We investigate the possible bounds which could be placed on alternative
theories of gravity using gravitational wave detection from inspiralling
compact binaries with the proposed LISA space interferometer. Specifically, we
estimate lower bounds on the coupling parameter \omega of scalar-tensor
theories of the Brans-Dicke type and on the Compton wavelength of the graviton
\lambda_g in hypothetical massive graviton theories. In these theories,
modifications of the gravitational radiation damping formulae or of the
propagation of the waves translate into a change in the phase evolution of the
observed gravitational waveform. We obtain the bounds through the technique of
matched filtering, employing the LISA Sensitivity Curve Generator (SCG),
available online. For a neutron star inspiralling into a 10^3 M_sun black hole
in the Virgo Cluster, in a two-year integration, we find a lower bound \omega >
3 * 10^5. For lower-mass black holes, the bound could be as large as 2 * 10^6.
The bound is independent of LISA arm length, but is inversely proportional to
the LISA position noise error. Lower bounds on the graviton Compton wavelength
ranging from 10^15 km to 5 * 10^16 km can be obtained from one-year
observations of massive binary black hole inspirals at cosmological distances
(3 Gpc), for masses ranging from 10^4 to 10^7 M_sun. For the highest-mass
systems (10^7 M_sun), the bound is proportional to (LISA arm length)^{1/2} and
to (LISA acceleration noise)^{-1/2}. For the others, the bound is independent
of these parameters because of the dominance of white-dwarf confusion noise in
the relevant part of the frequency spectrum. These bounds improve and extend
earlier work which used analytic formulae for the noise curves.Comment: 16 pages, 9 figures, submitted to Classical & Quantum Gravit