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One fundamental goal of the newly born gravitational wave astronomy is discovering the origin of the observed binary black hole mergers. Towards this end, identifying features in the growing wealth of data may help in distinguishing different formation pathways. While large uncertainties still affect the binary formation models, spin-mass relations remain characteristic features of specific classes of channels. By focusing on the effective inspiral spin \\(_eff\\), the best reconstructed spin-related merger parameter, we show that current GWTC-3 data support the hypothesis that a fraction of events may display mass-spin correlations similar to one expected by dynamical formation channels of either astrophysical or primordial nature. We quantify the Bayesian evidence in favour of those models, which are substantially preferred when compared to the Gaussian phenomenological model adopted to describe the distribution of \\(_eff\\) in the recent LIGO/Virgo/KAGRA population analyses.

We revisit the scenario in which stable particles of a dark sector are produced through the complete evaporation of light primordial black holes (PBHs) formed in the early Universe. We investigate in detail the role of isocurvature perturbations that may arise in this framework. PBHs inherit Poisson fluctuations on unobservable small scales at formation; however, in the presence of primordial non-Gaussianity that couples long- and short-wavelength modes, these fluctuations can source isocurvature perturbations on cosmological scales. Such perturbations are unavoidably transferred to the dark sector particles emitted via Hawking evaporation. We highlight the potential impact of isocurvature constraints on dark sector particles produced through PBH evaporation. Along the way, we re-assess the constraints on this scenario arising from the overproduction of dark matter (DM), accounting for both PBH evaporation and gravitational production (freeze-in) during (after) inflation, as well as bounds from warm DM and the overproduction of scalar-induced gravitational waves.

Primordial Black Holes (PBH) can form in the early universe and might comprise a significant fraction of the dark matter. Interestingly, they are accompanied by the generation of Gravitational Wave (GW) signals and they could contribute to the merger events currently observed by the LIGO/Virgo Collaboration (LVC). In this thesis, we study the PBH scenario, addressing various properties at the formation epoch and the computation of abundance beyond the Gaussian paradigm, while also developing the theoretical description of PBH evolution through accretion and mergers, with particular focus on modelling their GW signatures. In a second part, we compare the primordial scenario with current GW data, seizing the possible contribution of PBH binaries to LVC signals and forecasting the potential of future GW detectors, such as Einstein Telescope and LISA, to detect mergers of primordial binaries and the stochastic GW background induced at second order by the PBH formation mechanism.

Several bright and massive galaxy candidates at high redshifts have been recently observed by the James Webb Space Telescope. Such early massive galaxies seem difficult to reconcile with standard \\(\\Lambda\\) Cold Dark Matter model predictions. We discuss under which circumstances such observed massive galaxy candidates can be explained by introducing primordial non-Gaussianity in the initial conditions of the cosmological perturbations.

Microscopic horizonless relics could form in the early universe either directly through gravitational collapse or as stable remnants of the Hawking evaporation of primordial black holes. In both cases they completely or partially evade cosmological constraints arising from Hawking evaporation and in certain mass ranges can explain the entirety of the dark matter. We systematically explore the stochastic gravitational-wave background associated with the formation of microscopic dark-matter relics in various scenarios, adopting an agnostic approach and discussing the limitations introduced by existing constraints, possible ways to circumvent the latter, and expected astrophysical foregrounds. Interestingly, this signal is at most marginally detectable with current interferometers but could be detectable by third-generations instruments such as the Einstein Telescope, strengthening their potential as discovery machines.

We propose that the totality of dark matter in the universe might ascribe its origin to one of the key properties of cosmological inflation, that it may be eternal: regions that at the end of the primordial accelerated expansion of the universe never reheated, but keep eternally inflating, manifest themselves as primordial black holes in our observable universe. This mechanism can provide a primordial black hole abundance which is larger than the standard one due to the gravitational collapse of sizeable overdensities in the radiation phase. It also predicts a broad spectrum for the curvature perturbation and a flat stochastic gravitational wave background at a level of \\(_GW h^2 10^-10\\) up to the mHz.

In the Standard Model, the Higgs potential develops an instability at high field values when the quartic self-coupling runs negative. Large quantum fluctuations during cosmic inflation could drive the Higgs field beyond the potential barrier, creating regions that would be catastrophic for our observable universe. We point out that the extreme-value statistics describing the peaks (maxima) of the Higgs values is the correct statistics to infer the condition to avoid vacuum instability. Even if this statistics delivers a bound on the Hubble rate during inflation which is only a factor \\(\\sqrt{2}\\) stronger than the one commonly adopted in the literature, it is qualitatively distinct and we believe worthwhile communicating it.

Making use of both the stochastic approach to the tunneling phenomenon and the threshold statistics, we offer a simple argument to show that critical bubbles may be correlated in first-order phase transitions and biased compared to the underlying scalar field spatial distribution. This happens though only if the typical energy scale of the phase transition is sufficiently high. We briefly discuss possible implications of this result, e.g. the formation of primordial black holes through bubble collisions.

The merger rate of primordial black holes depends on their initial clustering. In the absence of primordial non-Gaussianity correlating short and large-scales, primordial black holes are distributed à la Poisson at the time of their formation. However, primordial non-Gaussianity of the local-type may correlate primordial black holes on large-scales. We show that future experiments looking for CMB \\(\\mu\\)-distortion would test the hypothesis of initial primordial black hole clustering induced by local non-Gaussianity, while existing limits already show that significant non-Gaussianity is necessary to induce primordial black hole clustering.

Cosmological observations precisely measure primordial variations in the density of the Universe at megaparsec and larger scales, but much smaller scales remain poorly constrained. However, sufficiently large initial perturbations at small scales can lead to an abundance of ultradense dark matter minihalos that form during the radiation epoch and survive into the late-time Universe. Because of their early formation, these objects can be compact enough to produce detectable microlensing signatures. We investigate whether the EROS, OGLE, and HSC surveys can probe these halos by fully accounting for finite source size and extended lens effects. We find that current data may already constrain the amplitudes of primordial curvature perturbations in a new region of parameter space, but this conclusion is strongly sensitive to yet undetermined details about the internal structures of these ultradense halos. Under optimistic assumptions, current and future HSC data would constrain a power spectrum that features an enhancement at scales \\(k \\sim 10^7/{\\rm Mpc}\\), and an amplitude as low as \\(\\mathcal{P}_\\zeta\\simeq 10^{-4}\\) may be accessible. This is a particularly interesting regime because it connects to primordial black hole formation in a portion of the LIGO/Virgo/Kagra mass range and the production of scalar-induced gravitational waves in the nanohertz frequency range reachable by pulsar timing arrays. These prospects motivate further study of the ultradense halo formation scenario to clarify their internal structures.