  Motivated by the parameterized post-Einsteinian (ppE) scheme devised by Yunes
and Pretorius, which introduces corrections to the post-Newtonian coefficients
of the frequency domain gravitational waveform in order to emulate alternative
theories of gravity, we compute analytical time domain waveforms that, after a
numerical Fourier transform, aim to represent (phase corrected only) ppE
waveforms. In this formalism, alternative theories manifest themselves via
corrections to the phase and frequency, as predicted by General Relativity
(GR), at different post-Newtonian (PN) orders. In order to present a generic
test of alternative theories of gravity, we assume that the coupling constant
of each alternative theory is manifestly positive, allowing corrections to the
GR waveforms to be either positive or negative. By exploring the capabilities
of massive black hole binary GR waveforms in the detection and parameter
estimation of corrected time domain ppE signals, using the current eLISA
configuration (as presented for the ESA Cosmic Vision L3 mission), we
demonstrate that for corrections arising at higher than 1PN order in phase and
frequency, GR waveforms are sufficient for both detecting and estimating the
parameters of alternative theory signals. However, for theories introducing
corrections at the 0 and 0.5 PN order, GR waveforms are not capable of covering
the entire parameter space, requiring the use of non-GR waveforms for detection
and parameter estimation.
