Constraining Dark Matter properties with the Inter-Galactic Medium and other probes

According to the standard cosmological (ΛCDM) model, the universe today is mainly composed by a cosmological constant, denoted by Λ, and by Cold Dark Matter (CDM). Whereas this standard paradigm is tremendous agreement with Cosmic Microwave Background (CMB) and Large-Scale Structure (LSS) data, some discrepancies exist, on the cosmological and local determination of the Hubble parameter H 0 , and on the measurement of the amplitude of the matter fluctuations, σ 8 . Additionally, assuming the ΛCDM model, cosmological N -body simulations predict too many dwarf galaxies and too much (C)DM in the innermost regions of galaxies, with respect to observations. Moreover, the dynamical properties of the most massive Milky Way satellites are not reproduced in simulations. The inclusion of baryon feedback is crucial to give a realistic picture of the aforementioned problems, and it shows that baryons can indeed mitigate this CDM “small-scale crisis”. Nevertheless, in the absence of a solution within the ΛCDM framework, and driven by the fact that the fundamental nature of the dark sector is still unrevealed, alternative DM scenarios emerged as a possible way to explain the tensions. In fact, many non-cold (nCDM) candidates have been proposed in order to provide a better description of the structure formation and distribution at small scales, with respect to the ΛCDM model. The effect of the existence of a nCDM particle is a suppression of the matter power spectrum P (k) on small scales, induced, e.g., by its small mass or some non- standard interaction. The suppression in the power spectrum can be described by the so-called transfer function T (k), namely the square root of the ratio of the matter power spectrum in the presence of nCDM with respect to that in the presence of CDM only. Most of the constraints from structure formation data obtained so far, refer to a specific shape of the power suppression, corresponding to the case of thermal Warm DM (WDM), i.e., candidates with a Fermi-Dirac/Bose-Einstein momentum distribution. However, most of the viable particle DM candidates do not feature a thermal momentum distribution, making the oversimplified notion of thermal WDM incapable to describe the shape of their transfer functions. Besides particle DM scenarios, another intriguing possibility that can be tested against small-scale observations is the case where a significant fraction of DM is made by Primordial Black Holes (PBHs), given that Poisson fluctuations in the PBH number density induce a small-scale power enhancement departing from the standard CDM prediction. In this thesis, we firstly introduce a new analytic parametrisation for the transfer function, simple yet versatile enough to describe the gravitational clustering signal of large classes of non-thermal nCDM models, such as sterile neutrinos, ultra-light scalar DM, mixed DM fluids, and interacting DM. The goal is to systematically test these models against the most constraining data set for small-scale deviations with respect to ΛCDM, i.e., high-resolution and high-redshift measurements of the Lyman-α forest, the absorption line pattern produced by intervening inter-galactic neutral hydrogen in the spectra of distant quasars. We thus illustrate how to exploit such observable to constrain practically any non-standard DM scenarios without the need to run any specific numerical simulations, due to the novel parametrisation proposed, to a large suite of pre-computed hydrodynamic simulations, and to an advanced scheme efficiently interpolating across different cosmological models. We demonstrate that the shape of the linear matter power spectrum for thermal WDM models is in mild tension (∼ 2σ C.L.) with data, compared to non-thermal scenarios, and we probe for the first time the small-scale shape of the DM power spectrum for a large set of nCDM models, through extensive Monte Carlo Markov Chain (MCMC) analyses. We then use the Lyman-α data to update current constraints on ultra-light scalar DM models, and we further investigate the cosmological implications at high and low redshifts. For scalar DM constituting more than 30% of the whole of the DM, we obtain a lower limit m & 10 −21 eV for the scalar DM mass, which implies an upper limit on the initial field displacement of φ . 10 16 GeV. We derive limits on the energy scale of cosmic inflation and determine an upper bound on the tensor-to-scalar ratio of r < 10 −3 , in the presence of scalar DM. We also find that there is very little room for scalar DM to solve the CDM small-scale crisis without hitting the Lyman-α bounds. We then focus on quantifying the impact of the Quantum Potential (QP) during the non-linear evolution explored by our hydrodynamic simulations. We improve upon the nearly universally adopted approximation to encode the non-standard nature of the DM candidate in the transfer function used to produce the initial conditions for the simulation, by accurately following the scalar DM evolution in a N -body set-up without approximating its dynamics. Since the new constraints do not depart significantly from the previous ones, this represents the first direct validation of the approximations generally adopted in the literature. Furthermore, we perform a thorough characterisation of the DM halo properties, determining the typical mass scale below which the QP has a significant impact. We then focus on interacting DM scenarios, specifically on models where the dark sector is composed by two types of relic particles, possibly interacting with each other: non-relativistic DM, and relativistic Dark Radiation (DR). Based on the general parametri- sation previously discussed, we introduce a new Lyman-α likelihood, applicable to a wide range of non-standard cosmological models, with complementary scale and redshift coverage with respect to CMB and Baryon Acoustic Oscillation (BAO) data. In fact, for two of the considered interacting scenarios, we find that Lyman-α data strengthen the CMB+BAO bounds on the DM-DR interaction rate by many orders of magnitude. However, models solving the missing satellite problem are still compatible with the new bounds. For the third class of models, Lyman-α data bring no stronger constraints on the interaction rate than CMB+BAO data, except for extremely small values of the DR density. Using a theory-motivated prior on the minimal density of DR, we also find that in this framework the H 0 tension can be reduced from 4.1σ to 2.7σ, while simultaneously accommodating smaller values for σ 8 , as hinted by cosmic shear data. Finally, we present Lyman-α constraints on the PBH mass and abundance, by means of a new grid of high-resolution hydrodynamic simulations. We obtain a marginalised upper limit on the product of the PBH mass and fraction of f PBH M PBH ∼ 60 M at 2σ C.L., when a Gaussian prior on the reionisation redshift is imposed, preventing its posterior distribution to peak on very high values, which are in disagreement with various recent independent measurements. Such constraint weakens to f PBH M PBH ∼ 170 M , when a more conservative flat prior is instead assumed. Both limits improves previous bounds from the same observable by roughly 2 orders of magnitude. We also extend our predictions to non-monochromatic PBH mass distributions, ruling out large parts of the parameter space for two of the most accredited PBH extended mass functions