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 massive black hole in the center of our Galaxy (${\text{SgrA}}^{*}$) 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 $\zeta$ at the level of ${10}^{-1}$ to an accuracy of ${10}^{-3}$. For high-eccentricity sources, XMRIs can put bounds on the parameter $\zeta$ at the level of ${10}^{-1}$ to an accuracy of ${10}^{-6}$. Furthermore, using the time-frequency Markov Chain Monte Carlo 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 $1\sigma$ 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 $\zeta$, the estimation accuracy reaches $\mathrm{\Delta }{\log }_{10}\zeta =0.08$ for high eccentricity sources and 1.27 for low eccentricity sources.

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• Alternative gravity theories
• Gravitational waves