Fundamental theoretical bias in gravitational wave astrophysics and the parametrized post-Einsteinian framework

Abstract

We consider the concept of fundamental bias in gravitational wave astrophysics as the assumption that general relativity is the correct theory of gravity during the entire wave-generation and propagation regime. Such an assumption is valid in the weak field, as verified by precision experiments and observations, but it need not hold in the dynamical strong-field regime where tests are lacking. Fundamental bias can cause systematic errors in the detection and parameter estimation of signals, which can lead to a mischaracterization of the Universe through incorrect inferences about source event rates and populations. We propose a remedy through the introduction of the parametrized post-Einsteinian framework, which consists of the enhancement of waveform templates via the inclusion of post-Einsteinian parameters. These parameters would ostensibly be designed to interpolate between templates constructed in general relativity and well-motivated alternative theories of gravity, and also include extrapolations that follow sound theoretical principles, such as consistency with conservation laws and symmetries. As an example, we construct parametrized post-Einsteinian templates for the binary coalescence of equal-mass, nonspinning compact objects in a quasicircular inspiral. The parametrized post-Einsteinian framework should allow matched filtered data to select a specific set of post-Einsteinian parameters without a priori assuming the validity of the former, thus either verifying general relativity or pointing to possible dynamical strong-field deviations.

Effect of massive perturbers on extreme mass-ratio inspiral waveforms

“…(31). In fact, we see that the result obtained here can be mapped to the parameterized postEinsteinian framework [44] with the choice α = 0, β = 25 1248…”

“…Although on the one hand, one could potentially extract some astrophysical information, on the other, these effects could make it difficult to test general relativity [44]. For such tests to be possible, one must have complete control of the waveforms within general relativity.…”

“…Ignoring such possible acceleration effects could introduce a bias in the extraction of parameters via matched filtering [43,44]. Imagine, for example, that an EMRI GW is detected with vacuum templates.…”

“…Eq. 1 in [44]). As found in that paper, however, there are no known alternative theories to date that could potentially lead to the frequency dependence found in Eq.…”

Black Hole Spectroscopy with Coherent Mode Stacking

“…Furthermore, this method could be adapted to constrain or search for other smallamplitude features that might be shared by a population of events, e.g. common parameterized post-Einsteinianlike [43] corrections to the inspiral phase of the mergers, or common equation-of-state-discriminating frequencies excited in hypermassive remnants of binary neutron star mergers [44][45][46][47][48][49][50][51][52][53][54]. In this latter example, one issue in adapting the coherent stacking method would be achieving phase alignment, due to the challenge in accurately calculating the details of the matter dynamics post-merger.…”