Gravitational-wave constraints on noncommutative spacetime from GW190814

Recent advances in noncommutative geometry and string theory have stimulated increasing research on noncommutative gravity. The detection of gravitational waves~(GW) opens a new window for testing this theory using observed data. In particular, the leading correction from noncommutative gravity to the GW of compact binary coalescences appears at the second post-Newtonian~(2PN) order. This correction is proportional to the dimensionless parameter $\Lambda\equiv|\theta^{0i}|/(l_Pt_P)$, where $\theta^{0i}$ denotes the antisymmetric tensor characterizing noncommutative spacetime, and $l_P, t_P$ represent the Plank length and time, respectively. Previous study have used the phase deviation from general relativity at the 2PN order, as measured in GW150914, to constrain noncommutative gravity, resulting in an upper bound of $\sqrt{\Lambda}\lesssim3.5$. Another analysis, based on multiple events from the GWTC-1 catalog, has obtained consistent bounds. In this work, we construct the noncommutative gravity waveform in the Parameterized Post-Einsteinian framework. Based on the \texttt{IMRPhenomXHM} template, we incorporate both the dominant (2,2) mode and several higher-order modes, including (2,1), (3,3), (3,2), and (4,4). We first reanalyze the GW150914 with a Bayesian parameter estimation and derive a 95th percentile upper bound on noncommutative gravity, obtaining $\sqrt{\Lambda}<0.68$. We then analyze GW190814 and obtain an even tighter 95th percentile upper bound of $\sqrt{\Lambda}<0.46$, which corresponds to a characteristic noncommutative gravity energy scale above $2.2\,E_P$ or a length scale below $0.46\,l_P$. This represent the strongest constraint on noncommutative gravity derived from real GW observations to date.