Observation of gravitational waves (GWs) in two different frequency bands is referred to as multiband GW astronomy. With the planned Laser Interferometric Space Antenna (LISA) operating in the ${10}^{-4}–0.1\mathrm{Hz}$ range, and third-generation (3G) ground-based detectors such as the Cosmic Explorer (CE) and Einstein Telescope (ET) operating in the $1–{10}^4\mathrm{Hz}$ range, multiband GW astronomy could be a reality in the coming decades. In this paper, we present the potential of multiband observations of intermediate-mass binary black holes (IMBBHs) of component masses $\sim {10}^2–{10}^3{M}_{\odot }$ to test general relativity (GR). We show that mutiband observations of IMBBHs would permit multiparameter tests of GR—tests where more than one post-Newtonian (PN) coefficient is simultaneously measured—yielding more rigorous constraints on possible modifications to GR. We also find that the improvement due to multibanding can often be much larger than the best of the bounds from either of the two observatories. The origin of this result, as we shall demonstrate, can be traced to the lifting of degeneracies among the various parameters when the information from LISA and 3G is taken together. A binary of redshifted total mass of $200M_{\odot }$ gives the best bounds. Such a system at 1 Gpc and mass ratio $m_1/m_2=2$ would bound the deviations on all the PN coefficients to below 10% when they are measured individually, and additionally place simultaneous bounds on the first seven PN coefficients to below 50%.

• Received 23 June 2020
• Revised 30 November 2020
• Accepted 22 December 2020

DOI:https://doi.org/10.1103/PhysRevD.103.024036