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The recent direct detections of gravitational waves have opened a new window of observation for phenomena in which gravity, instead of light, is the messenger. A few black hole and neutron star mergers have been reported and a plethora of new events, possibly involving new physics, are expected to be detected in the future: we are entering a new era in the history of astronomy and astrophysics. Beyond the astrophysical aspects, gravitational waves can be useful to explore new fundamental physics. The scope of my research project is to explore new ways to investigate new fundamental physics through gravitational waves. Interestingly, gravitational waves provide a unique tool to investigate the very early Universe. In fact, while the early Universe was opaque to light, gravitational waves travel unaltered since their emission and can deliver important information about their source in the early Universe. In order to be produced, gravitational waves need large tensor anisotropies, a condition hard to be achieved in the early Universe, whose homogeneity and isotropy are well established observationally. Hence, extreme events such as preheating and phase transitions are necessary in order to produce a sizeable amount of gravitational waves. Such production mechanisms typically involve non-linear and/or non-perturbative physics and for this reason, they need careful numerical simulations to be investigated. During the last decade, various publicly available lattice codes, such as LatticeEasy have been developed, to help the study of such non-perturbative phenomena. Most of the simulations done so far for the study of non-perturbative dynamics in the early Universe, e.g. LatticeEasy, evolve the Klein-Gordon equation on a fixed grid in an expanding Universe, neglecting the effects of gravity beyond the expansion. However, sometime this approximation misses important effects. GRChombo, on the other hand, is a physics code built around the publicly-available adaptive-mesh framework Chombo. It evolves the GR equations on a grid and uses a fully Adaptive Mesh Refinement (AMR) technique that ensures that all the regions of interest in the simulation remain properly resolved. GRChombo has been (and keeps being) developed in the UK, in a collaboration including scientists based in London, Oxford and Cambridge. In this project, I propose the use of numerical relativity techniques and the code GRChombo to better understand possible signatures of new fundamental physics, with a particular focus on the physics of the early Universe. In particular, I suggest to explore the following physical processes that potentially lead to the production of gravitational waves: i) the stability of inflation in the presence of a light scalar field; ii) preheating; iii) compact solutions in string landscape (i.e. in the presence of multiple fields); iv) phase transitions in the early Universe; v) early matter era; vi) binary boson stars. The final goal is to extract concrete predictions from these processes, in order to identify possible signatures of new fundamental physics in terms of gravitational waves.
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