Axion gravitodynamics, Lense-Thirring effect, and gravitational waves

We investigate physical implications of a gravitational analog of axion electrodynamics with a parity-violating gravitoelectromagnetic theta term. This is related to the Nieh-Yan topological invariant in gravity with torsion, in contrast to the well-studied gravitational Chern-Simons term quadratic in curvature, coupled via a dynamical axionlike scalar field. Axion gravitodynamics is the corresponding linearized theory. We find that potentially observable effects are over 80 orders of magnitude stronger than for its Chern-Simons counterpart and could be in reach for detection by experiments in the near future. For a near-Earth scenario, we derive corrections to the Lense-Thirring effect and compare them to data from satellite-based experiments (Gravity Probe B). For gravitational waves, we find modified dispersion relations, derive the corresponding polarization-dependent modified group and phase velocities, and compare them to data from neutron star mergers (GW170817) to derive even stronger bounds.

Figure 1

The ratio $\alpha$ in (20) for the Gravity Probe B mission. The $x$ axis is logarithmic in the variable $|\ell \dot{\theta }|$. The gray region enclosed by the dashed lines $\alpha =\pm 0.19$ represents the 19% accuracy with which the Gravity Probe B final results confirm general relativity.