Cosmic transients as probes of stellar and galaxy evolution. Pair-instability supernovae and the initial-mass function.

The goal of my PhD was to shed light on several uncertain aspects in both stellar and galaxy evolution, by employing the cosmic rates of transients of stellar origin. These comprise type-Ia supernovae (SNe Ia), core-collapse supernovae (CCSNe), long gamma-ray bursts (LGRBs), and pair-instability supernovae (PISNe). Indeed, given the wide range of progenitor masses, from ∼ 2M⊙ up to 300M⊙, SNe and LGRBs offer a unique opportunity to uncover the evolution and properties of intermediate-mass, massive and very-massive stars. Moreover, their rate of occurrence depends not only on the stellar progenitors, but also on the properties of the galactic environment where they are hosted. In particular, the amount of gas mass that is initially available to form stars, its metallicity, and star-formation rate, crucially determine the emergence of these transients. Therefore, in order to accurately compute their rate, one needs to account for both the evolution of their progenitors, and that of their host galaxies. A particularly crucial quantity, that lies in the intersection between these two domains, is the stellar initial-mass function (IMF). This quantity describes the mass distribution assumed by stars after a single episode of star formation, from the collapse and fragmentation of a molecular gas cloud. Since the occurrence of SNe and LGRBs is strictly dependent on the mass of the progenitor, the IMF is key in order to compute their rate. Conversely, the observed rates of such transients can provide an independent way to pose constraints on the IMF. Very-massive stars, above 100 M⊙, are surrounded by especial uncertainties. Indeed, we only have a relatively-low number of direct observations, with mass estimates that can vary. Moreover, most of them are expected to lie in binaries, which might suggest that they are actually the result of previous mergers. Whether such massive stars can be formed in isolation, should not be taken for granted. In this thesis, I present the main projects of my PhD, following an ascending order with progenitor mass. In Chapter 2, I describe our work on constraining the stellar IMF based on the cosmic rates of SNe Ia, CCSNe, and LGRBs. In Chapter 3, I present our study on the cosmic rate of PISNe, and how it can be used to solve the uncertainties surrounding very-massive stars and galaxy evolution. Finally, in Chapter 4, I show our work on PISN occurrence in dense star clusters, aimed at extending the theoretical framework to binary progenitors, and dynamical formation channels. I conclude with a summary of my results, and some future outlooks, in Chapter 5.