Post-Newtonian inspiral waveform model for eccentric precessing binaries with higher-order modes and matter effects

We introduce , a post-Newtonian (PN) inspiral waveform model for eccentric and spin-precessing compact binaries that includes higher-order modes and matter effects. Accurate and efficient waveform models capturing these effects are essential for probing compact-binary formation channels and exploiting current and future gravitational-wave (GW) observations. extends , significantly improving its physical content and accuracy. In particular, we show that above 2.5PN order the quasicircular contributions to the orbital phasing dominate at each PN order, and we incorporate all available higher-order quasicircular PN corrections to the phasing, including adiabatic tidal effects. We generalize the multiple-scale analysis solution of the spin-precession equations, extending it to higher PN orders and including all available quasicircular corrections. Finally, we add eccentric corrections up to 1PN order in the waveform amplitudes, including the GW multipoles ( l , | m | ) = ( 2 , 2 ) , ( 2 , 1 ) , ( 2 , 0 ) , ( 3 , 3 ) , ( 3 , 2 ) , ( 3 , 1 ) , ( 3 , 0 ) , ( 4 , 4 ) , ( 4 , 2 ) , ( 4 , 0 ) . We validate against existing analytical waveform models and numerical relativity simulations, showing that it provides a robust and computationally efficient description of the inspiral, with good agreement across a broad region of parameter space and up to close to merger. The accuracy degrades in the late inspiral for systems with very unequal masses ( m 2 / m 1 ≲ 0.1 ), significant spins aligned with the orbital angular momentum ( | χ eff | ≳ 0.5 ), and high eccentricities ( e ≳ 0.6 ), where the PN expansion is expected to break down. represents a significant step toward physically complete and efficient waveform modeling of eccentric and precessing binaries, providing a foundation for future extensions including higher-order corrections, calibration to numerical relativity, and merger-ringdown modeling.