The Universe is undergoing a late time acceleration. We investigate the idea that this 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 (GW) siren observations to probe this phenomenon and constrain the parameters of phenomenological models of this gravitational leakage. A gravitational space interferometer such as LISA will observe massive black hole binary (MBHB) merger events at cosmological distances, and will also provide sky localization information that may permit optical and other electromagnetic (EM) surveys to identify an EM counterpart of these events. 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 LISA to probe this modified gravity on large scales, specifically in the Dvali, Gabadadze and Porrati (DGP) model. Additionally, we include a Supernova Ia sample at lower redshift in order to explore the efficacy of this cosmological probe across a range of redshifts. We then use previously published simulated catalogues of cosmologically distant MBHB merger events detectable by LISA, and which are likely to produce an observable EM counterpart. 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 distance measurements. A relatively small number of sources (∼ 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 ∼ 4 times the Hubble radius. Conversely, if the number of sources observed amounts to a four-year average of ∼ 27, then in the most favourable cosmological scenarios LISA has the potential to place meaningful constraints on the cosmological parameters—with a precision of ∼ 1% on the number of dimensions and ∼ 7.5% on the scale beyond which gravity is modified, thereby probing the late expansion of the universe up to a redshift of ∼ 8, i.e. on scales not yet tested by present EM observations.

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We study the nonlinear evolution of unstable flux compactifications, applying numerical relativity techniques to solve the Einstein equations in D dimensions coupled to a q-form field and positive cosmological constant. We show that initially homogeneous flux compactifications are unstable to dynamically forming warped compactifications. In some cases, we find that the warping process can serve as a toy-model of slow-roll inflation, while in other instances, we find solutions that eventually evolve to a singular state. Analogous to dynamical black hole horizons, we use the geometric properties of marginally trapped surfaces to characterize the lower dimensional vacua in the inhomogeneous and dynamical settings we consider. We find that lower-dimensional vacua with a lower expansion rate are dynamically favoured, and in some cases find spacetimes that undergo a period of accelerated expansion followed by contraction.