Gravitational-Wave Constraints on an Effective Field-Theory Extension of General Relativity

TL;DR

This paper addresses testing gravity in the strong-field regime by constraining an effective-field-theory extension of GR (EFTGR) that adds higher-curvature terms suppressed by a cutoff $\Lambda$, using gravitational-wave observations from LIGO/Virgo. It develops EFTGR-inspired inspiral waveform templates and derives leading 2PN-like corrections to the orbital dynamics and GW phasing, expressed in the SPA phase $\Psi_{\rm SPA}(f)$, and performs Bayesian model comparison between EFTGR and GR for GW151226 and GW170608, with careful treatment of the EFT regime via a soft UV completion and a cutoff scale $f_\Lambda = (1/\pi) \sqrt{M/d_\Lambda^3}$. The main result is that coupling scales around $d_\Lambda = 1/\Lambda \sim 150$ km are strongly disfavored, with bounds depending on $f_{\rm high}$ and strengthened by combining the two events. The study demonstrates a practical route to tighten EFTGR bounds with future GW observations and underscores the importance of UV completion assumptions in interpreting strong-field tests.

Abstract

Gravitational-wave observations of coalescing binary systems allow for novel tests of the strong-field regime of gravity. Using data from the Gravitational Wave Open Science Center (GWOSC) of the LIGO and Virgo detectors, we place the first constraints on an effective field-theory based extension of General Relativity in which only higher-order curvature terms are added to the Einstein-Hilbert action. We construct gravitational-wave templates describing the quasi-circular, adiabatic inspiral phase of binary black holes in this extended theory of gravity. Then, after explaining how to properly take into account the region of validity of the effective field theory when performing tests of General Relativity, we perform Bayesian model selection using the two lowest-mass binary black-hole events reported to date by LIGO and Virgo -- GW151226 and GW170608 -- and constrain this theory with respect to General Relativity. We find that these data disfavors the appearance of new physics on distance scales around $\sim 150$ km. Finally, we describe a general strategy for improving constraints as more observations will become available with future detectors on the ground and in space.

Figures (6)

• Figure 1: The phenomenological consequences of EFTGR in binary BH systems and the regimes of applicability of perturbative approximations in which they are computed. The vertical axis schematically depicts the corrections to a generic observable (here taken to be the orbital phase $\phi_\text{orb}$) relative to its prediction in GR as function of the inverse cutoff scale $\Lambda_c^{-1}$. For extensions to GR at distance scales below the Schwarzschild radii of the BHs $r_s$, one can use BH perturbation theory to compute the finite-size effects that influence the binary dynamics Cardoso:2018ptl, shown in dark blue. For $\Lambda_c^{-1} \gtrsim r_s$, this approximation scheme breaks down, shown in gray, and the finite-size effects cannot be computed explicitly; however, the assumption of a soft UV completion ensures that these effects saturate at $\Lambda_c \sim 1/r_s$, changing by no more than a factor of order one for cutoff energies below this value. Similarly, new orbital effects Endlich:2017tqa are computed using the PN approximation; these corrections are subdominant to the aforementioned finite-size effects when the cutoff distance scale $\Lambda_c^{-1}$ is much smaller than the orbital separation $r$, but dominate when $\Lambda_c \sim 1/r$. However, by construction, $\texttt{EFTGR}$ is only valid over distance scales larger than the $\Lambda_c^{-1}$, and so the PN prediction of new orbital effects cannot be extended to separations below $\Lambda_c^{-1}$. Thus, as shown in cyan, the PN approximation can be applied when $\Lambda_c^{-1} \lesssim r_s$, where both finite-size and orbital effects are known or when $\Lambda_c^{-1} \lesssim r$, where orbital effects are known and finite-size effects are small enough to be neglected.
• Figure 2: Comparison between the posterior density distributions of the detector's frame chirp mass when using an IMR approximant (SEOBNRv4) and a inspiral-only PN approximant (TaylorF2) with different values of $f_{\rm high}$. For both GW151226 (left panel) and GW170608 (right panel) the results when using the PN approximant are in good agreement with the IMR result.
• Figure 3: The natural logarithm of the Bayes factor of the EFTGR versus GR waveform model for different choices of $d_{\Lambda}$ (in km) when using the inspiral-only PN waveform model. We use different values for $f_{\rm high}$ when computing the likelihood function \ref{['eq:lik']} to account for the different systematic uncertainties mentioned in the text. To compute $f_{\Lambda}$ we use the median source's frame total masses obtained with IMR templates as reported in Refs. Abbott:2016nmjAbbott:2017gyy. We show the results for the two lowest-mass GW events detected so far: GW151226 with total mass $M_{\rm tot}\simeq 22 M_{\odot}$ (left panel) and GW170608 with total mass $M_{\rm tot}\simeq 19 M_{\odot}$ (right panel). For reference we mark the threshold $\ln B_{\rm GR}^{\rm {\tt EFTGR}}= -5$ with a grey solid curve.
• Figure 4: The log Bayes factors of the EFTGR versus GR waveform when combining the results shown in Fig. \ref{['fig:BF_TaylorF2']}.
• Figure 5: The natural logarithm of the Bayes factors of the EFTGR versus GR waveform for GW170608 in the regime where $d_{\Lambda}\lesssim M$, with $M$ the mass of either BH in the binary, with corresponding $m_{\Lambda}$ shown in the top $x$-axis, when using the PN waveform model. We fix the minimum mass $M_{\rm min}$ in the priors for the BH masses such that $d_{\Lambda}< M$ is always satisfied in the GW template. To account for the systematic uncertainty in the validity of the waveform model, we use different values for the minimum mass in the prior $M_{\rm min}$ as shown by the different curves.