Preliminary forecasting constraint on scalar charge with LISA in non-vacuum environments

Abstract We compute the gravitational wave signal from eccentric extreme-mass-ratio inspirals (EMRIs) embedded within beyond-vacuum environments, where the secondary object carries a scalar charge and evolves in the presence of both an accretion disk and a dark matter halo. The waveform modification is derived by incorporating the scalar charge correcting the fluxes and orbital trajectories of the secondary. Our results indicate that, under suitable parameter configurations, the influence of the scalar charge on EMRIs waveform in such environments can be distinguished from that in vacuum spacetime. For the EMRIs signal modified by the astrophysical environments, the future space-borne detector can determine the relative error of scalar charge constrained by LISA at the level of $$\sim 0.1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>0.1</mml:mn> </mml:mrow> </mml:math> , providing a preliminary prediction of detecting scalar charge in the beyond-vacuum spacetime.