Are Parametrized Tests of General Relativity with Gravitational Waves Robust to Unknown Higher Post-Newtonian Order Effects?

Abstract

Gravitational wave observations have great potential to reveal new information about the fundamental nature of gravity, but extracting that information can be difficult. One popular technique is the parametrized inspiral test of general relativity (a realization of the parametrized post-Einsteinian framework), where the gravitational waveform, as calculated in Einstein's theory as a series expansion in the orbital velocity, is parametrically deformed at a given set of orders in velocity. However, most current approaches usually only analyze the data while considering a single, specific modification at a time. Are then constraints placed with a single modification robust to our ignorance of higher post-Newtonian order corrections? We show here that for a wide class of theories, specifically those that admit a post-Newtonian expansion, single-parameter tests are indeed robust. In particular, through a series of full Bayesian parameter estimation studies on several different sets of synthetic data, we show that single-parameter constraints are not degraded but rather are improved by the inclusion of multiple parameters, provided one includes information about the mathematical structure of the series. We then exemplify this with a specific theory of gravity, shift-symmetric scalar Gauss-Bonnet theory, where the waveform has been calculated to higher post-Newtonian orders than leading. We show that the inclusion of these higher order terms strengthens single-parameter constraints, instead of weakening them, and that the strengthening is very mild. This analysis therefore provides strong evidence that single-parameter post-Einsteinian tests of general relativity are robust to ignorance of high post-Newtonian order terms in the general relativistic deformations.

Theory-agnostic framework for inspiral tests of general relativity with higher-harmonic gravitational waves

“…(2.13), truncated to 1PN order and evaluated at x = x1 . The truncation of the modification to the amplitude at 1 PN order will probably not affect the constraints one can place on the GR deformations, as found in the analogous phase study of [76]; a verification of this confirmation is outside the scope of this paper. Note that, regardless of whether the waveforms used to extract Eq.…”

Spin-induced dynamical scalarization, de-scalarization and stealthness in scalar-Gauss-Bonnet gravity during black hole coalescence

“…Such emission of dipole or quadrupole radiation accelerates the inspiral, and thus affect the GW phase at −1PN and 0PN respectively, as shown in shift-symmetric theories [34][35][36][37][38][39]. These effects in the inspiral are observable and can thus be constrained with current ground-based [8,[22][23][24][25] and future detectors [118,119] within the parameterized post-Einsteinian framework [120][121][122][123], provided the binary is of sufficiently low mass such that enough of the inspiral is observed [119]. In fact, a constraint of this type was recently obtained using the GW190814 event [124] in [21].…”

Measuring the propagation speed of gravitational waves with LISA

“…In fact, ppE is sufficiently general to include distinct modifications at each PN order of the phase, and can also encapsulate departures from the GR generation of GWs (not just propagation effects, as in the present work). The price paid for this powerful generality is an increased number of modified gravity parameters, such that these are usually varied and constrained one by one (see [99] for recent discussion). By focussing on a modification to c T alone, our work effectively links amplitude and various PN phase terms to vary in concert, creating a distinct signal.…”