Gravitational Tests of Lorentz Symmetry

Quentin G. BaileyAlan Kostelecký

Indiana University

Signals for Lorentz Violation in Post-Newtonian Gravity, PRD 2006, gr-qc/0603030

Outline

• Background, motivation• Standard-Model Extension (SME)• Gravitational sector• Post-Newtonian limit• Experiments

– Overview– Gravity Probe B

• Summary

Background

Global Lorentz symmetry

Local Lorentz symmetry

Standard Model of particle physics

Quantum field theory

Local gauge symmetries, fermions, bosons, …

General Relativity

Classical geometrical theory

Diffeomorphism symmetry, EP, geodesics, …

• Lorentz symmetry– Symmetry underlying Special & General

Relativity – Rotations and Boosts

• Our best, current fundamental theories

• 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 violationaffects low-energy physics

• 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.)

Standard-Model Extension (SME)

Usual SM fieldsAll possible Lorentz-violating terms constructed from SM & GR fields and background coefficients

Colladay and Kostelecký PRD 97, 98; Kostelecký PRD 04

Usual GR lagrangian

• 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, …)

SME experiments (to date)

SME Theory • over 500 papers to date• topics include:• classical electrodynamics

• QED: stability, causality, renormalizability • gravitational couplings• connection to NCQFT, SUSY, …

Only ~1/3 of minimal QED sector explored Gravitational couplings unexplored

See next talk by Jay Tasson: Tests of Lorentz Symmetry with Gravitationally Coupled Fermions

• 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

Kostelecký PRD 04 Bluhm, Kostelecký PRD 05

SME in curved spacetime

Pure-gravity sector (minimal SME)• Basic lagrangian (Riemann spacetime limit):

Einstein-Hilbert term (GR)

Leading Lorentz-violating couplings

Contains ordinary matter, dynamics for coefficient fields

• Leads to modified Einstein equations:

Spontaneous Lorentz-symmetry breaking

Ordinary matter

Lorentz-violating corrections

s00

s01

vev fluctuations

• 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

• 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

Example: Bumblebee models

See talk by Igor Vlasov

Kostelecký, Samuel PRD’89Moffat IJMP'93Kostelecký, Lehnert PRD'01Jacobson, Mattingly PRD'01Kostelecký, PRD'04

Carroll,Lim PRD'04 Eling, Jacobson PRD'04Gripaios, JHEP'04Bluhm, Kostelecký PRD'05Altschul, Kostelecký PLB'05Bailey, Kostelecký PRD 06, and more …

• 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

Post-Newtonian limit

• Orbital dynamics lunar/satellite ranging binary pulsar perihelion shift of planets • Light propagation time-delay effect, light bending binary pulsar

Experimental Tests

• Local frames of reference free fall: gyroscope experiment accelerated/rotating:

gravimeter tests torsion-pendulum tests

Today

Details: Bailey, Kostelecký PRD 06

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

*Schiff 1960 †GPB collaboration: Everitt, Keiser, …

See symposium talk by Francis Everitt on Space, GPB and Will

• Spin precession for gyroscope in Earth orbit

Lorentz-violating precession

Mean orbital velocity

Value of g for orbit

Gravitomagnetic precession

Conventional geodetic precession

Polar GPB orbit

• Standard general relativity contributions

• Dominant SME contributions

• Assuming GPB angular resolutions of order 10-4’’ C-1 can obtain 10-4 on coeffs

Along orbital angular momentum axis σ

Along Earth’s spin axis Z

Along perpendicular axis n

Coefficients referred to standard SME Sun-centered frame

• 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, …)

Summary