A Parametrized Test of General Relativity for LISA Massive Black Hole Binary Inspirals

Laser Interferometer Space Antenna (LISA) observations of massive black hole binaries (MBHBs) will provide long duration inspiral signals with high signal-to-noise ratio (SNR) data, ideal for testing general relativity (GR) in the strong-field and relativistic regime regime. We present an extension of the Flexible Theory-Independent (FTI) framework, adapted to gravitational waves (GWs) from MBHBs observed with LISA, to perform parametrized inspiral tests of GR. This approach introduces generic deviations to the post-Newtonian (PN) coefficients of the frequency-domain GW phase while accounting for the time- and frequency-dependent instrument response, thus effectively identifying potential deviations from GR by constraining modifications to the PN phasing formula. Complementary analyses using Fisher matrix and full Bayesian approaches confirm that LISA observations could improve constraints on agnostic, scale-independent deviations from GR by at least two orders of magnitude compared to the most recent LIGO-Virgo-KAGRA measurements. Since LISA’s sensitivity to different GW phases – inspiral, merger, and ringdown – varies across the MBHB parameter space with masses between $10^4$ and $10^7M_{\odot}$, the optimal regime for testing agnostic deviations is not known a priori. Our results illustrate how the strength of these constraints depends significantly on both the total mass and the SNR, reflecting the trade-off between inspiral and merger-ringdown contributions to the observed signal. We also investigate the interplay between inspiral-only versus inspiral-merger-ringdown analyses in constraining these inspiral deviation parameters. This work contributes to the development of robust tests of GR with LISA, enhancing our ability to probe the nature of gravity and BHs with GW observations.

💡 Research Summary

This paper presents a comprehensive methodology for testing General Relativity (GR) using gravitational-wave (GW) observations of Massive Black Hole Binaries (MBHBs) with the future space-based detector LISA (Laser Interferometer Space Antenna). The core of the work is the adaptation and extension of the Flexible Theory-Independent (FTI) framework, originally developed for ground-based detectors like LIGO-Virgo-KAGRA (LVK), to the unique context of LISA and MBHB signals.

The proposed test is a parametrized inspiral test. It introduces generic deviation parameters (δφ_n) to the Post-Newtonian (PN) coefficients of the frequency-domain GW phase. This approach is “agnostic,” meaning it does not assume a specific alternative theory of gravity but rather probes for any systematic deviation from GR’s predictions across different PN orders (from -2PN to 3.5PN). The method carefully accounts for LISA’s time- and frequency-dependent antenna response and ensures a smooth transition of the modified phase back to the GR prediction during the merger-ringdown phase using a tapering function.

Through complementary analyses employing Fisher matrix calculations and full Bayesian inference on synthetic MBHB signals, the study makes several key projections:

1. Dramatically Improved Constraints: For agnostic, scale-independent deviations from GR, LISA observations are projected to improve upon the latest LVK constraints by at least two orders of magnitude (a factor of 100 or more).
2. Mass-Dependent Sensitivity: The effectiveness of the inspiral test strongly depends on the total mass of the MBHB. Low-mass systems (~10^4 solar masses) have long, inspiral-dominated signals in LISA’s band, providing direct sensitivity to phase deviations. High-mass systems (~10^7 solar masses) are merger-ringdown dominated. Interestingly, even for these systems, the high-SNR merger-ringdown signal—though assumed to be unmodified from GR—tightens the measurement of intrinsic parameters (masses, spins), thereby providing indirectly stronger constraints on the inspiral deviation parameters.
3. Value of Full Signal Analysis: A comparative analysis between “inspiral-only” and “inspiral-merger-ringdown” waveform models demonstrates that including the merger-ringdown portion generally leads to tighter constraints on the inspiral deviation parameters. This is because the precise characterization of the late-time signal breaks degeneracies and better determines the binary’s intrinsic properties, against which the inspiral phase is measured.

The paper also discusses important caveats. The projected hierarchy with LISA outperforming LVK assumes deviations are scale-independent. For theories where deviations depend on curvature scale (stronger in weaker fields), ground-based observations of stellar-mass binaries could remain more sensitive. Furthermore, the current implementation uses a single-parameter test (varying one PN coefficient at a time) to avoid degeneracies, though multi-parameter or Principal Component Analysis (PCA) approaches are noted as future directions.

In summary, this work provides a robust and adaptable framework for performing fundamental tests of GR with LISA. It quantitatively forecasts that LISA will revolutionize our ability to probe gravity in the strong-field regime, offering unprecedented precision to confirm GR or discover potential deviations through the observation of massive black hole binaries.