DINGO-TGR cuts a six-parameter gravity test to 38 minutes, and 1,000 noise injections find GW150914's offset unremarkable
Synopsis
DINGO-TGR infers binary parameters and six post-Newtonian phase-deformation parameters jointly with neural posterior estimation, then reweights the network's approximate posterior by importance sampling. For GW150914 the inference takes about 38 minutes against roughly 177 hours for bilby-tgr with dynesty, and about 4.4 hours against 238 hours for the higher signal-to-noise GW250114. GW150914 shows a mild offset from general relativity in the leading principal-component mode, but 115 of 1,000 general-relativity injections resembling GW150914 reach or exceed that offset, an empirical upper-tail p-value of about 0.115 that does not reject the general-relativity null at the 5% level.
Interpretation
Multiparameter gravitational-wave tests of general relativity can now return binary parameters and six post-Newtonian phase-deformation parameters in one joint inference, compressed into the few combinations the data actually constrain. Earlier multiparameter tests were limited by strong correlations among these phase deformations, which left individual deformation posteriors broad, while repeated Bayesian sampling made large injection campaigns expensive. In 16 zero-noise general-relativity injections, zero lies within the credible intervals of both the leading and subleading principal-component modes; in 12 beyond-general-relativity injections, the injected mode values lie within the corresponding intervals, and general relativity is excluded from the leading-mode interval for the uniform positive and increasing deformation patterns.
The pipeline first learns a mapping from observed data to a parameter posterior with a normalizing flow, then reweights the network samples by the target likelihood and prior, and finally diagonalizes the posterior covariance of the six deformation parameters. A normalizing flow is an invertible neural transformation that maps a simple base distribution onto a data-conditioned posterior density; importance sampling weights each sample by the ratio of target likelihood and prior, correcting the gap between the network proposal and the true posterior. For GW150914, 350,000 proposal samples give an effective sample size of about 4,231; for GW250114, 2.5 million proposal samples give 1,037, and both analyses retain only the leading and subleading modes whose Jensen–Shannon divergence from the prior exceeds 0.1 bit.
Perspective
The demonstrated scope is quasicircular binaries, the single waveform approximant IMRPhenomXPHM, and six deformation parameters from 1.5PN to 3.5PN within the TIGER framework; the real-event analysis covers GW150914 and GW250114, and the noise study fixes a GW150914-like general-relativity injection with fixed O1 power spectral densities.
The offset in the leading GW150914 mode is not judged a violation of general relativity, but the analysis also does not identify its origin; effects of nonstationary detector noise and waveform-modeling error are not quantified, and non-Gaussian noise transients are known to induce apparent phase deviations. The injection set does not test a resolvable nonzero subleading-mode offset, and the PCA basis need not correspond to the same post-Newtonian combination across injections and events.