We study a very light dilaton, arising from a scale-invariant ultraviolet theory of the Higgs sector in the standard model  of particle physics. Imposing the scale symmetry below the ultraviolet scale of the Higgs sector, we alleviate the fine-tuning problem associated with the Higgs mass. When the electroweak symmetry is spontaneously broken radiatively  a la Coleman-Weinberg, the dilaton develops a vacuum expectation value away from the origin to give an extra contribution  to the Higgs potential so that the Higgs mass is around the electroweak scale.

LISA may be able to detect the gravitational waves from a first order phase transition at the electroweak scale. We present results from a large campaign of simulations studying a model of such phase transitions, and determine the shape of the power spectrum with unparalleled accuracy. We make concrete predictions of the detectability of sound waves from such a scenario, and note that an accurate measurement could place constraints on the underlying phase transition parameters.

The effective-one-body (EOB) approach has proven to be a very powerful framework to describe analytically the coalescence of compact binary systems in general relativity (GR).  In this seminar, we address the question of extending it to the frame of modified gravities, focussing on the first building block of the EOB approach; that is, mapping the conservative part of the two-body dynamics to the Hamiltonian of a single test particle in effective external fields.

We will briefly review the issue of "information loss" during the Hawking evaporation of a black hole, and argue that the quantum dynamical reduction theories, which have been developed to address the  measurement problem in quantum mechanics,  possess the elements to diffuse the ``paradox”  at the qualitative and at the quantitative level, leading to what seems to be an overall coherent picture.

Post-Newtonian theory enables us to predict the waveform of the gravitational waves emitted by a system of two compact objects coalescing in its inspiral phase. State-of-the-art works provide the phase of the expected signal up to 3.5PN (i.e. up to 1/c^7). Comparison with numerical relativity, as well as the promising evolution of gravitational wave detectors incite us to pursue this computation to a higher order. In our current attempt, we are reaching the phase of the signal at the 4.5PN order (i.e. 1/c^9). For this purpose, the flux emitted by such a system has to be known at 4.5PN.