Constraining extra dimensions on cosmological scales with LISA future
  gravitational wave siren data
  We investigate the idea that current cosmic acceleration could be the
consequence of gravitational leakage into extra dimensions on cosmological
scales rather than the result of a non-zero cosmological constant, and consider
the ability of future gravitational-wave siren observations to probe this
phenomenon and constrain the parameters of phenomenological models of this
gravitational leakage. In theories that include additional non-compact
spacetime dimensions, the gravitational leakage intro extra dimensions leads to
a reduction in the amplitude of observed gravitational waves and thereby a
systematic discrepancy between the distance inferred to such sources from GW
and EM observations. We investigate the capability of a gravitational space
interferometer such as LISA to probe this modified gravity on large scales. We
find that the extent to which LISA will be able to place limits on the number
of spacetime dimensions and other cosmological parameters characterising
modified gravity will strongly depend on the actual number and redshift
distribution of sources, together with the uncertainty on the GW measurements.
A relatively small number of sources ($\sim 1$) and high measurement
uncertainties would strongly restrict the ability of LISA to place meaningful
constraints on the parameters in cosmological scenarios where gravity is only
five-dimensional and modified at scales larger than about $\sim 4$ times the
Hubble radius. Conversely, if the number of sources observed amounts to a
four-year average of $\sim 27$, then in the most favourable cosmological
scenarios LISA has the potential to place meaningful constraints on the
cosmological parameters with a precision of $\sim 1\%$ on the number of
dimensions and $\sim 7.5\%$ on the scale beyond which gravity is modified,
thereby probing the late expansion of the universe up to a redshift of $\sim
8$.
