-2eV 101 102 103 104 matter coupling energy M [GeV] 10-10 10-8 10-6 10-4 10-2 100 102 self-coupling λ unscreened fifth forces excluded for µ = 10-3eV µ = 3×10-4eV µ = 3 × 1

3

e V µ = 10-2eV

Symmetron effective potential: Veff = 1

2

ρ

M2 − µ2

φ2 + λ

4!φ4

E¨

t-Wash probes λ ∼ 1, µ ∼ 10−3 eV (dark energy),

M ∼ 1 TeV (beyond the Standard Model)

AU, PRL 110:031301(2013)[arXiv:1210.7804]

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Neutrons in a gravitational field

− 2

2mN d2 dz2 + mNΨ + βmmN MPl φ

|N = E |N

Ψ(z) = gz is gravitational field φ(z) is chameleon field (nonlinear in z) energy levels E of bouncing neutrons quantized (∆E ∼ 1 peV)

P. Brax and G. Pignol, PRL

107:111301(2011)[arXiv:1105.3420]

n 1 2 3 4 5 6 7 8 β

10

10

8

10

6

10

4

10

2

10 1

2

10

4

10

6

10

8

10

12

10 n 1 2 3 4 5 6 7 8 β

10

10

8

10

6

10

4

10

2

10 1

2

10

4

10

6

10

8

10

12

10

EXCLUDED

Grenoble experiments GRANIT sensitivity

ultimate gravitational levels

EXCLUDED E P t e s t s f

r

c e l i m i t s

th

5 m µ shell thickness < 10

Amol Upadhye High-intensity searches for dark energy and modified gravity 13

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Neutron interferometry

Amol Upadhye High-intensity searches for dark energy and modified gravity 14

Constraints from neutron interferometry: split neutron beam into two sent one beam through vacuum chamber with scalar “bubble”,

ther beam through chamber containing phase-neutral gas

climbing out of scalar potential well slows down beam passing through vacuum chamber ⇒ phase shift

n 1 2 3 4 5 6 7 8 β 1 10

2

10

3

10

4

10

5

10

6

10

7

10

8

10

9

10

11

10

12

10 n 1 2 3 4 5 6 7 8 β 1 10

2

10

3

10

4

10

5

10

6

10

7

10

8

10

9

10

11

10

12

10 EXCLUDED

Q Bounce neutron interferometry

GRANIT sensitivity ultimate gravitational levels force limits

th

5

Brax,Pignol,Roulier(2013) [arXiv:1306.6536]

neutrons, µ=10-3eV neutrons, µ=10-4eV Eot-Wash, µ=10-3eV E

t
W

a s h , µ = 1

4

e V 1 10 100 1000 10000 matter coupling scale M [GeV] 1e-10 1e-08 1e-06 0.0001 0.01 1 self-coupling λ neutrons, µ=10-3eV neutrons, µ=10-4eV Eot-Wash, µ=10-3eV E

t
W

a s h , µ = 1

4

e V 1 10 100 1000 10000 matter coupling scale M [GeV] 1e-10 1e-08 1e-06 0.0001 0.01 1 self-coupling λ

W. M. Snow, AU, et al., NIST proposal

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Part III: Dark energy particles

Amol Upadhye High-intensity searches for dark energy and modified gravity 15

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How dark is dark energy? Searches for photon couplings

Oscillation: Photon coupling term

βγ 4MPl FµνF µνφ ⇒ dark energy

particles produced from photons in magnetic field Containment: Dark energy particles reflect from matter. Windows perform quantum measurements.

5 10 15 20 x [meff

1]

density ρ chameleon mass chameleon perturbation δφ photon Amol Upadhye High-intensity searches for dark energy and modified gravity 16

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Afterglow experiments

An afterglow experiment has two phases: (a) Production phase: photons streamed through B0 region; some

scillate into chameleons

(b) Afterglow phase: chameleons slowly oscillate back into photons, escaping chamber Systematics: • adiabatic evolution

emission from vacuum materials
diffuse reflection
scattering from atoms
effects of chamber geometry

Thorough review: AU, Steffen, Chou, PRD 86:035006(2012)[arXiv:1204.5476].

Amol Upadhye High-intensity searches for dark energy and modified gravity 17

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CHASE (CHameleon Afterglow SEarch)

Amol Upadhye High-intensity searches for dark energy and modified gravity 18

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Expected afterglow signal

Amol Upadhye High-intensity searches for dark energy and modified gravity 19

0.01 1 100 10000 1e+06 1e+08 1e+10 1e+12

1500 -1000
500

500 1000 1500 2000 2500 3000 afterglow rate [sec-1] time [sec] 0.45 T 1.0 T 2.2 T 5.0 T

bservation period

βγ=1e11

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Expected afterglow signal

Amol Upadhye High-intensity searches for dark energy and modified gravity 19

0.01 1 100 10000 1e+06 1e+08 1e+10 1e+12

1500 -1000
500

500 1000 1500 2000 2500 3000 afterglow rate [sec-1] time [sec] 0.2 T 0.45 T 1.0 T 2.2 T 5.0 T

bservation period

βγ=3e11

SLIDE 27

Expected afterglow signal

Amol Upadhye High-intensity searches for dark energy and modified gravity 19

0.01 1 100 10000 1e+06 1e+08 1e+10 1e+12

1500 -1000
500

500 1000 1500 2000 2500 3000 afterglow rate [sec-1] time [sec] 0.05 T 0.09 T 0.2 T 0.45 T 1.0 T 2.2 T 5.0 T

bservation period

βγ=1e12

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Expected afterglow signal

Amol Upadhye High-intensity searches for dark energy and modified gravity 19

0.01 1 100 10000 1e+06 1e+08 1e+10 1e+12

1500 -1000
500

500 1000 1500 2000 2500 3000 afterglow rate [sec-1] time [sec] 0.05 T 0.09 T 0.2 T 0.45 T 1.0 T 2.2 T 5.0 T

bservation period

βγ=3e12

SLIDE 29

Expected afterglow signal

Amol Upadhye High-intensity searches for dark energy and modified gravity 19

0.01 1 100 10000 1e+06 1e+08 1e+10 1e+12

1500 -1000
500

500 1000 1500 2000 2500 3000 afterglow rate [sec-1] time [sec] 0.05 T 0.09 T 0.2 T 0.45 T 1.0 T 2.2 T 5.0 T

bservation period

βγ=1e13

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Expected afterglow signal

Amol Upadhye High-intensity searches for dark energy and modified gravity 19

0.01 1 100 10000 1e+06 1e+08 1e+10 1e+12

1500 -1000
500

500 1000 1500 2000 2500 3000 afterglow rate [sec-1] time [sec] 0.05 T 0.09 T 0.2 T 0.45 T 1.0 T 2.2 T 5.0 T

bservation period

βγ=3e13

SLIDE 31

Expected afterglow signal

Amol Upadhye High-intensity searches for dark energy and modified gravity 19

0.01 1 100 10000 1e+06 1e+08 1e+10 1e+12

1500 -1000
500

500 1000 1500 2000 2500 3000 afterglow rate [sec-1] time [sec] 0.05 T 0.09 T 0.2 T 0.45 T 1.0 T 2.2 T 5.0 T

bservation period

βγ=1e14

SLIDE 32

Expected afterglow signal

Amol Upadhye High-intensity searches for dark energy and modified gravity 19

0.01 1 100 10000 1e+06 1e+08 1e+10 1e+12

1500 -1000
500

500 1000 1500 2000 2500 3000 afterglow rate [sec-1] time [sec] 0.05 T 0.09 T 0.2 T 0.45 T 1.0 T 2.2 T 5.0 T

bservation period

βγ=3e14

SLIDE 33

Expected afterglow signal

Amol Upadhye High-intensity searches for dark energy and modified gravity 19

0.01 1 100 10000 1e+06 1e+08 1e+10 1e+12

1500 -1000
500

500 1000 1500 2000 2500 3000 afterglow rate [sec-1] time [sec] 0.05 T 0.09 T 0.2 T 0.45 T 1.0 T 2.2 T 5.0 T

bservation period

βγ=1e15

SLIDE 34

Expected afterglow signal

Amol Upadhye High-intensity searches for dark energy and modified gravity 19

0.01 1 100 10000 1e+06 1e+08 1e+10 1e+12

1500 -1000
500

500 1000 1500 2000 2500 3000 afterglow rate [sec-1] time [sec] 0.05 T 0.09 T 0.2 T 0.45 T 1.0 T 2.2 T 5.0 T

bservation period

βγ=3e15

SLIDE 35

Expected afterglow signal

Amol Upadhye High-intensity searches for dark energy and modified gravity 19

0.01 1 100 10000 1e+06 1e+08 1e+10 1e+12

1500 -1000
500

500 1000 1500 2000 2500 3000 afterglow rate [sec-1] time [sec] 0.05 T 0.09 T 0.2 T 0.45 T 1.0 T 2.2 T 5.0 T

bservation period

βγ=1e16

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Chameleons in CHASE: a thorough study

Oscillation

1e-16 1e-14 1e-12 1e-10 1e-08 1e-06 0.0001 0.0001 0.001 0.01 0.1 rates [Hz] effective chameleon mass meff [eV] afterglow (MC) decay (MC)

Atom scattering

1e-20 1e-15 1e-10 1e-05 1 100000 1e+10 1e+15 1e+20 2e-16 4e-16 6e-16 8e-16 1e-15 1.2e-15 1.4e-15 r [m] φ [eV] meff [eV]

Matter lattice

0.01 0.1 1 10 100 1000 10000 100000 1 100000 1e+10 1e+15 1e+20 chameleon mass in lattice mlattice [eV] matter coupling βm n

2
1

4 6

Other potentials

1
0.5

0.5 1 1.5 1 10 100 phase shift ξV number of wavelengths from wall, x/λ ξV = π/3 chameleon energy 2×100 eV 2×10-2 eV 2×10-4 eV 2×10-6 eV

Adiabaticity

1e-22 1e-20 1e-18 1e-16 1e-14 1e-12 1e-10 1 2 3 4 5 6 7 8 9 |ψγ|2 distance from entrance [m] chameleon mass 5e-4 eV 1e-3 eV 2e-3 eV 5e-3 eV 1e-2 eV

Diffuse ref.

1 10 1e-05 0.0001 0.001 0.01 0.1 1 rate(fdiff) / rate(standard) diffuse fraction fdiff afterglow decay

Chamber geom.

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0.1 1 10 rate / rate(CHASE) length / length(CHASE) l1 L l2

Data analysis

Collider constraints GammeV constraints 1e-05 0.0001 0.001 0.01 0.1 effective mass meff [eV] 1e+10 1e+11 1e+12 1e+13 1e+14 1e+15 1e+16 1e+17 photon coupling βγ

SIMULATION

Collider constraints GammeV constraints 1e-05 0.0001 0.001 0.01 0.1 effective mass meff [eV] 1e+10 1e+11 1e+12 1e+13 1e+14 1e+15 1e+16 1e+17 photon coupling βγ

SIMULATION

AU, Steffen, Chou, PRD 86:035006(2012)[arXiv:1204.5476].

Amol Upadhye High-intensity searches for dark energy and modified gravity 20

SLIDE 37

Adiabatic transition suppresses oscillation

B(z) transition distance ≫ oscillation length 4πE/∆m2

⇒ adiabatic transition ⇒ no chameleon production internal measurement (window) mitigates this effect No internal measurement

1e-22 1e-20 1e-18 1e-16 1e-14 1e-12 1e-10 1 2 3 4 5 6 7 8 9 |ψγ|2 distance from entrance [m] chameleon mass 5e-4 eV 1e-3 eV 2e-3 eV 5e-3 eV 1e-2 eV

One measurement

1e-19 1e-18 1e-17 1e-16 1e-15 1e-14 1e-13 1e-12 1e-11 1e-10 1 2 3 4 5 6 7 8 9 |ψγ|2 distance from entrance [m] B entrance window meff [eV] 5e-4 1e-3 2e-3 5e-3 1e-2

AU, Steffen, Chou, PRD 86:035006(2012)[arXiv:1204.5476].

Amol Upadhye High-intensity searches for dark energy and modified gravity 21

SLIDE 38

“Orange glow:” a transient systematic photon flux

Amol Upadhye High-intensity searches for dark energy and modified gravity 22

0.0 0.5 1.0 1.5 2.0 2.5 1.4 1.6 1.8 2.0 2.2 2.4 Log time seconds Log Rate Hz

Steffen,AU,Baumbaugh,Chou,Tomlin, PRD 86:012003(2012)[arXiv:1205.6495]

SLIDE 39

CHASE constraints on V (φ) = M4

Λ(1 + MΛ/φ)

Amol Upadhye High-intensity searches for dark energy and modified gravity 23

matter coupling βm photon coupling βγ torsion pendulum qBounce GRANIT helioscope gγ = βγ / MPl [GeV-1] 1e-10 1e-9 1e-8 1e-7 1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 1 10000 1e+08 1e+12 1e+16 1e+08 1e+09 1e+10 1e+11 1e+12 1e+13 1e+14 1e+15 1e+16 1e+17 1e+18 neutrons (Grenoble) colliders (CLEO, precision EW) afterglow (GammeV-CHASE) matter coupling βm photon coupling βγ torsion pendulum qBounce GRANIT helioscope gγ = βγ / MPl [GeV-1] 1e-10 1e-9 1e-8 1e-7 1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 1 10000 1e+08 1e+12 1e+16 1e+08 1e+09 1e+10 1e+11 1e+12 1e+13 1e+14 1e+15 1e+16 1e+17 1e+18 neutrons (Grenoble) colliders (CLEO, precision EW) afterglow (GammeV-CHASE)

Theory: AU, Steffen, Chou, PRD 86:035006(2012)[arXiv:1204.5476],

AU, Steffen, Weltman, PRD 81:015013(2010)[arXiv:0911.3906]

Experiment: Steffen, AU, Baumbaugh, Chou, Mazur, Tomlin, Weltman,

Wester, PRL 105:261803(2010)[arXiv:1010.0988]

SLIDE 40

Chameleon fragmentation?

Amol Upadhye High-intensity searches for dark energy and modified gravity 24

100 102 104 106 108 1010 1012 1014 1016 1018 matter coupling βm 108 1010 1012 1014 1016 1018 1020 photon coupling βγ 10-40 10-30 10-20 10-10 100 1010 fragmentation rate [Hz]

P R E L I M I N A R Y

Chameleon particles can interact to produce a greater number of lower-energy chameleon particles.

P. Brax and AU (2013, in prep.)

SLIDE 41

Cavity afterglow experiments

http://www.phys.washington.edu/ groups/admx/cavity.html

|φ| [mm-1] 100 80 60 40 20

100
50

50 100 x [cm]

100
50

50 100 y [cm] 20 40 60 80 100 120 |φ| [mm-1]

Procedure:

1 source excites EM mode 2 turn off source; EM modes decay 3 EM modes regenerated from chameleon 4 adjust tuning rods for sensitivity to different mass range Amol Upadhye High-intensity searches for dark energy and modified gravity 25

SLIDE 42

ADMX constraints on photon-coupled chameleons

Amol Upadhye High-intensity searches for dark energy and modified gravity 26

G. Rybka, M. Hotz, L. Rosenberg, et al., PRL 105 051801 (2010)

SLIDE 43

Chameleons from the Sun

∼ keV photons oscillate into chameleons inside Sun chameleon particles reach Earth helioscope magnet regenerates photons for detection

Amol Upadhye High-intensity searches for dark energy and modified gravity 27

SLIDE 44

Helioscope forecasts

Amol Upadhye High-intensity searches for dark energy and modified gravity 28

log10(βγ) log10(β)

Solar chameleon spectrum peaked at 600 eV. Forecast constraints.

P. Brax, A. Lindner, K. Zioutas, PRD 85 043014 (2012)

Increase collecting area using an X-ray mirror.

O. K. Baker, A. Lindner,

AU, K. Zioutas (2012)

SLIDE 45

Conclusions

1 The physics responsible for the cosmic acceleration may differ

from a cosmological constant by evolving with time or by coupling to known particles. Couplings imply fifth forces.

2 Laboratory and cosmological experiments are complementary;

they probe models whose masses scale differently with density.

3 The E¨

t-Wash torsion pendulum experiment will be able to

exclude chameleon models with gravitation-strength couplings and small quantum corrections, as well as symmetron models with TeV-scale couplings. Neutron experiments can exclude chameleons and symmetrons with larger couplings.

4 The CHASE afterglow experiment has excluded a range of

light photon-coupled dark energy models. Upcoming afterglow and helioscope experiments promise to improve these constraints over the next few years.

Amol Upadhye High-intensity searches for dark energy and modified gravity 29

SLIDE 46

EXTRA SLIDES

Amol Upadhye High-intensity searches for dark energy and modified gravity 30

SLIDE 47

Symmetron mechanism

Amol Upadhye High-intensity searches for dark energy and modified gravity 31

effective potential: Veff(φ, ρ) = 1

2

ρ

M2 − µ2

φ2 + λ

4!φ4 1 2 3 4 5 6

4
3
2
1

1 2 3 4 Veff(φ) / MΛ

4

φ / MΛ VEV: φmin βeff: φminMPl/M2 VEV: 0 βeff: 0 bare potential low density high density

SLIDE 48

At which scale should we probe symmetrons?

Amol Upadhye High-intensity searches for dark energy and modified gravity 32

Fifth forces are predicted for ρm > µ2M2 > ρv at distances 1/µ.

M [GeV] µ [eV] 1 100000 1e+10 1e+15 1e+20 1e-40 1e-35 1e-30 1e-25 1e-20 1e-15 1e-10 1e-05 1 cosmology laboratory, solar system

SLIDE 49

Photons coupled to chameleon dark energy

The time-dependent equation of motion is φ = V ′

eff.

Equations of motion (Vφγ =

βγ 4MPl F µνFµνφ with βφ ≪ MPl):

∂µ

1 + βγφ

MPl

F µν

= 0 φ = V ′(φ) + βm

MPl ρmat + βγ 4MPl FµνF µν

Plane wave perturbations about background φ0 and B0 = B0ˆ x

(Raffelt and Stodolsky 1988; AU, Steffen, and Weltman 2010):

− ∂2

∂t2 −

k2 ψφ = m2

effψφ + βγkB0 MPl ˆ

x · ψγ

− ∂2

∂t2 −

k2

ψγ = ω2

P

ψγ + βγkB0

MPl ˆ

k × (ˆ x × ˆ k)ψφ φ → γ oscillation (low-mass, k ⊥ B0): Pγ↔φ ≈

β2

γB2 0L2

4M2

Pl Amol Upadhye High-intensity searches for dark energy and modified gravity 33