CMB tests of Lorentz invariance

Transcription

1 CMB tests of Lorentz invariance Matthew Mewes Marquette University Kostelecký & Mewes, in preparation Outline: motivation Standard-Model Extension (SME) Lorentz violation in photons non-minimal SME CMB and LV results and conclusions

2 Why break Lorentz symmetry? possible signal of Planck-scale physics (Kostelecký & Samuel 89, Kostelecký & Potting 9, 96) accessible to current technology E. & M., Newton s Laws Atoms, Molecules,... Cosmology, Astrophysics,... Newtonian Gravity Standard Model General Relativity Quantum Mechanics Lorentz Symmetry Curved Spacetime Theory of Everything

3 Why break Lorentz symmetry? possible signal of Planck-scale physics (Kostelecký & Samuel 89, Kostelecký & Potting 9, 96) accessible to current technology Theory of Everything Quantum Mechanics Lorentz Symmetry Curved Spacetime Standard Model General Relativity Newton s Laws E. & M., Atoms, Molecules,... Cosmology, Astrophysics,... Newtonian Gravity Standard Model General Relativity Newton s Laws E. & M., Atoms, Molecules,... Cosmology, Astrophysics,... Newtonian Gravity

4 Why framework: break Standard-Model Lorentz symmetry? Extension (SME) possible describes signalgeneral of Planck-scale Lorentz violation physics accessible to current technology (Kostelecký Colladay & Samuel & Kostelecký 89, Kostelecký 97, 98, & Potting Kostelecký 9, 96) 4 see also Colladay & Altschul, this meeting Newton s Laws Newton s Laws E. & M., E. & M., Atoms, Atoms, Molecules,... Molecules,... Standard Model Standard Model Cosmology, Cosmology, Astrophysics,... Astrophysics,... Newtonian Gravity Newtonian Gravity General Relativity General Relativity Quantum Mechanics Lorentz Symmetry Curved Spacetime Theory of Everything

5 SME construction: L LV = (coefficient) (standard tensor operator) example: QED extension L = 2 i ψγ µ D µ ψ m ψψ 4 F µν F µν + c µν 2 i ψγ µ D ν ψ + d µν 2 i ψγ 5 γ µ D ν ψ + advantages/features: quantum field theory, spin statistics, locality, microcausality, conservation principles, observer independence, systematic, very general disadvantages: systematic, very general (infinite # of violations)

6 minimal SME preserve: - power-counting renormalizability (finite # of violations) break: - usual gauge invariance charge conservation - usual invariance under spacetime translations energy-momentum conservation - Lorentz invariance minimal photon sector L = 4 F µν F µν 4 (k F ) αβµν F αβ F µν (conventional) (CPT-even) + 2 (k AF ) α ɛ αβµν A β F µν (CPT-odd)

7 SME experimentation neutrino oscillations K,D,B oscillations Katori et al. 6, LSND 5 BaBar 6, FOCUS 3, KTeV, BELLE, OPAL 97 clock-comparison tests Wolf et al. 6, Cané et al. 4 Humphrey et al. 4, Bear et al. muons Deile et al. 2, Hughes et al. Penning traps Dehmelt et al. 99, Mittleman et al. 99, Gabrielse et al. 99 spin-polarized pendulum Heckel et al. 6, Hou et al. EM-resonators Stanwix et al. 6, Antonini et al. 5, Tobar et al. 5, Herrmann et al. 5 vacuum birefringence Feng et al. 6, Kosteleck ý & Mewes 6, 2,, Nodland & Ralston 97, Carroll et al. 9

8 types of signals velocity dependences boost violations orientation dependences rotation violations example: EM-resonators used to test CPT-even violations look for changes in resonant frequency with orientation/velocity Müller et al. oscillations neutral-meson oscillations neutrino oscillations photon birefringence

9 example: neutrino oscillations Kostelecký & Mewes 4 h eff = E mass term (seesaw) ( 2 m2 3 2 ( m2 ) 6 ) E Lorentz-violating term ( Λνν Λ ν ν Λ νν 3 6 Λ ν ν ) 3 6 basis: ν e ν µ ν τ ν e ν µ C A ν τ

10 birefringence breakdown of usual degeneracy in polarization causes rotation of polarization as light propagates RH circular polarization ellipse linear s = Stokes vector s s 2 s 3 = Q U V LH circular

11 birefringence rotation of Stokes vector by δφ δv L CPT-odd case CPT-even case rotation axis ς bigger L bigger effect higher E bigger effect (for CPT-even violations)

12 CPT-even case

13 birefringence tests CPT-odd Carroll, Field, & Jackiw 9 Feng et al. 6 galaxies (radio) (k AF ) < 42 GeV CMB (k AF ) 6 43 GeV CPT-even Kostelecký & Mewes 2, Kostelecký & Mewes 6 galaxies (near-optical) components of k F < 32 GRB s 4 components of k F < 37

14 going beyond the minimal SME drop renormalizability keep gauge invariance keep translation invariance Why? leading-order (renormalizable?) remnants 7 known physics SM + GR = TOE higher-order nonrenormalizable remnants

15 construction (photon sector) ) write general action contribution with dimension d operator δs (d) = d 4 x K α α 2 α 3...α d (d) 2) decompose into irreducible representations A α α3... αd A α2 K α α 2 α 3...α d (d) 3) eliminate gauge-violating terms K α α 2 α 3...α d (d) { CPT-even CPT-odd

16 nonrenormalizable E&M L = 4 F µνf µν + 2 ɛκλµν A λ (ˆk AF ) κ F µν 4 F κλ(ˆk F ) κλµν F µν (ˆk AF ) κ = d=odd (ˆk F ) κλµν = d=even (k (d) AF ) κα...α (d 3) α... α(d 3) (k (d) F )κλµνα...α (d 4) α... α(d 4) for birefringence tests make tensor-spherical-harmonic decomposition (k (d) AF ) α...α (d 3) κ k (d) (V )lm (k (d) F )κλµνα...α (d 4) k (d) (E)lm, k(d) (B)lm

17 Stokes rotation axis ς = depends on direction depends on photon energy ς ς 2 ς 3 C A CPT-odd rotations about poles ς 3 = P dlm Ed 4 Y lm k (d) (V )lm CPT-even rotations about line through equator ς iς 2 = P dlm Ed 4 ±2Y lm (k (d) (E)lm ± ik(d) (B)lm )

18 CMB radiation temperature T = P lm a (T )lm Y lm polarization NASA/WMAP s is 2 = P lm (a (E)lm ± ia (B)lm ) ±2 Y lm s 3 = P lm a (V )lm Y lm correlations NASA/WMAP C X X 2 l = 2l+ P m a (X )l m a (X2 )l 2 m 2

19 conventional picture small E modes much smaller B component no V (circular) component correlation between T and E only effects of LV Lorentz violation causes a change in polarization as light propagates. mixes E, B, and V modes. potential signals B modes V modes (CPT-even case only) correlations TB, TV, EB,...

20 example: k (3) (V ) = 2 42 GeV C l XX l(l + )/2π (µk 2 ) EE BB V V T E T B T V EB EV BV l angular size

21 example: k (4) (E)2 = 2 29 C l XX l(l + )/2π (µk 2 ) EE BB V V T E T B T V EB EV BV l angular size

22 search look for birefringence in BOOMERANG data Why BOOMERANG? high frequencies higher sensitivity narrow frequency band angular size T E of cmb from Boomerang 3 Thomas E. Montroy et al., astro-ph/5754 Fig.. The T E power spectrum band powers for the NA (filled circles) and IT (open circles) pipelines. The upper part of the plot reports data with errorbars, the fiducial model (ΛCDM model fit to WMAP (year ), Acbar, and CBI) as a black curve and the binned fiducial model as histogram. The middle and bottom plots are the results of two different consistency tests, obtained splitting the data in channels (WX-YZ) and in time (half 2 - half ) respectively. In the low-l part of the plot is evident the effect of a different weighting scheme between IT and NA, while at large multipoles the result is dominated by the same instrumental performances. (hereafter deep region), a shallow observation on a region of covering the.8% of the sky (including the deep region) centered in the same coordinates (hereafter shal- F. Piacentini et al., astro-ph/5757 Fig. 2. The T B power spectrum band powers for the NA (filled circles) and IT (open circles) pipelines. The upper part of the plot reports the T B data with error-bars. The middle and bottom plots are the results of two different consistency tests, obtained splitting the data in channels (WX-YZ) and in time (half 2 - half ) respectively.

23 likelihood (for a sample of 2 L.V. parameters) k (3) (V ) ( 43 GeV) k (3) (V ) ( 43 GeV) k (3) (V ) ( 43 GeV) relative likelihood k (4) (E)2 ( 3 ) k (4) (B)2 ( 3 ) k (5) (V ) ( 2 GeV ) k (5) (V ) ( 2 GeV ) k (5) (V )2 ( 2 GeV ) k (5) (V )3 ( 2 GeV ) k (6) (E)2 ( GeV 2 ) k (6) (E)3 ( GeV 2 ) k (6) (E)4 ( GeV 2 ) consistent with zero L.V. at 2σ (light blue) consistent with nonzero L.V. at σ (dark blue) agrees with Feng et al. result (includes WMAP): k (3) (V ) 6 43 GeV

24 results lots of possible nonrenormalizable violations σ signal in the CMB best bounds on some coefficients for LV first bounds on many coefficients for LV things to do determine robustness of signal incorporate CAPMAP, CBI, DASI, WMAP incorporate foregrounds, lensing, reionization things to look forward to Planck experiment