Testing general relativity and probing the merger history of massive black holes with LISA

Observations of binary inspirals with the proposed Laser Interferometer Space Antenna (LISA) will allow us to place bounds on alternative theories of gravity and to study the merger history of massive black holes (MBH). These possibilities rely on LISA's parameter estimation accuracy. We update previous studies of parameter estimation for inspiralling compact binaries of MBHs, and for inspirals of neutron stars into intermediate-mass black holes, including non-precessional spin effects. We work both in Einstein's theory and in alternative theories of gravity of the scalar-tensor and massive-graviton types. Inclusion of non-precessional spin terms in MBH binaries has little effect on the angular resolution or on distance determination accuracy, but it degrades the estimation of intrinsic binary parameters such as chirp mass and reduced mass by between one and two orders of magnitude. The bound on the coupling parameter omega(BD) of scalar-tensor gravity is significantly reduced by the presence of spin couplings, while the reduction in the graviton-mass bound is milder. LISA will measure the luminosity distance of MBHs to better than similar to 10% out to z similar or equal to 4 for a (10(6) + 10(6))M-circle dot binary, and out to z similar or equal to 2 for a (10(7) + 10(7))M-circle dot binary. The chirp mass of a MBH binary can always be determined with excellent accuracy. Ignoring spin effects, the reduced mass can be measured within similar to 1% out to z = 10 and beyond for a (10(6)+ 10(6)) MD binary, but only out to z similar or equal to 2 for a (10(7) + 10(7))M-circle dot binary. Present-day MBH coalescence rate calculations indicate that most detectable events should originate at z similar to 2-6: at these redshifts LISA can be used to measure the two black-hole masses and their luminosity distance with sufficient accuracy to probe the merger history of MBHs. If the low-frequency LISA noise can only be trusted down to 10(-4) Hz, parameter estimation for MBHs (and LISA's ability to perform reliable cosmological observations) will be significantly degraded.