Lab Tests of Dark Energy Robert Caldwell Dartmouth College Dark Energy Accelerates the Universe

Lab Tests of Dark Energy Robert Caldwell Dartmouth College Dark Energy Accelerates the Universe Collaboration with Mike Romalis (Princeton), Deanne Dorak & Leo Motta (Dartmouth) “Possible laboratory search for a quintessence field,” MR+RC, arxiv:1302.1579 Dark Energy vs. The Higgs Higgs: Let there be mass m(φ)=gφ a/a¨ > 0 Quintessence: Accelerate It! Dynamical Field Clustering of Galaxies in SDSS-III / BOSS: Cosmological Implications, Sanchez et al 2012 Dynamical Field Planck 2013 Cosmological Parameters XVI Dark Energy Cosmic Scalar Field 1 = (∂φ)2 V (φ)+ + L −2 − Lsm Lint V (φ)=µ4(1 + cos(φ/f)) Cosmic PNGBs, Frieman, Hill and Watkins, PRD 46, 1226 (1992) “Quintessence and the rest of the world,” Carroll, PRL 81, 3067 (1998) Dark Energy Couplings to the Standard Model 1 = (∂φ)2 V (φ)+ + L −2 − Lsm Lint φ µν Photon-Quintessence = F F Lint −4M µν φ = E" B" ! M · “dark” interaction: quintessence does not see EM radiation Dark Energy Coupling to Electromagnetism Varying φ creates an anomalous charge density or current 1 ! E! ρ/# = ! φ B! ∇ · − 0 −Mc∇ · ∂E! 1 ! B! µ " µ J! = (φ˙B! + ! φ E! ) ∇× − 0 0 ∂t − 0 Mc3 ∇ × Magnetized bodies create an anomalous electric field Charged bodies create an anomalous magnetic field EM waves see novel permittivity / permeability Dark Energy Coupling to Electromagnetism Cosmic Solution: φ˙/Mc2 H ∼ φ/Mc2 Hv/c2 ∇ ∼ 42 !H 10− GeV ∼ • source terms are very weak • must be clever to see effect Dark Energy Coupling to Electromagnetism Cosmic Birefringence: 2 ˙ ∂ 2 φ wave equation µ ! B# B# = # B# 0 0 ∂t2 −∇ Mc∇× ˙ 2 2 2 φ dispersion ω /c k = k − L,R ±Mc L,R 1 ∆φ birefringence ∆θ = φ˙ dt = 2Mc2 2Mc2 ! Dark Energy Coupling to Electromagnetism Cosmic Birefringence: CMB polarization rotates propto evolution of quintessence ∆θ = ∆φ/2Mc2 Absence of CMB B-modes as upper bound on rotation of E-modes 1.41◦ < ∆θ < 0.91◦ (95%CL) − Komatsu et al (WMAP7), ApJS 192, 18 (2011) Dark Energy Coupling to Electromagnetism Anisotropic Cosmic Birefringence: Rotation varies across sky due to quintessence fluctuations ∆θ(ˆn)=∆φ(ˆn)/2Mc2 Model of fluctuations, correlation with T, forecasts RC, Gluscevic, Kamionkowski, PRD 84, 043504 (2011) First CMB constraints on direction-dependent birefringence Gluscevic et al, PRD 86, 103529 (2012) Also: Yadav et al, PRD 79 123009 (2009), PRD 86 083002 (2012) Dark Energy Coupling to Electromagnetism In a weak gravitational field: φ = V ! φ φ + δφ ! → 0 d2 2 d + δφ = V !!δφ +2UV ! dr2 r dr 0 0 ! " !g = ! U −∇ 2 local gradient ! δφ = 2(V !/V !!)!g/c ∇ 0 0 2 !γ =2V !/V !!Mc Dark Energy Coupling to Electromagnetism 2 2 Local solution: δφ/Mc # g/c ∇ ∼ γ 2 32 !!γ g/c 10− GeV ∼ 2 !γ =2V !/V !!Mc Dark Energy Coupling to Electromagnetism # ! E! ρ/# = γ !g B! ∇ · − 0 − c · ∂E! " ! B! µ " µ J! = γ !g E! ∇× − 0 0 ∂t − 0 c2 × Lab Tests neutron as magnetized sphere charge due to the local field 2" δq = γ #g µ# 3c3 · 32 10− e ! 21 qN = 0.4( 1.1) 10− e 2 − ± × B! = µ M! Baumann et al, PRD 37, 3107 (1988) 3 0 Spinning superconducting shell? Precession of a drag-free gyro: Ω is too small Lab Tests proton as charged, magnetized sphere spin-flip in the local field µ q# r2 δB" = 0 γ 5"g + (("g rˆ)ˆr 2"g) 20πRc R2 · − ! " 2µ q# !τ = 0 γ µ! !g 5πRc × qr ! 4µ0q!γ 34 E = 3 rˆ ∆ = µg 10− !γ GeV 4π#0R E 5πRc ! 2 B! = µ M! 3 0 Flambaum et al, PRD 80, 105021 (2009) Within grasp of experiments? Brown et al, PRL 105, 151604 (2010) anomalous couplings of neutron? Lab Tests Brown et al, PRL 105, 151604 (2010) ∆ = µβ! !σ E − · 33 < 3.7 10− GeV (68%CL) × Seek out Mike Romalis’ group! Lab Tests macroscopic electric field magnetic field due to the local field 19 V "γ δB = (1.8 10− T) × 100 kV 5 ! " # $ 17 1/2 projected sensitivity 10− T/Hz Within grasp of experiments? Observe at 1σ after 1 hour integration Romalis & RC 2013 Lab Tests macroscopic magnetized cylinder voltage due to the local field B D 2 ! ∆V = (0.4 nV) γ 1T 20 cm 5 ! "! " # $ projected sensitivity 4nV/Hz1/2 Observe at 4σ after 1 hour integration Romalis & RC 2013 Lab Tests of Dark Energy Robert Caldwell Dartmouth College .

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