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 present a semi‐analytical model for the formation and evolution of a high‐redshift quasar (QSO). We reconstruct a set of hierarchical merger histories of a 1013‐M⊙ dark matter halo and model the evolution of the corresponding galaxy and of its central supermassive black hole. The code gamete/QSOdust consistently follows (i) the black hole assembly via both coalescence with other black holes and gas accretion; (ii) the build‐up and star formation history of the quasar host galaxy, driven by binary mergers and mass accretion; (iii) the evolution of gas, stars and metals in the interstellar medium (ISM), accounting for mass exchanges with the external medium (infall and outflow processes); (iv) the dust formation in supernova (SN) ejecta and in the stellar atmosphere of asymptotic giant branch (AGB) stars, dust destruction by interstellar shocks and grain growth in molecular clouds; and (v) the active galactic nucleus feedback which powers a galactic‐scale wind, self‐regulating the black hole growth and eventually halting star formation. We use this model to study the case of SDSS J1148+5251 observed at redshift 6.4. We explore different star formation histories for the QSO host galaxy and find that Population III stars give a negligible contribution to the final metal and dust masses due to rapid enrichment of the ISM to metallicities >Zcr= 10−6–10−4 Z⊙ in progenitor galaxies at redshifts >10. If Population II/I stars form with a standard initial mass function (IMF) and with a characteristic stellar mass of mch= 0.35 M⊙, a final stellar mass of (1–5) × 1011 M⊙ is required to reproduce the observed dust mass and gas metallicity of SDSS J1148+5251. This is a factor of 3–10 higher than the stellar mass inferred from observations and would shift the QSO closer or on to the stellar bulge–black hole relation observed in the local Universe; alternatively, the observed chemical properties can be reconciled with the inferred stellar mass, assuming that Population II/I stars form according to a top‐heavy IMF with mch= 5 M⊙. We find that SNe dominate the early dust enrichment and that, depending on the shape of the star formation history and on the stellar IMF, AGB stars contribute at z < 8–10. Yet, a dust mass of (2–6) × 108 M⊙ estimated for SDSS J1148+5251 cannot be reproduced considering only stellar sources, and the final dust mass is dominated by grain growth in molecular clouds. This conclusion is independent of the stellar IMF and star formation history.

With the aim of investigating whether stellar sources can account for the ≥10 8 M dust masses inferred from mm/sub-mm observations of samples of 5 < z < 6.4 quasars, we develop a chemical evolution model which follows the evolution of metals and dust on the stellar characteristic lifetimes, taking into account dust destruction mechanisms. Using a grid of stellar dust yields as a function of the initial mass and metallicity over the range 1-40 M and 0-1 Z , we show that the role of asymptotic giant branch (AGB) stars in cosmic dust evolution at high redshift might have been overlooked. In particular, we find that (i) for a stellar population forming according to a present-day Larson initial mass function (IMF) with m ch = 0.35 M , the characteristic time-scale at which AGB stars dominate dust production ranges between 150 and 500 Myr, depending both on the assumed star formation history and on the initial stellar metallicity; (ii) this result is only moderately dependent on the adopted stellar lifetimes, but it is significantly affected by variations of the IMF: for a m ch = 5 M , dust from AGB starts to dominate only on time-scales larger than 1 Gyr and SNe are found to dominate dust evolution when m ch ≥10 M . We apply the chemical evolution model with dust to the host galaxy of the most distant quasar at z = 6.4, SDSS J1148+5251. Given the current uncertainties on the star formation history of the host galaxy, we have considered two models: (i) the star formation history obtained in a numerical simulation by Li et al. which predicts that a large stellar bulge is already formed at z = 6.4, and (ii) a constant star formation rate of 1000 M yr −1 , as suggested by the observations if most of the far-infrared luminosity is due to young stars. The total mass of dust predicted at z = 6.4 by the first model is 2 × 10 8 M , within the range of values inferred by observations, with a substantial contribution (∼80 per cent) of AGB dust. When a constant star formation rate is adopted, the contribution of AGB dust decreases to ∼50 per cent but the total mass of dust formed is a factor of 2 smaller. Both models predict a rapid enrichment of the interstellar medium with metals and a relatively mild evolution of the carbon abundance, in agreement with observational constraints. This supports the idea that stellar sources can account for the dust observed but show that the contribution of AGB stars to dust production cannot be neglected, even at the most extreme redshifts currently accessible to observations.

The growth of the first super massive black holes (SMBHs) at z > 6 is still a major challenge for theoretical models. If it starts from black hole (BH) remnants of Population III stars (light seeds with mass ∼ 100 M ) it requires super-Eddington accretion. An alternative route is to start from heavy seeds formed by the direct collapse of gas onto a ∼ 10 5 M BH. Here we investigate the relative role of light and heavy seeds as BH progenitors of the first SMBHs. We use the cosmological, data constrained semi-analytic model GAMETE/QSOdust to simulate several independent merger histories of z > 6 quasars. Using physically motivated prescriptions to form light and heavy seeds in the progenitor galaxies, we find that the formation of a few heavy seeds (between 3 and 30 in our reference model) enables the Eddington-limited growth of SMBHs at z > 6. This conclusion depends sensitively on the interplay between chemical, radiative and mechanical feedback effects, which easily erase the conditions that allow the suppression of gas cooling in the low metallicity gas (Z < Z cr and J LW > J cr ). We find that heavy seeds can not form if dust cooling triggers gas fragmentation above a critical dust-to-gas mass ratio (D D cr ). In addition, the relative importance of light and heavy seeds depends on the adopted mass range for light seeds, as this dramatically affects the history of cold gas along the merger tree, by both SN and AGN-driven winds.