The direct detection of Gravitational Waves (GWs) by the ground-based LIGO interferometers in 2015 has opened up gravitational wave astronomy in the regime of high-frequencies.  New sources have already been found – namely black-holes with masses larger than those expected from remnants of supernovae explosions and stellar evolution – and it is likely that other unexpected phenomena will be revealed by GW observations in the low redshift universe. Furthermore, with LIGO one can start to probe fundamental physics, as for example cosmic strings, exotic inflationary scenarios and possible modifications to Einstein Gravity. It is however the space-based interferometer LISA (Laser Interferometer Space Antenna) that has the biggest potential in probing fundamental physics and cosmology. It will access low-frequency, high-redshift, regimes out of the reach of ground-based interferometers, and provide a GW window on the TeV energy-scale in the early universe. GW interferometers, possibly in conjunction with electromagnetic and neutrino telescopes for the detection of counterparts, will provide very valuable information helping cosmologists to tackle some of the many puzzles of our universe, namely dark energy (measure of its equation of state through standard sirens), dark matter (could dark matter consist of massive primordial black holes?), and the processes occurring in the early universe “dark era” going from the end of inflation to the occurrence of the QCD phase transition (unaccessible by only other means since photons are tightly coupled).

The subject of this PhD is the study of different aspects of early and late time cosmology in the context of the science behind LISA/LIGO.  The first part deals with phase transitions in the early universe, which can produce a stochastic background of GWs. In first order phase transitions, the signal has at least four origins:  the direct collision of the bubble walls ; the sound waves in the hot plasma surrounding the bubbles created by the bubble expansion ; the magnetohydrodynamic turbulence due to the bubble wall collisions; finally, if the phase transition gives rise to topological defects such as cosmic strings, they can also act as powerful sources of gravitational radiation. Initially, and following on from the stage, the focus will be on sound waves and the possible generation of shocks leading to turbulence in the plasma, both through analytical modeling and numerical estimations. In the context, we will also study possible signatures from the formation of current currying cosmic strings. Finally we will turn to the use of the GW signal from compact binaries to probe late time cosmology, and in particular, we will develop two aspects: first, the effect of the large-scale matter perturbations on the GW propagation and the possibility to use cross-correlation of GW catalogues and large scale galactic surveys to probe the cosmological parameters; second, we will investigate the traces of modified gravity theories in the GW-form, concentrating in particular on those theories which are of interest to solve the cosmological puzzle of the accelerated expansion of the universe, and assess whether GW observations can be useful probes of these modified gravity theories.