The Standard-Model Extension (SME) is an action-based expansion describing
general Lorentz violation for known matter and fields, including gravity. In
this talk, I will discuss the Lorentz-violating gravity couplings in the SME.
Toy models that match the SME expansion, including vector and two-tensor
models, are reviewed. Finally I discuss the status of experiments and
observations probing gravity coefficients for Lorentz violation.Comment: 5 pages, Presented at the Fifth Meeting on CPT and Lorentz Symmetry,
  Bloomington, Indiana, June 28-July 2, 201

Bailey, Quentin G.

English

arXiv

QUENTIN G. BAILEY

Crossref

GRAVITY COUPLINGS IN THE STANDARD-MODEL EXTENSION

The Standard-Model Extension (SME) is an action-based expansion describing general Lorentz violation for known matter and fields, including gravity. In this talk, I will discuss the Lorentz-violating gravity couplings in the SME. Toy models that match the SME expansion, including vector and two-tensor models, are reviewed. Finally I discuss the status of experiments and observations probing gravity coefficients for Lorentz violation

Embry-Riddle Aeronautical University

Publications 12-2010 Gravity Couplings in the Standard-Model Extension Quentin G. Bailey Embry-Riddle Aeronautical University, baileyq@erau.edu Follow this and additional works at: https://commons.erau.edu/publication  Part of the Cosmology, Relativity, and Gravity Commons Scholarly Commons Citation Bailey, Q. G. (2010). Gravity Couplings in the Standard-Model Extension. , (). https://doi.org/10.1142/9789814327688_0030 This Conference Proceeding is brought to you for free and open access by Scholarly Commons. It has been accepted for inclusion in Publications by an authorized administrator of Scholarly Commons. For more information, please contact commons@erau.edu. August 3, 2010 0:8 WSPC - Proceedings Trim Size: 9in x 6in bailey1GRAVITY COUPLINGS IN THESTANDARD-MODEL EXTENSIONQUENTIN G. BAILEYPhysics Department, Embry-Riddle Aeronautical University3700 Willow Creek Road, Prescott, AZ 86301, USAEmail: baileyq@erau.eduThe Standard-Model Extension (SME) is an action-based expansion describ-ing general Lorentz violation for known matter and fields, including gravity. Inthis talk, I will discuss the Lorentz-violating gravity couplings in the SME. Toymodels that match the SME expansion, including vector and two-tensor mod-els, are reviewed. Finally I discuss the status of experiments and observationsprobing gravity coefficients for Lorentz violation.1. IntroductionGeneral Relativity (GR) and the Standard Model of particle physics providea comprehensive and successful description of nature. Nonetheless, it isexpected that an underlying unified description containing both theories aslimiting cases exists, presumably at the Planck scale. So far, such a completeunified theory remains largely unknown. Moreover, direct measurements atthe Planck scale are infeasible at present so experimental clues about thisunderlying theory are sparse.One promising approach is to study suppressed effects that may comefrom the underlying theory. An intriguing class of signals that are poten-tially detectable in modern sensitive experiments are minuscule violationsof local Lorentz symmetry.1 A comprehensive effective field theory frame-work exists called the Standard-Model Extension (SME)2,3 that describesthe observable signals of Lorentz violation. In this framework, the degree ofLorentz violation for each type of matter or field is controlled by its coeffi-cients for Lorentz violation, which vanish when Lorentz symmetry holds.So far, theoretical and experimental work on the SME has mostly in-volved the Minkowski-spacetime limit.4 Lorentz violation in the gravita-tional sector remains comparatively unexplored. In this talk, we focus onAugust 3, 2010 0:8 WSPC - Proceedings Trim Size: 9in x 6in bailey2two basic types of Lorentz violation involving gravity: pure-gravity cou-plings and matter-gravity couplings. For a more detailed discussion of thesetopics, the reader is referred to Refs. 5–7.2. TheoryThe SME with both gravitational and nongravitational couplings was pre-sented in the context of a Riemann-Cartan spacetime in Ref. 3. In thematter sector of the SME, Dirac spinor fields can be used for describingthe matter-gravity couplings that are expected to dominate in many exper-imental scenarios. In this limit the Lagrange density takes the formLm =12ieeµaψ(γa−cνλeλaeνbγb+...)↔Dµψ−eψ(m+aµeµaγa+...)ψ+..., (1)where the ellipses represent additional coefficients in the SME omitted herefor simplicity. The standard vierbein (e aµ ) formalism is used to incorporatethe spinor fields ψ and the gamma matrices γa into the tangent space ateach point in the spacetime. Both the spacetime connection and the U(1)connection are included in the covariant derivative. The quantities cµν andaµ are species-dependent coefficients for Lorentz violation.In the Riemann-spacetime limit, the Lagrange density for the pure-gravity sector of the SME takes the formLg =12κe[(1− u)R+ sµνRTµν + tκλµνCκλµν ] + L′. (2)The 20 coefficients for Lorentz violation u, sµν , and tκλµν control the leadingLorentz-violating gravitational couplings in this expression. The curvaturetensors appearing are the Ricci scalar R, the trace-free Ricci tensor RTµνand the Weyl conformal tensor Cκλµν . By convention κ = 8piG, where Gis Newton’s gravitational constant. The additional term L′ contains thematter sector and possible dynamical terms governing the 20 coefficients.General coordinate invariance is maintained by the SME action while localLorentz transformations and diffeomorphisms of the matter and gravita-tional fields are not respected by the SME action when L′ = 0.Some geometric constraints arise when Lorentz violation is introduced inthe context of Riemann-Cartan geometry. When the coefficients for Lorentzviolation in the matter and gravity sectors are nondynamical or prescribedfunctions this generally conflicts with the Bianchi identities. However, whenthe coefficients arise through a dynamical process, conflicts with the geom-etry are avoided.3 This includes spontaneous Lorentz-symmetry breakingscenarios. The coefficients for Lorentz violation are treated as arising fromspontaneous Lorentz-symmetry breaking in the approach of Refs. 5–7.August 3, 2010 0:8 WSPC - Proceedings Trim Size: 9in x 6in bailey3It is generally a challenging task to study the gravitational effects inEqs. (1) and (2) in a generic, model-independent way. It turns out thatsome simplifications to the analysis arise in the linearized gravity regimeand it is then possible to extract effective linearized Einstein equations andmodified equations of motion for matter, under certain assumptions on thedynamics of the coefficients for Lorentz violation. These equations thenonly involve the vacuum expectation values of the coefficients for Lorentzviolation which are denoted as aµ, cµν , and sµν . Due to species dependence,aµ and cµν contain 12 and 27 independent coefficients for ordinary matter,respectively. In the pure-gravity sector, only the 9 species-independent sµνcoefficients appear in the linearized gravity limit.In the post-newtonian limit, the metric for the SME can be constructedfrom the effective Einstein equations. An interesting feature arises thatterms in the metric acquire a novel species dependence from the aµ and cµνcoefficients. One can also attempt to match to the standard ParametrizedPost-Newtonian (PPN) formalism.8 This involves constraining sµν to anisotropic form in a special coordinate system with only one independentcoefficient s00. Therefore there is a partially overlapping relationship be-tween the two approaches, and the SME offers new types of signals forgravitational tests.53. Toy modelsSeveral models of spontaneous Lorentz-symmetry breaking exist that havea connection to the general formalism described above. The simplest typesof models involve a dynamical vector field Bµ that acquires a vacuum expec-tation value bµ via a potential term in the lagrangian, which are genericallycalled bumblebee models. Bumblebee models can produce effective sµν , cµν ,and aµ terms.5,7 Another interesting class of models involves an antisym-metric two-tensor field Bµν .9 The modes appearing in a minimal version ofthese models can include a scalar as well as nondynamical massive modes,in addition to producing a background vacuum expectation value bµν . Fur-thermore, flat spacetime theories with a self interacting Bµν field may onlybe stable and renormalizable when the potential admits a nontrivial min-ima bµν , thus spontaneously breaking Lorentz symmetry. When nonminimalcouplings to gravity are included, these models can also produce effectivesµν coefficients. Furthermore, it can be shown that these effective sµν coef-ficients cannot be reduced to an isotropic form, and so lie outside of PPNanalysis.August 3, 2010 0:8 WSPC - Proceedings Trim Size: 9in x 6in bailey44. Matter-gravity testsThe dominant effects from the coefficients aµ and cµν are modified equationsof motion for bodies interacting gravitationally. Due to the particle speciesdependence of these coefficients, the motion of a macroscopic body in agravitational field will depend on its internal composition. This constitutesa violation of the weak equivalence principle (WEP), so the coefficientscontrol WEP violation as well.7 Existing and proposed tests that can probethese coefficients include ground-based gravimeter, atom interferometry,and WEP experiments. Also of interest are lunar and satellite laser rangingobservations as well as measurements of the perihelion precession of theplanets.Among the most sensitive tests are proposed satellite missions designedto test WEP in a microgravity environment. The observable of interestfor these tests is the relative acceleration of two test bodies of differentcomposition. When the relative acceleration is calculated in the satellitereference frame in the presence of SME coefficients aµ and cµν , some in-teresting time-dependent effects arise. The standard reference frame forreporting coefficient measurements in the SME is the Sun-centered celes-tial equatorial reference frame or SCF for short.10 Upon relating the satel-lite frame coefficients to the SCF, oscillations in the relative accelerationoccur at a number of different frequencies including multiples and combi-nations of the satellite’s orbital and rotational frequencies, as well as theEarth’s orbital frequency. This time dependence allows for the extractionof Lorentz-violating amplitudes independently of the standard tidal effects.Future space-based WEP tests offer sensitivities ranging from 10−7 GeV to10−16 GeV for aµ and 10−9 to 10−16 for cµν . Of particular interest are theSTEP,11 MicroSCOPE,12 and Galileo Galilei13 experiments.5. Pure-gravity sector testsThe primary effects due to the nine coefficients sµν in the pure-gravitysector of the SME can be obtained from the post-newtonian metric andthe standard geodesic equation for test bodies.5 Tests potentially probingthese coefficients include Earth-laboratory tests with gravimeters, torsionpendula, and short-range gravity experiments. Space-based tests includelunar and satellite laser ranging, studies of the secular precession of or-bital elements in the solar system and with binary pulsars, and orbitinggyroscope experiments.Some analysis placing constraints on the sµν coefficients has alreadyAugust 3, 2010 0:8 WSPC - Proceedings Trim Size: 9in x 6in bailey5been reported. Using lunar laser ranging data spanning over three decades,Battat, Chandler, and Stubbs placed constraints on 6 combinations of thesµν coefficients at levels of 10−7 to 10−10.14 The modified local accelerationon the Earth’s surface was measured by Mu¨ller et al. using an atom inter-ferometric gravimeter, resulting in 7 constraints on the sµν coefficients atthe level of 10−6 to 10−9.15Recently, the modifications of the classic GR time-delay effect due to thesµν coefficients were studied.16 By studying light propagation with the post-newtonian metric modified by the sµν coefficients, the correction to the lighttravel time for a signal passing near a mass M has been obtained. Time-delay tests could be particularly useful for constraining the isotropic sTTcoefficient, and future tests could yield competitive sensitivities to the sJKcoefficients. Measurements of sµν coefficients could be obtained by usingdata from time-delay tests such as Cassini and BepiColombo.17 Also understudy are modifications from sµν coefficients to the classic light-bendingformula in GR.18References1. R. Bluhm, Lect. Notes Phys. 702, 191 (2006).2. D. Colladay and V.A. Kostelecky´, Phys. Rev. D 55, 6760 (1997); Phys. Rev.D 58, 116002 (1998).3. V.A. Kostelecky´, Phys. Rev. D 69, 105009 (2004).4. Data Tables for Lorentz and CPT Violation, V.A. Kostelecky´ and N. Russell,2010 edition, arXiv:0801.0287v3.5. Q.G. Bailey and V.A. Kostelecky´, Phys. Rev. D 74, 045001 (2006).6. V.A. Kostelecky´ and J.D. Tasson, Phys. Rev. Lett. 102, 010402 (2009).7. V.A. Kostelecky´ and J.D. Tasson, arXiv:1006.4106v1.8. C.M. Will, Living Rev. Relativity 9, 3 (2006).9. B. Altschul et al., Phys. Rev. D 81, 065028 (2010).10. V.A. Kostelecky´ and M. Mewes, Phys. Rev. D 66, 056005 (2002).11. T.J. Sumner et al., Adv. Space Res. 39, 254 (2007); P. Worden, these pro-ceedings.12. P. Touboul et al., Comptes Rendus de l’Acade´mie des Sciences, Series IV, 4,1271 (2001).13. A.M. Nobili et al., Exp. Astron. 23, 689 (2009).14. J.B.R. Battat et al., Phys. Rev. Lett. 99, 241103 (2007).15. H. Mu¨ller et al., Phys. Rev. Lett. 100, 031101 (2008); K.-Y. Chung et al.,Phys. Rev. D 80, 016002 (2009).16. Q.G. Bailey, Phys. Rev. D 80, 044004 (2009).17. B. Bertotti, L. Iess, and P. Tortura, Nature 425, 374 (2003); L. Iess and S.Asmar, Int. J. Mod. Phys. D 16, 2191 (2007).18. R. Tso, these proceedings.

Gravity Couplings in the Standard-Model Extension

https://commons.erau.edu/cgi/viewcontent.cgi?article=1702&amp;context=publication

Gravity Couplings in the Standard-Model Extension

Abstract

Similar works

Full text

Available Versions

Crossref

Embry-Riddle Aeronautical University