Constraining noncommutative spacetime with GW150914 and GW190814

Abstract

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 $Λ\equiv|θ^{0i}|/(l_Pt_P)$, where $θ^{0i}$ 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 $\sqrtΛ\lesssim3.5$. 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 $\sqrtΛ<0.68$. We then analyze GW190814 and obtain an even tighter 95th percentile upper bound of $\sqrtΛ<0.46$, 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.

Figures (3)

• Figure 1: The waveform of the real part of $h_\times$ for a GW150914-like event is shown for general relativity and noncommutative gravity. The left panel displays the GR waveform, the noncommutative gravity waveform with $\sqrt{\Lambda} = 3.5$ obtained in Ref. Kobakhidze:2016cqh, and the waveform corresponding to the 95th percentile upper bound on $\sqrt{\Lambda}=0.68$ for GW150914 derived in this work. The dashed vertical line denotes the MECO frequency of 22 mode. The right panel shows the waveform in the frequency range from 20 Hz to 22 Hz, with both the low-frequency cutoff and the reference frequency set to 20 Hz.
• Figure 2: The values of the noncommutative gravity phase correction $\beta_{lm}$ are presented for five modes: (2,2), (2,1), (3,3), (3,2), and (4,4), assuming $\sqrt{\Lambda} = 1$. The $\beta_{lm}$ value for the (2,2) mode is degenerate with that of the (3,2) mode according to Eq. \ref{['beta']}.
• Figure 3: Posterior distributions for GW150914 (left panel) and GW190814 (right panel). The GR results are shown as orange contours, while the results for noncommutative gravity are depicted in blue. The 2D contours represent with different credible intervals, denoting the 50% and 90% regions, while the vertical lines indicate the 90% region for the 1D marginalized posterior distribution.