Early- and late-time cosmology with Gravitational waves: latest results with a focus on topological defects

The recent evidence for a stochastic Gravitational Waves background (SGWB) in PTA datasets leaves open the question of whether the signal is astrophysical or cosmological, namely coming from the primordial universe and originating from physics beyond the Standard Model. In the first part of this talk, I discuss different sources of cosmological SGWB, focusing mainly on topological defects — and in particular cosmic strings of various kinds — which may be formed in symmetry breaking phase transitions in the early universe. Different SGWB curves from cosmic strings may be found in the literature, sometimes varying by orders of magnitude: I will try to explain their shape and the origin of the significant theoretical uncertainties behind them. I will also comment on constraints (current and expected) on these models in other frequency bands (LISA, LVK, ET.) In the second part of the talk I will turn to the late-time universe. If a cosmic string is sufficiently close, it emits a characteristic burst of GWs that can, like for inspiring binary black holes, be searched for individually. I will discuss the properties of these burst signals as well as constraints from their non-observation to date. In the third and last part, I will turn to the sources which have been detected individually — namely compact binary coalescences from the O3 run of LVK and O4a runs — which can be used to measure the Hubble constant H0, and I will highlight the recent results, uncertainties, and prospects for the measurement of H0 with LVK.