Fundamental Theoretical Bias in Gravitational Wave Astrophysics and the Parameterized Post-Einsteinian Framework (0909.3328v2)

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 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.

• The paper introduces the ppE framework to enhance GR waveform templates for testing strong-field deviations.
• It reveals that assuming GR in extreme regimes can lead to significant systematic errors in GW data analysis.
• The proposed approach enables rigorous post-detection analysis, improving astrophysical characterization and testing alternative gravity theories.

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

The paper in question explores a significant concern within the field of gravitational wave (GW) astrophysics: the intrinsic bias originating from the assumption that General Relativity (GR) correctly describes gravitational phenomena across all pertinent regimes, specifically the wave-generation and propagation phases. While GR remains robustly validated in relatively weak-field conditions, such as those observable in the Solar System and binary pulsars, the lack of rigorous testing in the dynamical strong-field regime suggests potential for significant systematic errors in current GW analysis methodologies.

Sources and Consequences of Bias

The authors identify this fundamental theoretical bias as distinct from experimentally-induced systematics, concentrating instead on post-processing and analysis biases embedded within the tools developed for GW data interpretation. The a priori acceptance of GR as the definitive theory in the strong-field regime can result in misleading inferences about the astrophysical properties and event rates detected by instruments like LIGO, VIRGO, and GEO. Considering GR has been insufficiently tested in the dynamical strong-field, regions where spacetime curvature is extreme, the authors raise justified concerns over its uncritical application.

Parameterized Post-Einsteinian Framework

Addressing this issue, the paper proposes the parameterized post-Einsteinian (ppE) framework. Developed analogously to the parameterized post-Newtonian (ppN) approach, the ppE framework suggests systematic enhancements to existing GR waveform templates by integrating post-Einsteinian parameters that bridge GR with potentially plausible alternative theories of gravity.

These parameters aim to allow waveform models to be sufficiently flexible to embody deviations that could arise in non-GR scenarios without losing consistency with foundational physical principles such as conservation laws and symmetries. The core objective is to utilize these expanded waveform templates in matched filtering techniques, permitting the identification or exclusion of strong-field deviations from GR without pre-emptively negating the potential attributes of alternative theoretical frameworks.

Implications and Future Directions

An essential contribution of this proposal is its potential application in the analysis workflows post-GW detection. By re-examining detected signals using ppE-enhanced templates, researchers can both check for GR consistency and enhance the detection of potential strong-field deviations, thus providing a more reliable basis for the characterization of astrophysical sources.

The immediate implications of this methodological evolution include facilitating rigorous tests of GR even in the challenging dynamical strong-field regime while preparing the groundwork for detecting potential deviations from GR—deviations which could unveil new physical insights or necessitate modifications to existing gravitational theories.

Future advancements in this line of research could yield more nuanced ppE templates tailored for an array of astrophysical sources beyond the binary coalescence of non-spinning, equal-mass compact objects which were the paper's starting point. This work also suggests that interdisciplinary collaboration could be critical in evolving how alternative gravitational theories can motivate the development of nuanced, beyond-GR waveform templates.

While direct detection using ppE templates might encounter practical limitations because of increased computational demands, such frameworks possess substantial potential in post-detection analysis, enhancing the science return from current and next-generation GW observatories.