Fundamental Theoretical Bias in Gravitational Wave Astrophysics and the Parameterized Post-Einsteinian Framework

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 parameterized 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 parameterized post-Einsteinian templates for the binary coalescence of equal-mass, non-spinning compact objects in a quasi-circular 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.

💡 Research Summary

The paper opens by identifying a subtle but potentially serious source of systematic error in gravitational‑wave (GW) astronomy that the authors term “fundamental bias.” This bias arises because all current GW searches and parameter‑estimation pipelines assume, from the outset, that General Relativity (GR) provides the exact description of gravity throughout both the generation and propagation of the waves. While this assumption is well justified in the weak‑field regime—thanks to a plethora of solar‑system tests, binary‑pulsar timing, and other precision experiments—it has never been directly verified in the highly dynamical, strong‑field regime that characterises binary black‑hole or neutron‑star coalescences. If the true theory of gravity deviates from GR in this regime, then using GR‑only templates can (i) reduce detection efficiency, (ii) bias the recovered source parameters (masses, spins, distances, sky locations), and consequently (iii) lead to incorrect astrophysical inferences such as event‑rate estimates or population synthesis results.

To mitigate this problem the authors propose the Parameterized Post‑Einsteinian (PPE) framework. The core idea is to augment the standard GR waveform with a set of dimensionless “post‑Einsteinian” coefficients that smoothly interpolate between pure‑GR templates and those derived from well‑motivated alternative theories (scalar‑tensor, Einstein‑Æther, higher‑dimensional models, etc.). Each coefficient is associated with a specific post‑Newtonian (pN) order and encodes a distinct physical effect—e.g., a modification of the GW phase evolution, an anomalous amplitude damping, or a change in the propagation speed. Crucially, the authors impose theoretical consistency conditions (energy‑momentum conservation, Lorentz invariance, gauge symmetries) on the allowed forms of these coefficients, ensuring that the resulting waveforms remain physically sensible.

The paper provides a concrete construction of PPE waveforms for the simplest inspiral scenario: equal‑mass, non‑spinning compact objects on quasi‑circular orbits. Starting from the GR amplitude (A_{\rm GR}(f)) and phase (\psi_{\rm GR}(f)) expressed as a pN series in the dimensionless frequency variable (x = (\pi M f)^{2/3}), the authors introduce amplitude corrections (\alpha_i) and phase corrections (\beta_i) at each pN order: \