1. Gravitational Tests of Lorentz Symmetry
Quentin G. Bailey
Alan Kostelecký
Indiana University
Signals for Lorentz Violation in Post-Newtonian Gravity, PRD 2006, gr-qc/

2. Outline Background, motivation Standard-Model Extension (SME)
Gravitational sector
Post-Newtonian limit
Experiments
Overview
Gravity Probe B
Summary

3. Background Lorentz symmetry
Symmetry underlying Special & General Relativity
Rotations and Boosts
Our best, current fundamental theories
Standard Model of particle physics
Quantum field theory
Local gauge symmetries, fermions, bosons, …
Global Lorentz symmetry
General Relativity
Classical geometrical theory
Diffeomorphism symmetry, EP, geodesics, …
Local Lorentz symmetry

4. Why study Lorentz violation?
Lorentz symmetry is fundamental Must be tested in as many ways as possible
Possible connection to a unified theory
Experiments searching for Lorentz violation offer alternative way to discover new physics
Fundamental theory (Mpl = 1019 GeV) (strings, noncommutative geometry, loop quantum gravity, spacetime foam, …)
Lorentz-symmetry breaking
(spontaneous?)
Miniscule Lorentz violation
affects low-energy physics

5. Standard-Model Extension (SME)
General theoretical framework
for studying Lorentz violation
Based on effective field theory, action principle assumed
Basic construction:
Special subset: minimal SME (gauge inv., renormalizable in flat spacetime, etc.)
Usual SM fields
All possible Lorentz-violating terms constructed from SM & GR fields and background coefficients
Usual GR lagrangian
Colladay and Kostelecký PRD 97, 98; Kostelecký PRD 04

6. SME experiments (to date)
cosmological birefringence
pulsar timing
synchrotron radiation
meson oscillations (BABAR, BELLE, DELPHI, FOCUS, KTeV, OPAL, …)
neutrino oscillations (LSND, Minos, Super K,… )
muon tests (Hughes, BNL g-2)
spin-polarized torsion pendulum tests (Adelberger, Hou, …)
tests with resonant cavities (Lipa, Mueller, Peters, Schiller, Wolf, …)
clock-comparison tests (Hunter, Walsworth, Wolf, …)
Penning-trap tests (Dehmelt, Gabrielse, …)
Only ~1/3 of minimal QED sector explored Gravitational couplings unexplored
SME Theory
over 500 papers to date
topics include:
classical electrodynamics
QED: stability, causality, renormalizability
gravitational couplings
connection to NCQFT, SUSY, …
See next talk by Jay Tasson: Tests of Lorentz Symmetry with Gravitationally Coupled Fermions

7. SME in curved spacetime
Key results:
1) Local Lorentz violation  diffeomorphism violation
2) Explicit Lorentz breaking
-in general incompatible with Riemann geometry
(one exception – Minkowski spacetime)
3) Spontaneous Lorentz-symmetry breaking
-compatible with Riemann geometry
Pure-gravity sector (minimal SME)
Leads to modified Einstein equations:
Basic lagrangian (Riemann spacetime limit):
Einstein-Hilbert term (GR)
Leading Lorentz-violating couplings
Contains ordinary matter, dynamics for coefficient fields
Kostelecký PRD 04 Bluhm, Kostelecký PRD 05

8. Spontaneous Lorentz-symmetry breaking
Coefficient fields
acquire vacuum expectation values
(analogous to the Higgs mech.) V(s00,s01,…)
Fields are expanded
about vacuum values
e.g.,
Linearized limit
Decouple the fluctuations
, ~
Arrive at effective linearized field equations
vev
fluctuations
s00
s01
Ordinary matter
Lorentz-violating corrections

9. Example: Bumblebee models
These are vector field theories with potentials V inducing spontaneous Lorentz breaking
Typical form of lagrangian:
Have been studied by many:
Linearization (in ghost-free theories)
matches our SME formalism V B
Kostelecký, Samuel PRD’89
Moffat IJMP'93
Kostelecký, Lehnert PRD'01
Jacobson, Mattingly PRD'01
Kostelecký, PRD'04
Carroll,Lim PRD'04
Eling, Jacobson PRD'04
Gripaios, JHEP'04
Bluhm, Kostelecký PRD'05
Altschul, Kostelecký PLB'05
Bailey, Kostelecký PRD 06, and more …
See talk by Igor Vlasov

10. Post-Newtonian limit
Parametrized Post-Newtonian (PPN) formalism (Will, Nordtvedt APJ 70’s)
General post-newtonian metric expansion
Isotropic parameters in the Universe Rest Frame
SME – general action-based expansion
Partial match of PPN with SME possible
SME isotropic limit
18 coefficients outside PPN

11. Experimental Tests Orbital dynamics lunar/satellite ranging
binary pulsar
perihelion shift of planets
Light propagation
time-delay effect, light bending
Local frames of reference
free fall: gyroscope experiment
accelerated/rotating: gravimeter tests
torsion-pendulum tests
Today
Details: Bailey, Kostelecký PRD 06

12. Gravity Probe B (GPB) GR predicts the precession of the spin
of a test body in free-fall (or acc.)
in curved spacetime*
Idea of GPB†: measure the precession
of a gyroscope spin in orbit due to:
1) presence of the Earth (geodetic precession)
precession about orbital ang. mom. axis
2) Earth’s spin (dragging of inertial frames)
precession about Earth’s spin axis
New SME prediction:
-Spin precession due to Lorentz violation
-Occurs (also) about an axis perpendicular to 1 & 2
See symposium talk by Francis Everitt on Space, GPB and Will
*Schiff 1960
†GPB collaboration: Everitt, Keiser, …

13. Spin precession for gyroscope in Earth orbit
Mean orbital velocity
Value of g for orbit
Gravitomagnetic precession
Polar GPB orbit
Lorentz-violating precession
Conventional geodetic precession

14. Standard general relativity contributions
Dominant SME contributions
Assuming GPB angular resolutions of order 10-4’’ C-1 can obtain 10-4 on coeffs
Coefficients referred to standard SME Sun-centered frame
Along orbital angular momentum axis σ
Along Earth’s spin axis Z
Along perpendicular axis n

15. Summary Gravitational sector of the minimal SME
Action-based description of Lorentz violation in gravity
Lorentz violation described by 19 coefficients
Linearized effective equations derived assuming spontaneous Lorentz-symmetry breaking
Experimental tests
Gravity probe B
Can make the first measurements of coeffs
Other tests possible with
Lunar laser ranging, binary pulsars, gravimeters, torsion-pendulum tests, classic tests (time-delay, light bending, …)