New Constraints on Lorentz Invariance Violation from Combined Linear and
  Circular Optical Polarimetry of Extragalactic Sources
  Expanding on our prior efforts to search for Lorentz invariance violation
(LIV) using the linear optical polarimetry of extragalactic objects, we propose
a new method that combines linear and circular polarization measurements. While
existing work has focused on the tendency of LIV to reduce the linear
polarization degree, this new method additionally takes into account the
coupling between photon helicities induced by some models. This coupling can
generate circular polarization as light propagates, even if there is no
circular polarization at the source. Combining significant detections of linear
polarization of light from extragalactic objects with the absence of the
detection of circular polarization in most measurements results in
significantly tighter constraints regarding LIV. The analysis was carried out
in the framework of the Standard-Model Extension (SME), an effective field
theory framework to describe the low-energy effects of an underlying
fundamental quantum gravity theory. We evaluate the performance of our method
by deriving constraints on the mass dimension $d=4$ CPT-even SME coefficients
from a small set of archival circular and linear optical polarimetry
constraints and compare them to similar constraints derived in previous works
with far larger sample sizes and based on linear polarimetry only. The new
method yielded constraints that are an order of magnitude tighter even for our
modest sample size of 21 objects. Based on the demonstrated gain in
constraining power from scarce circular data, we advocate for the need for
future extragalactic circular polarization surveys.
