Gravitational waves from eccentric extreme mass-ratio inspirals as probes of scalar fields

Abstract: We study eccentric orbits of the Schwarzschild spacetime for extreme mass ratio system (EMRI) in modified gravity theories with additional scalar fields. Due to the additional energy and angular momentum carried away by the scalar field, the orbit of the EMRI in modified gravity decays faster than that in general relativity. The time that it takes the eccentricity $e$ to reach the minimum is smaller and the values of the semi-latus rectum $p$ and $e$ at the turning point when $e$ reaches the minimum are bigger for larger scalar charge $d$. In addition to the calculation of energy fluxes with numerical method, we also use the Post-Newtonian expansion of the rate of energy carried away by the scalar field in eccentric orbits to understand the behaviors of the energy emission. By adding the scalar flux to the open code FastEMRIWaveforms of the Black Hole Perturbation Toolkit, we numerically generate fast gravitational waveforms for eccentric EMRIs with scalar fields and use the faithfulness between waveforms with and without the scalar charge to discuss the detection of scalar charge $d$. The detection error of the scalar charge is also estimated with method of Fisher information matrix.