Gravity Theories with Background Fields and Spacetime Symmetry Breaking

An overview is given of effective gravitational field theories with fixed background fields that break spacetime symmetry. The behavior of the background fields and the types of excitations that can occur depend on whether the symmetry breaking is explicit or spontaneous. For example, when the breaking is spontaneous, the background field is dynamical and massless Nambu–Goldstone and massive Higgs excitations can appear. However, if the breaking is explicit, the background is nondynamical, and in this case additional metric or vierbein excitations occur due to the loss of local symmetry, or these excitations can be replaced by dynamical scalar fields using a Stuckelberg approach. The interpretation of Noether identities that must hold in each case differs, depending on the type of symmetry breaking, and this affects the nature of the consistency conditions that must hold. The Noether identities also shed light on why the Stuckelberg approach works, and how it is able to restore the broken spacetime symmetry in a theory with explicit breaking.

[1]  M. Seifert.  Vector models of gravitational Lorentz symmetry breaking , 2009, 0903.2279.

[2]  C. Hernaski.  Spontaneous breaking of Lorentz symmetry with an antisymmetric tensor , 2016, 1608.00829.

[3]  Jean-Philippe Uzan,et al.  Varying Constants, Gravitation and Cosmology , 2010, Living reviews in relativity.

[4]  Noether identities in gravity theories with nondynamical backgrounds and explicit spacetime symmetry breaking , 2016, 1610.02892.

[5]  R. Bluhm.  Overview of the SME: Implications and phenomenology of Lorentz violation , 2005, hep-ph/0506054.

[6]  A. Kostelecký,et al.  Lorentz Violation with an Antisymmetric Tensor , 2009, 0912.4852.

[7]  C. Hernaski.  Quantization and stability of bumblebee electrodynamics , 2014, 1411.5321.

[8]  Jun Luo,et al.  Search for Lorentz violation in short-range gravity , 2014, 1412.8362.

[9]  Fundamental Constants in Physics and Their Time Variation , 2015, 1507.02229.

[10]  C. Le Poncin-Lafitte,et al.  Lorentz Symmetry Violations from Matter-Gravity Couplings with Lunar Laser Ranging. , 2017, Physical review letters.

[11]  Violations of fundamental symmetries in atoms and tests of unification theories of elementary particles , 2003, physics/0309054.

[12]  C. Lane.  Spacetime variation of Lorentz-violation coefficients at a nonrelativistic scale , 2016, 1607.05211.

[13]  M. Seifert.  Generalized bumblebee models and Lorentz-violating electrodynamics , 2009, 0909.3118.

[14]  Chern-Simons modification of general relativity , 2003, gr-qc/0308071.

[15]  D. Roote,et al.  Status Report , 2006, Journal of periodontology.

[16]  N. Yunes,et al.  Strong binary pulsar constraints on Lorentz violation in gravity. , 2013, Physical review letters.

[17]  A. Kostelecký,et al.  Testing local Lorentz invariance with gravitational waves , 2016, 1602.04782.

[18]  Kurt Hinterbichler.  Theoretical Aspects of Massive Gravity , 2011, 1105.3735.

[19]  Samuel,et al.  Phenomenological gravitational constraints on strings and higher-dimensional theories. , 1989, Physical review letters.

[20]  A. Kostelecký,et al.  Data Tables for Lorentz and CPT Violation , 2008, 0801.0287.

[21]  A. Kostelecký,et al.  Signals for Lorentz violation in post-Newtonian gravity , 2006, gr-qc/0603030.

[22]  J. Tasson,et al.  Matter-gravity couplings and Lorentz violation , 2010, 1006.4106.

[23]  J. Tasson,et al.  Prospects for large relativity violations in matter-gravity couplings. , 2008, Physical review letters.

[24]  A. Kostelecký,et al.  $CPT$ violation and the standard model , 1997, hep-ph/9703464.

[25]  A. Trautman.  Conservation laws in general relativity , 1962 .

[26]  R. Lehnert,et al.  Stability, causality, and Lorentz and CPT violation , 2000, hep-th/0012060.

[27]  A. Kostelecký,et al.  Short-Range Gravity and Lorentz Violation , 2014, 1410.6162.

[28]  L. Iorio.  Orbital effects of Lorentz-violating standard model extension gravitomagnetism around a static body: a sensitivity analysis , 2012, 1203.1859.

[29]  R. Bluhm.  Spacetime Symmetry Breaking and Einstein-Maxwell Theory , 2015, 1508.03888.

[30]  H. Belich,et al.  Lorentz violation and higher derivative gravity , 2014, 1409.5742.

[31]  Y. Nambu.  Quantum Electrodynamics in Nonlinear Gauge , 1968 .

[32]  R. Jackiw.  Lorentz Violation in a Diffeomorphism-Invariant Theory , 2007, 0709.2348.

[33]  H. Georgi,et al.  Effective field theory for massive gravitons and gravity in theory space , 2002, hep-th/0210184.

[34]  Claudia de Rham,et al.  Massive Gravity , 2014, Living reviews in relativity.

[35]  Lijing Shao.  New pulsar limit on local Lorentz invariance violation of gravity in the standard-model extension , 2014, 1412.2320.

[36]  George F. Smoot,et al.  General Relativity and Cosmology: Unsolved Questions and Future Directions , 2016, 1609.09781.

[37]  C. Le Poncin-Lafitte,et al.  Testing Lorentz Symmetry with Lunar Laser Ranging. , 2016, Physical review letters.

[38]  Christophe Le Poncin-Lafitte,et al.  Tests of Lorentz Symmetry in the Gravitational Sector , 2016, 1610.04682.

[39]  A. Kostelecký,et al.  Spontaneous Lorentz and diffeomorphism violation, massive modes, and gravity , 2007, 0712.4119.

[40]  A. Kostelecký.  Gravity, Lorentz violation, and the standard model , 2003, hep-th/0312310.

[41]  T. Jacobson.  Einstein-aether gravity: a status report , 2008, 0801.1547.

[42]  A. Kostelecký,et al.  Testing local Lorentz invariance with short-range gravity , 2016, 1611.10313.

[43]  Clifford M. Will,et al.  The Confrontation between General Relativity and Experiment , 2001, Living reviews in relativity.

[44]  Steven Chu,et al.  Atom-interferometry tests of the isotropy of post-Newtonian gravity. , 2007, Physical review letters.

[45]  Lorentz Breaking Effective Field Theory Models for Matter and Gravity: Theory and Observational Constraints , 2012, 1208.1071.

[46]  J. Tasson,et al.  What do we know about Lorentz invariance? , 2014, Reports on progress in physics. Physical Society.

[47]  Samuel,et al.  Gravitational phenomenology in higher-dimensional theories and strings. , 1989, Physical review. D, Particles and fields.

[48]  Samuel,et al.  Spontaneous breaking of Lorentz symmetry in string theory. , 1989, Physical review. D, Particles and fields.

[49]  L. Iorio.  Editorial for the Special Issue 100 Years of Chronogeometrodynamics: The Status of the Einstein's Theory of Gravitation in Its Centennial Year , 2015, 1504.05789.

[50]  A. Kostelecký,et al.  Gravity from spontaneous Lorentz violation , 2009, 0901.0662.

[51]  Einstein-aether waves , 2004, gr-qc/0402005.

[52]  S. Chiow,et al.  Atom interferometry tests of local Lorentz invariance in gravity and electrodynamics , 2009, 0905.1929.

[53]  J. Bjorken.  A Dynamical origin for the electromagnetic field , 1963 .

[54]  R. Bluhm,et al.  Constraints and stability in vector theories with spontaneous Lorentz violation , 2008, 0802.4071.

[55]  David Mattingly,et al.  Modern Tests of Lorentz Invariance , 2005, Living reviews in relativity.

[56]  J. Tasson,et al.  Constraints on Lorentz violation from gravitational Čerenkov radiation , 2015, 1508.07007.

[57]  C. Stubbs,et al.  Testing for Lorentz violation: constraints on standard-model-extension parameters via lunar laser ranging. , 2007, Physical review letters.

[58]  R. Bluhm.  Observational Constraints on Local Lorentz Invariance , 2013, 1302.1150.

[59]  Adrian C. Melissinos,et al.  Searching for photon-sector Lorentz violation using gravitational-wave detectors , 2016, 1608.02592.

[60]  L. Shao,et al.  Tests of local Lorentz invariance violation of gravity in the standard model extension with pulsars. , 2014, Physical review letters.

[61]  Alan Kostelecky,et al.  Lorentz-Violating Extension of the Standard Model , 1998 .