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We investigate the idea that current cosmic acceleration could be theconsequence of gravitational leakage into extra dimensions on cosmologicalscales rather than the result of a non-zero cosmological constant, and considerthe ability of future gravitational-wave siren observations to probe thisphenomenon and constrain the parameters of phenomenological models of thisgravitational leakage. In theories that include additional non-compactspacetime dimensions, the gravitational leakage intro extra dimensions leads toa reduction in the amplitude of observed gravitational waves and thereby asystematic discrepancy between the distance inferred to such sources from GWand EM observations. We investigate the capability of a gravitational spaceinterferometer such as LISA to probe this modified gravity on large scales. Wefind that the extent to which LISA will be able to place limits on the numberof spacetime dimensions and other cosmological parameters characterisingmodified gravity will strongly depend on the actual number and redshiftdistribution of sources, together with the uncertainty on the GW measurements.A relatively small number of sources ($\sim 1$) and high measurementuncertainties would strongly restrict the ability of LISA to place meaningfulconstraints on the parameters in cosmological scenarios where gravity is onlyfive-dimensional and modified at scales larger than about $\sim 4$ times theHubble radius. Conversely, if the number of sources observed amounts to afour-year average of $\sim 27$, then in the most favourable cosmologicalscenarios LISA has the potential to place meaningful constraints on thecosmological parameters with a precision of $\sim 1\%$ on the number ofdimensions 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 $\sim8$.

Constraining extra dimensions on cosmological scales with LISA future gravitational wave siren data