  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.
