Bounding the mass of the graviton with gravitational waves: effect of higher harmonics in gravitational waveform templates

Observations by laser interferometric detectors of gravitational waves from inspiraling compact binary systems can be used to search for a dependence of the waves' propagation speed on wavelength, and thereby to bound the mass or Compton wavelength of a putative graviton. We study the effect of including higher harmonics, as well as their post-Newtonian amplitude corrections, in the template gravitational waveforms employed in the process of parameter estimation using matched filtering. We consider the bounds that could be achieved using advanced LIGO, a proposed third generation instrument called an Einstein telescope and the proposed space interferometer LISA. We find that in all cases, the bounds on the graviton Compton wavelength are improved by almost an order of magnitude for higher masses when amplitude corrections are included.