Constraining parity violation in gravity with measurements of neutron-star moments of inertia

Neutron stars are sensitive laboratories for testing general relativity, especially when considering deviations where velocities are relativistic and gravitational fields are strong. One such deviation is described by dynamical, Chern-Simons modified gravity, where the Einstein-Hilbert action is modified through the addition of the gravitational parity-violating Pontryagin density coupled to a field. This four-dimensional effective theory arises naturally both in perturbative and nonperturbative string theory, loop quantum gravity, and generic effective field theory expansions. We calculate here Chern-Simons modifications to the properties and gravitational fields of slowly spinning neutron stars. We find that the Chern-Simons correction affects only the gravitomagnetic sector of the metric to leading order, thus introducing modifications to the moment-of-inertia but not to the mass-radius relation. We show that an observational determination of the moment-of-inertia to an accuracy of 10%, as is expected from near-future observations of the double pulsar, will place a constraint on the Chern-Simons coupling constant of ${\xi }^{1/4}\lesssim 5\mathrm{km}$, which is at least three-orders of magnitude stronger than the previous strongest bound.

Figure 1

The mass-radius relation for neutron stars calculated using the FPS EOS. Notice that for the FPS EOS, neutron stars are smaller than $2M_{\odot }$ and have radii $\sim 10\mathrm{km}$.

Figure 2

The CS sourcing function $m_{(0,0)}-4\pi r^3\rho /3$ as a function of radius in km. Close to the core, the function vanishes, while it reaches its maximum near the surface. The three curves correspond to stars with different central densities and hence with different masses.

Figure 3

The moment-of-inertia of neutron stars described by the FPS EOS, as a function of their masses.

Figure 4

The absolute value of the dipolar component of the scalar-field $\overline{\vartheta }$ as a function of radius, for three stars with different masses and radii.

Figure 5

The absolute value of the CS correction to the metric coefficient ${\overline{\omega }}_1$ as a function of radius inside and outside a neutron star, for stars with three different masses and radii.

Figure 6

The ratio between the CS correction to the moment-of-inertia and the GR value as a function of the CS coupling parameter ${\xi }^{1/4}$ in units of kilometers. The thick horizontal line corresponds to a measurement of the moment-of-inertia with an accuracy of 10%.