Constraints on Einstein-dilation-Gauss-Bonnet gravity from black hole-neutron star gravitational wave events

Recent gravitational wave observations allow us to probe gravity in the strong and dynamical field regime. In this paper, we focus on testing Einstein-dilation Gauss-Bonnet gravity which is motivated by string theory. In particular, we use two new neutron star black hole binaries (GW200105 and GW200115). We also consider GW190814 which is consistent with both a binary black hole and a neutron star black hole binary. Adopting the leading post-Newtonian correction and carrying out a Bayesian Markov-chain Monte Carlo analysis, we derive the 90% credible upper bound on the coupling constant of the theory as $\sqrt{{\alpha }_{\mathrm{GB}}}\lesssim 1.33\mathrm{km}$, whose consistency is checked with an independent Fisher analysis. This bound is stronger than the bound obtained in previous literature by combining selected binary black hole events in GWTC-1 and GWTC-2 catalogs. We also derive a combined bound of $\sqrt{{\alpha }_{\mathrm{GB}}}\lesssim 1.18\mathrm{km}$ by stacking GW200105, GW200115, GW190814, and selected binary black hole events. In order to check the validity of the effect of higher post-Newtonian terms, we derive corrections to the waveform phase up to second post-Newtonian order by mapping results in scalar-tensor theories to Einstein-dilation Gauss-Bonnet gravity. We find that such higher-order terms improve the bounds by 14.5% for GW200105 and 6.9% for GW200115, respectively.

Figure 1

Posterior probability distributions for $\sqrt{{\alpha }_{\mathrm{GB}}}$ from selected GW events. We also show an upper bound on $\sqrt{{\alpha }_{\mathrm{GB}}}$ at 90% credible level for each event as vertical lines, which indicates the result is consistent with GR. The posteriors are found by including only the leading EdGB correction to the phase at $-1\mathrm{PN}$ order.

Figure 2

A comparison of the posteriors on $\sqrt{{\alpha }_{\mathrm{GB}}}$ from the leading $-1\mathrm{PN}$ correction and those including higher PN corrections (up to 2PN) for GW200105 (top) and GW200115 (bottom). Observe that the 90% upper bounds on ${\sqrt{\alpha }}_{\mathrm{GB}}$ are improved by 14.5% for GW200105 and 6.9% for GW200115, respectively.

Figure 3

Posterior probability distributions for the EdGB coupling constant $\sqrt{{\alpha }_{\mathrm{GB}}}$, the chirp mass $\mathcal{M}$, and the mass ratio $q$ from GW200105 (left) and GW200115 (right). We compare the marginal posterior distributions for the case with the leading EdGB correction at $-1\mathrm{PN}$ order (blue) and the case including higher PN orders up to 2PN (orange). The purple shaded regions indicate the posterior probabilities of the latter case and the solid lines represent the 90% credible regions for the two cases. The vertical dashed lines show the one-sided 90% confidence interval for $\sqrt{{\alpha }_{\mathrm{GB}}}$ and the two-sided 90% credible intervals for $\mathcal{M}$ and $q$.

Figure 4

Comparison of EdGB corrections to the phase entering at different PN orders as a function of the GW frequency. We also present the leading phase in GR and the contribution from all of the EdGB corrections combined. For each contribution, we show the phase relative to that at a reference frequency chosen to be 20 Hz. We chose $(m_1,m_2)=(5.9,1.4)M_{\odot }$ and $({\chi }_1,{\chi }_2)=(0.31,0)$, corresponding to GW200115, and $\sqrt{{\alpha }_{\mathrm{GB}}}=1.33\mathrm{km}$ that is the 90% credible limit found through our Bayesian inference (see Table 2).