The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on ‘Black holes, Gravitational waves and Fundamental Physics’.

We report the first results of the LISA Pathfinder in-flight experiment. The results demonstrate that two free-falling reference test masses, such as those needed for a space-based gravitational wave observatory like LISA, can be put in free fall with a relative acceleration noise with a square root of the power spectral density of 5.2±0.1  fm s^{-2}/sqrt[Hz], or (0.54±0.01)×10^{-15}  g/sqrt[Hz], with g the standard gravity, for frequencies between 0.7 and 20 mHz. This value is lower than the LISA Pathfinder requirement by more than a factor 5 and within a factor 1.25 of the requirement for the LISA mission, and is compatible with Brownian noise from viscous damping due to the residual gas surrounding the test masses. Above 60 mHz the acceleration noise is dominated by interferometer displacement readout noise at a level of (34.8±0.3)  fm/sqrt[Hz], about 2 orders of magnitude better than requirements. At f≤0.5  mHz we observe a low-frequency tail that stays below 12  fm s^{-2}/sqrt[Hz] down to 0.1 mHz. This performance would allow for a space-based gravitational wave observatory with a sensitivity close to what was originally foreseen for LISA.

We show that current microlensing and dynamical observations of the Galaxy permit to set interesting constraints on the Dark Matter local density and profile slope towards the galactic centre. Assuming state-of-the-art models for the distribution of baryons in the Galaxy, we find that the most commonly discussed Dark Matter profiles (viz. Navarro-Frenk-White and Einasto) are consistent with microlensing and dynamical observations, while extreme adiabatically compressed profiles are robustly ruled out. When a baryonic model that also includes a description of the gas is adopted, our analysis provides a determination of the local Dark Matter density, 0 = 0.20-0.56 GeV/cm3 at 1, that is found to be compatible with estimates in the literature based on different techniques. We show that current microlensing and dynamical observations of the Galaxy permit to set interesting constraints on the Dark Matter local density and profile slope towards the galactic centre. Assuming state-of-the-art models for the distribution of baryons in the Galaxy, we find that the most commonly discussed Dark Matter profiles (viz. Navarro-Frenk-White and Einasto) are consistent with microlensing and dynamical observations, while extreme adiabatically compressed profiles are robustly ruled out. When a baryonic model that also includes a description of the gas is adopted, our analysis provides a determination of the local Dark Matter density, ρ0 = 0.20 − 0.56 GeV/cm 3 at 1σ, that is found to be compatible with estimates in the literature based on different techniques.

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In the months since the publication of the first results, the noise performance of LISA Pathfinder has improved because of reduced Brownian noise due to the continued decrease in pressure around the test masses, from a better correction of noninertial effects, and from a better calibration of the electrostatic force actuation. In addition, the availability of numerous long noise measurement runs, during which no perturbation is purposely applied to the test masses, has allowed the measurement of noise with good statistics down to 20  μHz. The Letter presents the measured differential acceleration noise figure, which is at (1.74±0.05)  fm s^{-2}/sqrt[Hz] above 2 mHz and (6±1)×10  fm s^{-2}/sqrt[Hz] at 20  μHz, and discusses the physical sources for the measured noise. This performance provides an experimental benchmark demonstrating the ability to realize the low-frequency science potential of the LISA mission, recently selected by the European Space Agency.