Stochastic Gravitational Wave Background from Primordial Black Holes

One of the biggest problems in modern cosmology is to assess the nature of dark matter. We propose Primordial Black Holes (PBHs) as a possible candidate and we investigate how this scenario can be probed with the Stochastic Gravitational Wave Background (SGWB). We begin by briefly analyzing the $\Lambda$CDM model, summarizing the main tools used for cosmology. After having described how PBHs could have formed in the early Universe, we present recent observational constraints on their masses. Moreover, we explore the possibility that two Primordial Black Holes form a binary either in the early Universe by decoupling from the Hubble flow, or in the late Universe by gravitational capture. Then, we investigate a tool to probe PBHs as dark matter candidate: we introduce gravitational waves, and in particular the stochastic gravitational wave background. We describe the SGWB that could be generated from PBH binaries and we review a numerical code for the computation of the SGWB from Astrophysical Black Holes. The final goal of this Master Thesis is to improve such tool so to include the SGWB from PBH binaries. Finally, we present the analysis of the SGWB from 5 different mass functions (3 monochromatic and 2 extended), both for early and late binaries. We conclude by emphasizing the importance of the SGWB as a new tool to be used by the next generation of gravitational wave detectors.