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Abstract

Observation of gravitational waves (GWs) in two different frequency bands is
referred to as {\it multiband GW astronomy}. With the planned Laser
Interferometric Space Antenna (LISA) operating in the $10^{-4}-0.1$ Hz range,
and third generation (3G) ground-based detectors such as the Cosmic Explorer
(CE) and Einstein Telescope (ET), operating in the $1$--$10^4$ Hz range,
multiband GW astronomy could be a reality in about a decade. In this paper we
present the potential of multiband observations of intermediate mass binary
black holes (IMBBHs) of component masses ${\sim}10^2$--$10^3M_{\odot}$ 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 are taken together. We obtain the best
multiband bounds for an IMBBH with a total redshifted mass of $200M_{\odot}$
and a mass ratio of 2. For single-parameter tests, this system at 1 Gpc would
allow us to constrain the deviations on all the PN coefficients to below 10\%
and derive simultaneous bounds on the first seven PN coefficients to below 50\%
(with low spins).