Tests of general relativity at the fourth post-Newtonian order

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 tail of the memory, tails of tails of tails, and tails of mass hexadecapole and current octupole moments. Therefore, it is instructive to assess the ability of current-generation (2G) detectors such as LIGO and Virgo; next-generation (XG) ground-based gravitational wave detectors such as the Cosmic Explorer and Einstein Telescope; and space-based detectors like LISA to test the predictions of PN theory at these orders. Employing the Fisher information matrix, we find that the projected bounds on the deviations from the logarithmic PN phasing coefficient at 4PN are $O\left({10}^{-2}\right)$ and $O\left({10}^{-1}\right)$ for XG and 2G detectors, respectively. Similarly, the projected bounds on the other three PN coefficients that appear at 4PN and 4.5PN are $O\left({10}^{-1}–{10}^{-2}\right)$ for XG and $O\left(1\right)$ for 2G detectors. LISA observations of supermassive BHs could provide the tightest constraints on these four parameters in the range $O\left({10}^{-4}–{10}^{-2}\right)$. The variation in these bounds is studied as a function of total mass and the mass ratio of the binaries in quasicircular 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.