Lab Tests of Dark Robert Caldwell Dartmouth College Accelerates the

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

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 -Quintessence = F F Lint −4M µν φ = E" B" ! M ·

“dark” interaction: quintessence does not see EM Dark Energy Coupling to

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