Signature of biased range in the non-dynamical Chern-Simons modified gravity and its measurements with satellite-satellite tracking missions: Theoretical studies

TL;DR

This paper investigates how satellite tracking missions can detect or constrain non-dynamical Chern-Simons gravity by analyzing characteristic range signals, providing potential bounds on the theory's parameters through observational data.

Contribution

It derives the range observable signature of non-dynamical Chern-Simons gravity in satellite tracking and estimates bounds on the theory's mass scale from satellite mission data.

Findings

Range signal characteristic of Chern-Simons gravity identified

Potential to constrain the mass scale M_CS to >1.9×10^{-9} eV with GRACE data

Stronger bounds expected from future GRACE FO mission

Abstract

Having great accuracy in the range and range rate measurements,he GRACE mission and the planed GRACE Follow On mission can in principle be employed to place strong constraints on certain relativistic gravitational theories. In this paper, we work out the range observable of the non-dynamical Chern-Simons modified gravity for the Satellite-to-Satellite Tracking (SST) measurements. We find out that a characteristic time accumulating range signal appears in non-dynamical Chern-Simons gravity, which has no analogue found in the standard parity-preserving metric theories of gravity. The magnitude of this Chern-Simons range signal will reach a few times of $\chi cm$ for each free flight of these SST missions, here $\chi$ is the dimensionless post-Newtonian parameter of the non-dynamical Chern-Simons theory. Therefore, with the 12 years data of the GRACE mission, one expects that the mass scale $M_{CS}=\frac{4\hbar c}{\chi a}$ of the non-dynamical Chern-Simons gravity could be constrained to be larger than $1.9\times10^{-9}eV$. For the GRACE FO mission that scheduled to be launched in 2017, the much stronger bound that $M_{CS}\geq5\times10^{-7}eV$ is expected.