Constraining modified theories of gravity through the detection of one extremely large mass-ratio inspiral

Abstract: Extremely large mass-ratio inspirals (XMRIs), formed by brown dwarfs inspiraling into a massive black hole, emit gravitational waves (GWs) that fall within the detection band of future space-borne detectors such as LISA, TianQin, and Taiji. Their detection will measure the astrophysical properties of the MBH in the center of our galaxy (SgrA$^\ast$) with unprecedented accuracy and provide a unique probe of gravity in the strong field regime. Here, we estimate the benefit of using the GWs from XMRIs to constrain the Chern-Simons theory. Our results show that XMRI signals radiated from the late stages of the evolution are particularly sensitive to differences between Chern-Simons theory and general relativity. For low-eccentricity sources, XMRIs can put bounds on the Chern-Simons parameter $ζ$ at the level of $10^{-1}$ to an accuracy of $10^{-3}$. For high-eccentricity sources, XMRIs can put bounds on the parameter $ζ$ at the level of $10^{-1}$ to an accuracy of $10^{-6}$. Furthermore, using the time-frequency MCMC method, we obtain the posterior distribution of XMRIs in the Chern-Simons theory. Our results show that almost all the parameters can be recovered within $1σ$ confidence interval. For most of the intrinsic parameters, the estimation accuracy reaches $10^{-3}$. For the brown dwarf mass, the estimation accuracy reaches $10^{-1}$, while for $ζ$, the estimation accuracy reaches $Δ\log_{10}ζ=0.08$ for high eccentricity sources and 1.27 for low eccentricity sources.