# Towards Constraining Parity-Violations in Gravity with Satellite Gradiometry

## TL;DR

This paper proposes using satellite gravity gradiometry to test for gravitational parity-violation effects predicted by dynamical Chern-Simons gravity, potentially tightening existing constraints significantly.

## Contribution

It introduces a theoretical framework for detecting parity-violation signals via satellite gravity measurements, enhancing constraints on Chern-Simons gravity parameters.

## Key findings

- Secular gravity gradient signals can improve constraints on Chern-Simons length scale.
- Satellite measurements could tighten bounds on parity-violation effects by two orders of magnitude.
- Method is feasible with future satellite gravity missions.

## Abstract

Parity violation in gravity, if existed, could have important implications, and it is meaningful to search and test the possible observational effects. Chern-Simons modified gravity serves as a natural model for gravitational parity-violations. Especially, considering extensions to Einstein-Hilbert action up to second order curvature terms, it is known that theories of gravitational parity-violation will reduce to the dynamical Chern-Simons gravity. In this letter, we outline the theoretical principles of testing the dynamical Chern-Simons gravity with orbiting gravity gradiometers, which could be naturally incorporated into future satellite gravity missions. The secular gravity gradient signals, due to the Mashhoon-Theiss (anomaly) effect, in dynamical Chern-Simons gravity are worked out, which can improve the constraint of the corresponding Chern-Simons length scale $\xi^{\frac{1}{4}}_{cs}$ obtained from such measurement scheme. For orbiting superconducting gradiometers or gradiometers with optical readout, a bound $\xi^{\frac{1}{4}}_{cs}\leq 10^6 \ km$ (or even better) could in principle be obtained, which will be at least 2 orders of magnitude stronger than the current one based on the observations from the GP-B mission and the LAGEOS I, II satellites.