At first glance our understanding of the universe seems to be solely anchored in classical gravity. Indeed, General Relativity (GR) is a powerful tool that provides a successful geometric description of the cosmos. However, if one scratches beneath the surface, the universe becomes a fascinating playground for thermal and quantum phenomena.

I will discuss the scattering of two compact objects interacting via gravity, using the so-called world-line Effective Field Theory approach in the post-Minkowskian expansion (i.e. expanding in the Newton's constant G but not in the velocities). In particular, I will focus on the computation of classical observables such as the total emitted momentum. This is obtained by phase-space integration of the graviton momentum weighted by the modulo squared of the radiation amplitude.

A first-order phase transition in the early universe would have given rise to a stochastic gravitational wave background which may be observable today. In this talk, I will focus on the crucial problem of making reliable predictions of the thermodynamics of such phase transitions in the face of infrared Bose enhancements at high temperature. Such enhancements lead to large theoretical uncertainties in perturbation theory at low orders. I will unravel the structure of the perturbative expansion in this context, and of the misalignment between loop and coupling expansions.

I will present a bit more extended version of the talk that I gave recently at the TAUP2021 conference, with overview of the recent developments in the multi-messenger astronomy.