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 the complete solution to a 95% scalar field cosmological model in which the dark matter is modeled by a scalar field Φ with the scalar potentialand the dark energy is modeled by a scalar field Ψ, endowed with the scalar potentialṼ (This model has only two free parameters, λ and the equation of state ωΨ.With this solution, the fine tuning and the cosmic coincidence problems are ameliorated. The dark matter consists of an ultra-light particle, whose mass could be mΦ ≥ 10 −26 eV . All the success of the standard cold dark matter model is recovered. In addition, we clarify the meaning of a scalar Jeans lenght. The model predicts a suppression of the Mass Power Spectrum for small scales having a wave number k > kmin,Φ, where kmin,Φ ≥ 0.3 Mpc −1 , that could help to explain the dearth of dwarf galaxies and the smoothness of galaxy core halos. In fact, the suppression scale depends on the parameter λ mentioned above. This implies that a scalar field could be a good candidate to be the dark matter of the Universe.PACS numbers: 98.80.-k, 95.35.+d

Using numerical techniques, we study the collapse of a scalar field configuration in the Newtonian limit of the spherically symmetric Einstein-Klein-Gordon system, which results in the so called Schrödinger-Newton ͑SN͒ set of equations. We present the numerical code developed to evolve the SN system and related topics, like equilibrium configurations and boundary conditions. Also, we analyze the evolution of different initial configurations and the physical quantities associated with them. In particular, we readdress the issue of the gravitational cooling mechanism for Newtonian systems and find that all systems settle down onto a zero-node equilibrium configuration.

Equilibrium configurations for a self-gravitating scalar field with self-interaction are constructed. The corresponding Schrödinger-Poisson (SP) system is solved using finite differences assuming spherical symmetry. It is shown that equilibrium configurations of the SP system are late-time attractor solutions for initially quite arbitrary density profiles, which relax and virialize through the emission of scalar field bursts; a process dubbed gravitational cooling. Among other potential applications, these results indicate that scalar field dark matter models (in its different flavors) tolerate the introduction of a self-interaction term in the SP equations. This study can be useful in exploring models in which dark matter in galaxies is not point-like.

Continuing with previous works, we present a cosmological model in which dark matter and dark energy are modeled by scalar fields Φ and Ψ, respectively, endowed with the scalar potentials V (Φ) = Vo [cosh (λ √ κoΦ) − 1] andṼ (Ψ) =Ṽo [sinh (α √ κoΨ)] β . This model contains 95% of scalar field. We obtain that the scalar dark matter mass is mΦ ∼ 10 −26 eV. The solution obtained allows us to recover the success of the standard CDM. The implications on the formation of structure are reviewed. We obtain that the minimal cutoff radio for this model is rc ∼ 1.2 kpc.PACS numbers: 98.80.-k, 95.35.+d For years, there has been a lot of evidence about the missing matter in the Universe. It is known that the components of the Universe are radiation, baryons, neutrinos, etc. but observations show that their contribution is less than 5 % of the total mass of the Cosmos, in agreement with Big Bang Nucleosynthesis predictions. This suggests that there must exist a non-baryonic type of matter in galaxies and clusters of galaxies [1,2]. Recently, the observations of Ia-type supernovae [3,4] showed that there must exist another component that accelerates the expansion of the Universe. This new component must have a negative equation of state ω < −1/3, where p = ωρ [5]. The observations point out into a flat Universe filled with radiation, plus baryons, plus neutrinos, etc. contributing with ∼ 5%, a dark matter component with ∼ 25% and the so called dark energy contributing with ∼ 70% to the total mass of the Cosmos [6]. One of the most successful models until now is the Λ Cold Dark Matter (ΛCDM) model, where the dark energy is a cosmological constant [7]. However, some problems of this model has not been solved yet. First of all, if a cosmological constant exists, why is its contribution to the total matter of the same order of magnitude as baryons and cold dark matter?. This is the cosmic coincidence problem. Also, the suggested value for the cosmological constant appears well below the values predicted by particle physics. On the other hand, the existence of a cosmological constant leads to a strong fine tuning problem over the initial conditions of the Universe.These last facts open the possibility for the scalar fields as strong candidates to be the missing matter of the Universe [8][9][10][11]. A reliable model for dark energy is a fluctuating, inhomogeneous scalar field, rolling down a scalar potential, called Quintessence (Q) [15]. For this case, great effort has been done to determine the appropriate scalar potential that could explain current cosmological observations [9,10,13]. One example, is the pure exponential potential [9,13]. It has the advantages that it mimics the dominant density background and it appears naturally as a solution for a completely scalar dominated Universe [14]. But nucleosynthesis constraints require that the scalar field contribution be Ω Φ ≤ 0.2, which indicates that the scalar field would never dominate the Universe [9]. However, a special group of scalar potentials has been proposed in orde...