Impact of numerical-relativity waveform calibration on parametrized post-Einsteinian tests

Abstract

Testing general relativity in the strong-field and highly dynamical regime is now possible through current gravitational-wave observations, where even a single high-quality detection can place competitive constraints on deviations from Einstein's theory. The parametrized post-Einsteinian framework provides a theory-agnostic approach to search for such deviations, but it typically assumes that systematic uncertainties in the base waveform model, particularly those arising from calibration to numerical relativity, are negligible. In this work, we investigate how calibration errors in the late-inspiral fitting coefficients of the IMRPhenomD waveform model can lead to spurious detections of departures from general relativity in parametrized tests. We use an uncertainty-aware version of IMRPhenomD, recalibrated to a set of numerical relativity surrogate waveforms and equipped with a probabilistic description of its fitting coefficients, to simulate general-relativity-consistent signals. We inject these signals into an O5 ground-based detector network and recover them with the original IMRPhenomD model augmented with a parametrized post-Einsteinian phase deformation. We find that false violations of general relativity using this model arise for network signal-to-noise ratios as low as 60. When the uncertainty-aware model is used instead, the inferred parametrized post-Einsteinian phase deformation remains consistent with zero even for signals with a signal-to-noise ratio up to 330. These results demonstrate the need to account for numerical relativity calibration uncertainty in order to perform reliable inspiral tests of general relativity. They also illustrate that explicitly incorporating numerical relativity calibration uncertainty into the waveform model preserves our ability to robustly test general relativity.

Figures (9)

• Figure 1: Phase evolution (top) and phase variability (bottom) for the lighter-mass binary system listed in Table \ref{['tab:injection_params']}, over the detector frequency range considered in this work. The top panel shows the GR phase $\phi_{\mathrm{GR}}$, as predicted by the vanilla IMRPhenomD model (orange) and its uncertainty-aware recalibration (blue). The bottom panel illustrates the variability of the phase residual $\phi_\mathrm{GR} - \bar{\phi}_{\mathrm{GR}}$, obtained by drawing 1000 samples of fitting coefficients from $\Pi(\boldsymbol{\lambda})$.
• Figure 2: Upper panel: threshold network SNR, $\rho_{\mathrm{th}}$, as a function of the PN order $(b+5)/2$ at which the ppE dephasing enters, shown for the lighter ($20\,M_\odot$, green) and heavier ($60\,M_\odot$, blue) BBH systems. Diamond markers indicate the best estimate of $\rho_{\mathrm{th}}$, and the bracketing runs at slightly higher and lower SNR provide an uncertainty interval. At all PN orders we find $\rho_{\mathrm{th}}\gtrsim 60$. Lower panel: $\log_{10}\mathrm{BF}_{\mathrm{ppE},\mathrm{GR}}$ evaluated at the corresponding $\rho_{\mathrm{th}}$, with the associated uncertainty. The Bayes factors remain small in magnitude, $|\log_{10}\mathrm{BF}_{\mathrm{ppE},\mathrm{GR}}|\lesssim 0.5$, so while model selection at $\rho=\rho_{\mathrm{th}}$ is inconclusive, it also does not rule out a beyond-GR signature.
• Figure 3: Marginal posterior distributions $p(\beta)$ for the ppE parameter $\beta$ at fixed network SNR $\rho=330$ for the lighter ($20\,M_\odot$, left panel) and the heavier ($60\,M_\odot$, right panel) BBH system, shown as histograms with kernel-density-estimate (KDE) overlays for ppE indices spanning $-1.5$ to $3.5$ PN order. Orange corresponds to recoveries with Model I, while blue corresponds to recoveries with Model II. Note that each PN order is displayed with its own $\beta$ range (and scale factor where indicated) to resolve the posterior, though all panels are aligned with $\beta = 0$ (black line). Despite $\rho$ exceeding the thresholds in Fig. \ref{['fig:threshold_snr']}, Model II remains consistent with $\beta=0$ across all PN orders. On the other hand, Model I exhibits systematic bias, in some cases exceeding $3\sigma$. Observe also that in the heavier system (right panel) Model I exhibits a bimodality at $0.5$ and $1$ PN order. Model II instead remains unimodal and consistent with $\beta=0$ across all PN orders, though its median is visibly shifted toward the median of Model I in most cases.
• Figure 4: Radar charts summarizing the fractional systematic bias defined in Eq. \ref{['eq:fractional-bias']} found in chirp mass, inverse mass ratio, and effective spin for the $20\,M_\odot$ (left panel) and $60\,M_\odot$ (right panel) injections recovered at $\rho=330$ with Model I. Each triangle corresponds to a different PN order at which $\beta$ enters the waveform phase (colors mapped to PN orders as indicated in the legend), and the three spokes report the bias in $\mathcal{M}$, $1/q$, and $\chi_{\mathrm{PN}}$, respectively. Concentric circles denote bias levels in units of $\sigma$. To accommodate the wide range of values, we use a nonlinear radial scaling that compresses large biases by plotting $\sqrt{|\delta\theta|/\sigma_\theta}$ instead of $|\delta\theta|/\sigma_\theta$.
• Figure 5: Corner plot showing the 1D marginals and 2D joint posteriors for $\mathcal{M}$, $1/q$, and $\chi_{\mathrm{PN}}$ for the $20\,M_\odot$ injection recovered at $\rho=330$ with Model I, comparing runs where the ppE phase term enters at $0$, $0.5$, $1$, and $1.5$ PN order (colors as labeled). Each contour encloses the 90% HPD credible region. Black lines mark the injected parameter values. Observe that at $0$ PN order the recovery is biased primarily in $\mathcal{M}$ but not in $1/q$ and $\chi_{\mathrm{PN}}$. Conversely, at $1.5$ PN order $\mathcal{M}$ and $1/q$ remain consistent with the injection while the dominant bias appears in $\chi_{\mathrm{PN}}$.