Constraining gravity with eccentric gravitational waves: projected upper bounds and model selection

Abstract

Gravitational waves allow us to test general relativity in the highly dynamical regime. While current observations have been consistent with waves emitted by quasi-circular binaries, eccentric binaries may also produce detectable signals in the near future with ground-and space-based detectors. We here explore how tests of general relativity scale with the orbital eccentricity of the source during the inspiral of compact objects up to e ∼ 0.8. We use a new, 3rd post-Newtonian-accurate, eccentric waveform model for the inspiral of compact objects, which is fast enough for Bayesian parameter estimation and model selection, and highly accurate for modeling moderately eccentric inspirals. We derive and incorporate the eccentric corrections to this model induced in Brans-Dicke theory and in Einstein-dilaton-Gauss-Bonnet gravity at leading post-Newtonian order, which suggest a straightforward eccentric extension of the parameterized post-Einsteinian formalism. We explore the upper limits that could be set on the coupling parameters of these modified theories through both a confidence-interval-and Bayes-factor-based approach, using a Markov-Chain Monte Carlo and a trans-dimensional, reversible-jump, Markov-Chain Monte Carlo method. We find projected constraints with signals from sources with e ∼ 0.4 that are one order of magnitude stronger than that those obtained with quasi-circular binaries in advanced LIGO. In particular, eccentric gravitational waves detected at design sensitivity should be able to constrain the Brans-Dicke coupling parameter ω 3300 and the Gauss-Bonnet coupling parameter α 1/2 0.5 km at 90% confidence. Although the projected constraint on ω is weaker than other current constraints, the projected constraint on α 1/2 is 10 times stronger than the current gravitational wave bound.

Repeated Bursts: Gravitational Waves from Highly Eccentric Binaries

“…1 therein). Similar non-trivial behavior of the constraint with increasing eccentricity was found by Moore & Yunes in [57], who studied constraints on Brans-Dicke theory and Enstein-dilaton-Gauss-Bonnet gravity. Using Markov-Chain Monte Carlo methods, Moore & Yunes found that the constraints are strongest for moderately eccentric systems with e ∼ 0.4, with the projected constraints being an order of magnitude better than current constraints with quasi-circular binaries.…”

Gravitational radiation from eccentric binary black hole system in dynamical Chern-Simons gravity

“…Similar to Brans-Dicke and Einstein-dilaton-Gauss-Bonnet gravity, it is expected that including the eccentricity into the binary parameters enhances the distinguishment between DCS gravity and GR [187]. To show that, we numerically calculate the mismatch between the frequency-domain waveforms in DCS theory and GR.…”

“…[126,129,137], the observation of the BBH system without eccentricity can not give the physically meaningful constraint. However, similar to Brans-Dicke and Einstein-dilaton-Gauss-Bonnet gravity, it is expected that including the eccentricity into the binary parameters enhances the constraint on DCS effects [187]. Especially, for the eccentric BBH system formed dynamically in densely populated environments [83][84][85], the DCS modification from GR is enhanced.…”

Constraint on Brans-Dicke theory from intermediate/extreme mass ratio inspirals

“…As discussed in [76], the degeneracy between the eccentricity and ω BD may deteriorate the accuracy of ω BD for e 0.1, but for moderate and large eccentricities, the constraint on ω BD becomes stronger. Due to the large eccentricity, the covariances between non-GR and GR parameters are broken, and the constraints on non-GR effects become stronger than quasicircular constraints for large eccentric I/EMRIs [77]. The above results are based on the FIM method and simple waveform templates.…”

“…The extra energy loss in BD theory makes both the orbital dynamics and the GW waveform of a compact binary system different from those in GR [54][55][56][57][58][59][60], so BD theory can also be probed by the observations of GWs [61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78]. However, the orbital evolution and gravitational radiation from binary black holes (BBHs) are identical in GR and BD theory, so GW observations of BBHs are unable to distinguish BD theory from GR [46,54,70].…”