A Model-Independent Precision Test of General Relativity using LISA Bright Standard Sirens

The upcoming Laser Interferometer Space Antenna (LISA), set for launch in the mid-2030s, will enhance our capability to probe the universe through gravitational waves (GWs) emitted from binary black holes (BBHs) across a broad range of cosmological distances. LISA is projected to observe three classes of BBHs: massive BBHs (MBBHs), extreme mass-ratio inspirals (EMRIs), and stellar mass BBHs. This study focuses on MBBHs, which are anticipated to occur in gas-rich environments conducive to producing powerful electromagnetic (EM) counterparts, positioning them as excellent candidates for bright sirens. By combining GW luminosity distance measurements from these bright sirens with Baryon Acoustic Oscillation (BAO) measurements derived from galaxy clustering and sound horizon measurements from the Cosmic Microwave Background (CMB), and spectroscopic redshift measurements from electromagnetic (EM) observations, we propose a data-driven model-independent method to reconstruct deviations in the variation of the effective Planck mass (in conjunction with the Hubble constant) as a function of cosmic redshift. Using this multi-messenger technique, we achieve precise measurements of deviations in the effective Planck mass variation with redshift (z), with a precision ranging from approximately $2.4\%$ to $7.2\%$ from redshift $z=1$ to $z=6$ with a single event. Additionally, we achieved a measurement of the Hubble constant with a precision of about $1.3\%$, accounting for variations in the effective Planck mass over 4 years of observation time ($T_{\mathrm{obs}}$). This assumes that EM counterparts are detected for $75\%$ of the events. This precision improves with observation time as $T_{\mathrm{obs}}^{-1/2}$. This approach not only has the potential to reveal deviations from General Relativity but also to significantly expand our understanding of the universe's fundamental physical properties.