Planck-scale modifications to electrodynamics characterized by a spacelike symmetry-breaking vector

Abstract

In the study of Planck-scale ("quantum-gravity-induced") violations of Lorentz symmetry, an important role was played by the deformed-electrodynamics model introduced by Myers and Pospelov. Its reliance on conventional effective quantum field theory, and its description of symmetry-violation effects simply in terms of a four-vector with a nonzero component only in the time direction, rendered it an ideal target for experimentalists and a natural concept-testing ground for many theorists. At this point however the experimental limits on the single Myers-Pospelov parameter, after improving steadily over these past few years, are "super-Planckian"; i.e. they take the model out of actual interest from a conventional quantum-gravity perspective. In light of this we here argue that it may be appropriate to move on to the next level of complexity, still with vectorial symmetry violation but adopting a generic four-vector. We also offer a preliminary characterization of the phenomenology of this more general framework, sufficient to expose a rather significant increase in complexity with respect to the original Myers-Pospelov setup. Most of these novel features are linked to the presence of spatial anisotropy, which is particularly pronounced when the symmetry-breaking vector is spacelike, and they are such that they reduce the bound-setting power of certain types of observations in astrophysics

Using CMB data to constrain non-isotropic Planck-scale modifications to Electrodynamics

“…In [18] it is described the behavior of photons in presence of non-isotropic violations of Lorentz invariance, resulting from the generalization of the Myers-Pospelov model, with nonzero spatial components of the four-vector. The Lagrangian density of the model is:…”

“…But a transverse linearly polarized field cannot be written as a linear combination of these two eigenstates, meaning that it does not belong to the solutions of the modified Maxwell equations following from the non-isotropic generalization of the Myers-Pospelov model. To overcome this difficulty, taking into account the fact that what we actually observe within the sensitivities presently available ‡ We use the notation of Jones three-dimensional vectors [18]: the polarization state of the field…”

“…The relevant equations for the dispersion relation and the eigenstates of the field propagation resulting from the above Lagrangian are [18] :…”

“…This model was also tested in several astrophysical contexts, leading to very stringent constraints [14,15,8,16,17]. In [18] it was observed that these bounds exploit significantly the spatial isotropy regained by the ad hoc choice of having a purely timelike symmetry-violating four-vector, and actually this choice is only available for a restricted class of frames of reference, since the four-vector will of course still acquire a spatial component in other boosted frames. This assumption can be limiting in two ways.…”

“…Constraints on one single component of a four vector derived in different reference frames (like the rest frame of two different astrophysical sources) cannot be compared without any information on the other components of the four-vector. Moreover in [18] it was shown that the limits placed assuming the four-vector to be purely timelike do not give reliable information on the most general case in which the four-vector has all the components different from zero, so that also space isotropy is violated.…”