Cosmic acceleration Evolution with time Coupling to known particles Amol Upadhye High-intensity searches for dark energy and modified gravity 2
Outline 1 Introduction Motivation: DE scale M Λ = 2 . 4 × 10 − 3 eV Dark energy: a phenomenological tool box Example: Chameleon screening 2 Fifth forces Quantum-stable chameleons E¨ ot-Wash constraints and forecasts Neutron experiments 3 New particles vacuum magnetic field region Hamamatsu pump (B = 5 Tesla) H7422P−40 PMT Production through photon coupling lens GammeV-CHASE afterglow experiment (BK7 glass) 532nm entrance Upcoming experiments window exit window Nd:YAG laser (BK7 glass) (BK7 glass) Amol Upadhye High-intensity searches for dark energy and modified gravity 3
Coupled dark energy from modified gravity A phenomenological toolbox: Modified gravity Effective scalar New physics 4-D modified action: Conformal trans.: matter coupling, R → f ( R ) ⇒ chameleon effective m ( ρ ) Amol Upadhye High-intensity searches for dark energy and modified gravity 4
Coupled dark energy from modified gravity A phenomenological toolbox: Modified gravity Effective scalar New physics 4-D modified action: Conformal trans.: matter coupling, R → f ( R ) ⇒ chameleon effective m ( ρ ) 4-D modified action: Conformal trans.: matter coupling, φ → − φ symmetry ⇒ symmetron uncoupled phase Amol Upadhye High-intensity searches for dark energy and modified gravity 4
Coupled dark energy from modified gravity A phenomenological toolbox: Modified gravity Effective scalar New physics 4-D modified action: Conformal trans.: matter coupling, R → f ( R ) ⇒ chameleon effective m ( ρ ) 4-D modified action: Conformal trans.: matter coupling, φ → − φ symmetry ⇒ symmetron uncoupled phase DGP, etc.: Decoupling limit matter coupling, non-compact extra (weak gravity) non-canonical dimension ⇒ Galileon kinetic term Amol Upadhye High-intensity searches for dark energy and modified gravity 4
Coupled dark energy from modified gravity A phenomenological toolbox: Modified gravity Effective scalar New physics 4-D modified action: Conformal trans.: matter coupling, R → f ( R ) ⇒ chameleon effective m ( ρ ) 4-D modified action: Conformal trans.: matter coupling, φ → − φ symmetry ⇒ symmetron uncoupled phase DGP, etc.: Decoupling limit matter coupling, non-compact extra (weak gravity) non-canonical dimension ⇒ Galileon kinetic term Kaluza-Klein, etc.: Small extra dim. matter coupling, compact extra dim. ⇒ radion 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
Chameleon mechanism effective potential: V eff ( φ, ρ ) = V ( φ ) + βρφ/ M Pl V( φ ) Amol Upadhye High-intensity searches for dark energy and modified gravity 5
Chameleon mechanism effective potential: V eff ( φ, ρ ) = V ( φ ) + βρφ/ M Pl V( φ ) V int = β mat ρ mat φ / M Pl Amol Upadhye High-intensity searches for dark energy and modified gravity 5
Chameleon mechanism effective potential: V eff ( φ, ρ ) = V ( φ ) + βρφ/ M Pl V( φ ) V eff ( φ,ρ low ) φ min ( ρ low ) 2 = V’’ is small) (m eff Amol Upadhye High-intensity searches for dark energy and modified gravity 5
Chameleon mechanism effective potential: V eff ( φ, ρ ) = V ( φ ) + βρφ/ M Pl V( φ ) V eff ( φ,ρ low ) V eff ( φ,ρ high ) φ min ( ρ high ) 2 is large) (m eff φ min ( ρ low ) 2 = V’’ is small) (m eff Amol Upadhye High-intensity searches for dark energy and modified gravity 5
At which scale should we probe each model? n − 2 V ( φ ) ∝ φ n + const . ⇒ m eff ∝ ρ 2 n − 2 (use lab for n � − 1 2 , n > 2) 1 1e-10 m eff ∝ ρ (n-2)/(2n-2) [eV] 1e-20 laboratory V( φ ) ∝ φ n 1e-30 cosmology n=-1 n=1/2 1e-40 n=2/3 n=4 1e-50 1e-30 1e-20 1e-10 1 density ρ [g/cm 3 ] AU, PRD 86 :102003(2012)[arXiv:1209.0211] Amol Upadhye High-intensity searches for dark energy and modified gravity 6
Part II: Fifth forces Amol Upadhye High-intensity searches for dark energy and modified gravity 7
Laboratory benchmark: “quantum-stable” chameleons ∆ V 1 − loop ( φ ) = m eff ( φ ) 4 � m eff ( φ ) 2 � log < V tree 64 π 2 µ 2 � 1 / 6 � 1 / 6 � 48 π 2 β 2 ρ 2 � βρ ⇒ m eff ≤ = 0 . 0073 eV M 2 10 g/cm 3 Pl 0.1 0.1 large quantum corrections large quantum corrections mass m φ ( ρ lab ) [eV] mass m φ ( ρ lab ) [eV] 0.01 0.01 Eot-Wash φ 4 Eot-Wash φ 4 0.001 0.001 excluded by Eot-Wash excluded by Eot-Wash 0.0001 0.0001 0.01 0.01 0.1 0.1 1 1 10 10 100 100 1000 1000 matter coupling β matter coupling β AU, Hu, Khoury, PRL 109 :041301(2012)[arXiv:1204.3906] Amol Upadhye High-intensity searches for dark energy and modified gravity 8
Fifth-force tests using a torsion pendulum E¨ ot-Wash Experiment http://www.npl.washington.edu/eotwash Amol Upadhye High-intensity searches for dark energy and modified gravity 9
E¨ ot-Wash constraints on chameleons 10 3 10 3 large quantum corrections large quantum corrections 10 2 10 2 10 1 10 1 self-coupling λ self-coupling λ 10 0 10 0 10 -1 10 -1 10 -2 10 -2 1Dpp approx. 1Dpp approx. 10 -3 10 -3 Eot-Wash Eot-Wash 10 -4 10 -4 linear linear 10 -5 10 -5 V ( φ ) = λ V ( φ ) = λ 4! φ 4 4! φ 4 10 -6 10 -6 0.001 0.001 0.01 0.01 0.1 0.1 1 1 10 10 100 100 1000 1000 matter coupling β matter coupling β E¨ ot-Wash: Adelberger, Heckel, Hoedl, Hoyle, Kapner, AU. PRL 98 131104 (2007) 1Dpp: AU, PRD 86 102003 (2012) [arXiv:1209.0211] Amol Upadhye High-intensity searches for dark energy and modified gravity 10
Next-generation E¨ ot-Wash: chameleon forecasts 10 4 10 4 10 4 10 4 large quantum corrections large quantum corrections 10 3 10 3 10 3 10 3 10 2 10 2 10 2 10 2 linear linear Eot-Wash Eot-Wash self-coupling γ self-coupling γ self-coupling λ self-coupling λ next-generation next-generation 10 1 10 1 Eot-Wash current Eot-Wash current 10 1 10 1 (1Dpp approx.) (1Dpp approx.) large quantum corrections large quantum corrections 10 0 10 0 Eot-Wash Eot-Wash 10 0 10 0 next-generation next-generation linear linear 10 -1 10 -1 (1Dpp approx.) (1Dpp approx.) 10 -1 10 -1 10 -2 10 -2 10 -2 10 -2 10 -3 10 -3 V ( φ ) = λ V ( φ ) = λ 4! φ 4 4! φ 4 V ( φ ) = γ M 5 V ( φ ) = γ M 5 Λ /φ Λ /φ 10 -4 10 -4 10 -3 10 -3 0.01 0.01 0.1 0.1 1 1 10 10 100 100 1000 1000 0.01 0.01 0.1 0.1 1 1 10 10 100 100 1000 1000 10000 10000 matter coupling β matter coupling β matter coupling β matter coupling β 20 20 -1 -1 Eot-Wash Eot-Wash 18 18 -5 -5 next-generation next-generation (1Dpp approx.) (1Dpp approx.) 16 16 linear linear linear linear power law index n power law index n power law index n power law index n large large -10 -10 14 14 quantum quantum corrections corrections 12 12 -15 -15 10 10 -20 -20 large large 8 8 V ( φ ) = M 4 − n V ( φ ) = M 4 − n φ n φ n quantum quantum Λ Λ corrections corrections 6 6 -25 -25 V ( φ ) = M 4 − n V ( φ ) = M 4 − n φ n φ n Eot-Wash Eot-Wash Λ Λ 4 4 next-generation (1Dpp approx.) next-generation (1Dpp approx.) -30 -30 0.01 0.01 0.1 0.1 1 1 10 10 100 100 1000 1000 0.01 0.01 0.1 0.1 1 1 10 10 100 100 matter coupling β matter coupling β matter coupling β matter coupling β AU, PRD 86 :102003(2012)[arXiv:1209.0211] Amol Upadhye High-intensity searches for dark energy and modified gravity 11
Estimated (1Dpp) E¨ ot-Wash constraints on symmetrons 10 2 10 2 10 2 µ =10 -2 eV µ =3 × 10 -3 eV 10 0 10 0 µ =10 -3 eV 10 0 µ = 10 -2 eV µ = 10 -2 eV µ =3 × 10 -4 eV V V e e µ =10 -4 eV 10 -2 10 -2 3 3 self-coupling λ self-coupling λ - - 0 0 torque [fN·m] 1 1 10 -2 × × 3 3 10 -4 10 -4 µ = 3 × 10 -4 eV µ = 3 × 10 -4 eV = = µ µ 10 -4 10 -6 10 -6 unscreened unscreened fifth forces fifth forces 10 -6 10 -8 10 -8 excluded for excluded for µ = 10 -3 eV µ = 10 -3 eV 10 -10 10 -10 10 -8 10 1 10 1 10 2 10 2 10 3 10 3 10 4 10 4 0.1 1 10 disk separation ∆ z S-T [mm] matter coupling energy M [GeV] matter coupling energy M [GeV] � ρ φ 2 + λ Symmetron effective potential: V eff = 1 M 2 − µ 2 � 4! φ 4 2 ot-Wash probes λ ∼ 1, µ ∼ 10 − 3 eV (dark energy), E¨ M ∼ 1 TeV (beyond the Standard Model) AU, PRL 110 :031301(2013)[arXiv:1210.7804] Amol Upadhye High-intensity searches for dark energy and modified gravity 12
Neutrons in a gravitational field � � − � 2 d 2 dz 2 + m N Ψ + β m m N M Pl φ | N � = E | N � β β 12 12 10 10 EXCLUDED 2 m N 10 10 10 10 Grenoble experiments 10 10 8 8 GRANIT sensitivity Ψ( z ) = gz is gravitational field 6 6 10 10 4 4 10 10 ultimate gravitational levels φ ( z ) is chameleon field (nonlinear in z ) 10 10 2 2 5 th f o r c e l i 1 1 m i t s energy levels E of bouncing neutrons -2 -2 shell thickness < 10 10 10 quantized (∆ E ∼ 1 peV) -4 -4 10 10 µ m -6 -6 10 10 P. Brax and G. Pignol, PRL EXCLUDED -8 -8 E P 10 10 t e s t s -10 -10 10 10 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 107 :111301(2011)[arXiv:1105.3420] n n Amol Upadhye High-intensity searches for dark energy and modified gravity 13
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