# Constraining Parity Violation in Gravity with Measurements of Neutron-Star Moments of Inertia

## TL;DR

This paper investigates how measurements of neutron star moments of inertia can constrain Chern-Simons modified gravity, providing significantly tighter bounds on the theory's coupling constant than previous methods.

## Contribution

It calculates the effects of Chern-Simons gravity on neutron star properties and demonstrates how upcoming observations can impose strong new constraints on the theory.

## Key findings

- Chern-Simons modifications affect the gravitomagnetic sector of neutron stars.
- Future measurements of neutron star moments of inertia can constrain the coupling constant to below 5 km.
- The new bounds are three orders of magnitude stronger than previous limits.

## Abstract

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 non-perturbative 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} < 5 km, which is at least three-orders of magnitude stronger than the previous strongest bound.