The discovery of gravitational waves in 2015 opened a new era in high energy and astroparticle physics. This project aims to contribute to this expanding field by looking for a stochastic background of gravitational waves (SBGW) with the LIGO-Virgo detector. A SBGW could emerge as a superposition of signals from a number of independent and unresolved sources (astrophysical origin) or it can be the result of extreme events occurring during the evolution of our
Universe (cosmological origin). The first goal of this PhD project is the development of new data analysis techniques and joining the LIGO-Virgo collaboration in the search for a SBGW from astrophysical origin. In this context, one of the biggest challenges remains the noise characterization and its proper subtraction from the data. The data from the current observation run (O3) will be used to obtain a deeper understanding of the noise and develop expertise which will be applied to the data of the next observation run (O4), planned to start in 2022. A complementary goal of this PhD is to develop Beyond the Standard Model physics models which could have generated a SBGW of cosmological origin, and derive the corresponding signal shapes. These signals will be used as templates to optimize the searches for a SBGW of cosmological origin at LIGO-Virgo, providing a link between the model-building and the data-analysis part of the PhD project.