Tests of general relativity at the fourth post-Newtonian order

TL;DR

This paper evaluates how well current and future gravitational wave detectors can test the predictions of general relativity at the fourth post-Newtonian order, including novel physical effects, using Fisher matrix analysis.

Contribution

It provides projected bounds on deviations from PN theory at 4PN and 4.5PN orders for various detectors, highlighting the potential for high-precision tests of general relativity.

Findings

XG detectors can constrain deviations to about 1-10% at 4PN.

LISA can provide constraints as tight as 0.01% on certain parameters.

Bounds vary with binary mass and mass ratio.

Abstract

The recently computed post-Newtonian (PN) gravitational-wave phasing up to 4.5PN order accounts for several novel physical effects in compact binary dynamics such as the {\it tail of the memory, tails of tails of tails and tails of mass hexadecupole and current octupole moments}. Therefore, it is instructive to assess the ability of current-generation (2G) detectors such as LIGO/Virgo, next-generation (XG) ground-based gravitational wave detectors such as Cosmic Explorer/Einstein Telescope and space-based detectors like LISA to test the predictions of PN theory at these orders. Employing Fisher information matrix, we find that the projected bounds on the deviations from the logarithmic PN phasing coefficient at 4PN is ${\cal O}(10^{-2})$ and ${\cal O}(10^{-1})$ for XG and 2G detectors, respectively. Similarly, the projected bounds on other three PN coefficients that appear at 4PN and 4.5PN are ${\cal O}(10^{-1}-10^{-2})$ for XG and ${\cal O}(1)$ for 2G detectors. LISA observations of supermassive BHs could provide the tightest constraints on these four parameters ranging from ${\cal O}(10^{-4}-10^{-2})$. The variation in these bounds are studied as a function of total mass and the mass ratio of the binaries in quasi-circular orbits. These new tests are unique probes of higher order nonlinear interactions in compact binary dynamics and their consistency with the predictions of general relativity.