Constraints on Lorentz Invariance Violation from Optical Polarimetry of Astrophysical Objects

Abstract

Theories of quantum gravity suggest that Lorentz invariance, the fundamental symmetry of the Theory of Relativity, may be broken at the Planck energy scale. While any deviation from conventional Physics must be minuscule in particular at attainable energies, this hypothesis motivates ever more sensitive tests of Lorentz symmetry. In the photon sector, astrophysical observations, in particular polarization measurements, are a very powerful tool because tiny deviations from Lorentz invariance will accumulate as photons propagate over cosmological distances. The Standard-Model Extension (SME) provides a theoretical framework in the form of an effective field theory that describes low-energy effects due to a more fundamental quantum gravity theory by adding additional terms to the Standard Model Lagrangian. These terms can be ordered by the mass dimension d of the corresponding operator and lead to a wavelength, polarization, and direction dependent phase velocity of light. Lorentz invariance violation leads to an energy-dependent change of the Stokes vector as photons propagate, which manifests itself as a rotation of the polarization angle in measurements of linear polarization. In this paper, we analyze optical polarization measurements from 63 Active Galactic Nuclei (AGN) and Gamma-ray Bursts (GRBs) to search for Lorentz violating signals. We use both spectropolarimetric measurements, which directly constrain the change of linear polarization angle, as well as broadband spectrally integrated measurements. In the latter, Lorentz invariance violation manifests itself by reducing the observed net polarization fraction. Any observation of non-vanishing linear polarization thus leads to constraints on the magnitude of Lorentz violating effects. We derive the first set limits on each of the 10 individual birefringent coefficients of the minimal SME with d = 4 , with 95% confidence limits on the order of 10−34 on the dimensionless coefficients.

In Vacuo Dispersion-Like Spectral Lags in Gamma-Ray Bursts

“…[12] on dimension-four operators added to the Standard-Model lagrangian, whereas the effects we here consider would be described in field-theory in terms of dimension-five operators. However, describing photons within the SME the effects of dispersion would be combined with birefringence [13][14][15][16][17], which we here assume to be absent consistently with results obtained in frameworks alternative to the SME, such as those studied in Refs. [1,3,7] and references therein).…”

Searches for Lorentz-Violating Signals with Astrophysical Polarization Measurements

“…In two recent papers, 3,4 we have combined more than 60 optical polarization measurements, both spectropolarimetric and broadband integrated measurements, to constrain individually all birefringent coefficients of mass dimensions d = 4 and d = 5. Constraints on the dimensionless coefficients k (4) (E)jm and k (4) (B)jm are <3 × 10 −34 , and the k (5) (V )jm are constrained to <7 × 10 −26 GeV −1 .…”

“…(V )jm , and c (6) (I)jm have been constrained using astrophysical polarization 3,4 and time-of-flight measurements, 5 and the k…”

Standard-Model Extension Constraints on Lorentz and CPT Violation from Optical Polarimetry of Active Galactic Nuclei

“…2,4,6,9 However, since ground-based optical polarimetry and spectropolarimetry have smaller statistical and systematic errors than the more expensive and difficult x-ray/γ-ray polarimetry measurements, optical studies of AGN-the brightest, continuous, highly polarized, extragalactic optical sources-represent the most cost-effective approach to improve constraints on anisotropic SME coefficients today. 1,2,10 One can test CPT-odd birefringent SME coefficients with broadband polarimetry as follows. [1][2][3] The k (d) (V )jm SME coefficients predict a rotation of the linear polarization plane.…”

“…Measuring a polarization fraction p ⋆ ± nσ p⋆ < p . A spherical-harmonic decomposition on the sky can then be used to combine sufficient numbers of line-of-sight constraints to bound all N (d) parameters at a given d. 2,10 These can also include lineof-sight constraints from spectropolarimetry, which can be about two or three orders of magnitude more sensitive than broadband polarimetry for d = 5. 2 Tests of CPT-even d = 4 SME coefficients are discussed in Ref.…”