Improved post-Newtonian waveform model for inspiralling precessing-eccentric compact binaries

The measurement of spin precession and orbital eccentricity in gravitational-wave (GW) signals is a key priority in GW astronomy, as these effects not only provide unique insights into the astrophysical formation and evolution of compact binaries, but also, if neglected in waveform models, could introduce significant biases in parameter estimation, searches, and tests of general relativity. Despite the growing potential of upcoming LIGO-Virgo-KAGRA observing runs and future detectors to measure eccentric-precessing signals, accurately and efficiently modeling them remains a significant challenge. In this work, we present py, a frequency-domain post-Newtonian (PN) waveform model for the inspiral of precessing-eccentric compact binaries. py improves upon previous models by introducing analytical expressions for the Fourier mode amplitudes, enhancing the numerical stability of the multiple scale analysis framework, and adding recently derived PN corrections, critical to accurately describe signals in GW detectors. Additionally, we simplify the numerical implementation and introduce a scheme to interpolate the polarization amplitudes, achieving a speedup of up to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mo>∼</a:mo><a:mrow><a:mi mathvariant="script">O</a:mi><a:mrow><a:mo stretchy="false">(</a:mo><a:mn>15</a:mn><a:mo stretchy="false">)</a:mo></a:mrow></a:mrow></a:mrow></a:math> in the waveform computations, making the model practical for data analysis applications. We thoroughly validate py by comparing it to other waveform models in the quasicircular and eccentric-spin-aligned limits, finding good agreement. Additionally, we demonstrate py ’s capability to analyze simulated GW events, accurately recovering the parameters of signals described by both py and henom. While py still lacks important physical effects, such as higher-order PN corrections, higher-order modes, mode asymmetries, tidal interactions, or the merger-ringdown phase, it represents a significant step toward more complete waveform models, offering a flexible and efficient framework that can be extended in future work to incorporate these effects.