“…A neutron star background was considered in (Kuan et al, 2023) with a modification of SACRA-MPI code (Kiuchi et al, 2017;Yamamoto et al, 2008). Whilst order-reduced methods like those in (Doneva et al, 2022;Elley et al, 2022;Evstafyeva et al, 2023;Okounkova et al, 2019Okounkova et al, , 2020Okounkova et al, , 2023Okounkova, 2020;R. et al, 2023;Richards et al, 2023;Silva et al, 2021;Witek et al, 2019) provide an estimate of the scalar dynamics and associated energy losses, they may miss information about the fully non-linear impact on the metric and suffer from the accumulation of secular errors over long inspirals.…”