Fourier domain gravitational waveforms for spinning, precessing eccentric binaries

Accurate and efficient gravitational wave templates for merging spinning compact binaries in eccentric orbits are required to extract physics and astrophysics from GW events in the advanced LIGO/VIRGO era. This talk describes efforts to build two  inspiral waveform families for precessing 
spinning compact binaries in eccentric orbits in the Fourier domain. To achieve this, we use a small eccentricity expansion of the waveform amplitudes in order to separate the periastron precession timescale from the orbital timescale, and employ the method of Shifted Uniform Asymptotics (SUA)
to  compute the Fourier transform in the presence of spin-induced precession. We show that the resulting waveforms can yield a median faithfulness above 0.992 when compared to an equivalent time domain waveform with an initial eccentricity of e_0 ~ 0.3. We also show that when spins are large or the accumulated number of cycles is large, using a circular waveform can potentially lead to significant biases 
in the recovery of the parameters, even when the system has fully circularized. This is an effect of the residual eccentricity present when the objects forming the binary have non-vanishing spin components in the orbital plane.