In the wake of gravitational wave cosmology, we will access information about remote epochs in the history of our universe that eluded us so far. In our isotropic universe, gravitational waves from cosmological sources will present themselves as an isotropic stochastic gravitational wave background —distinguishable from the astrophysical one. Typical sources of cosmic stochastic gravitational wave backgrounds are phase transitions, cosmic strings, gravitational waves generated during inflation (out of quantum fluctuations or exotic particle content) and secondary gravitational waves. Very promisingly, all these sources generate a background that falls within the observational window of future detectors like LISA, DECIGO, MAGIS and PTA. Together with higher precision surveys of the B-mode polarisation of the cosmic microwave background —a unique signature of gravitational waves in the largest scales in the early universe— we will be able to unravel the most fundamental nature of gravity and perhaps find signatures of any modification of general relativity. With this very exciting prospect, the theoretical predictions must match the precision of the experiments and this implies understanding cosmological perturbation theory involving gravitational waves up to second order in perturbation theory. Unfortunately, while the first order calculations are well understood there is a conceptual difficulty in the extension to second order; tensor degrees of freedom mix with scalar degrees and present an ambiguity in their relation to gravitational waves. In other words, the theoretical results of secondary waves so far depend on the gauge (coordinate) choice. Thus, it is the purpose of this project to clarify the ambiguity, get rid of gauge artefacts and provide a gauge invariant formulation of the SGWB and the B-mode polarisation at second order in perturbation theory and, as an application, to look for signatures of modifications of gravity. This research will be widely used in works of gravitational wave cosmology.

Guillem  Domènech Fuertes - INFN PADOVA

Dr. Guillem Domenech is a researcher at the INFN Padova unit. He obtained his doctoral degree in Physics in 2017 at Kyoto University supported by the Monbukagakusho scholarship. He has extensively worked in the field of early universe cosmology contributing to inflation, cosmological perturbation theory, signatures of new physics in the cosmic microwave background, theories of gravity and gravitational waves. His current interest is to explore the history of the early universe using gravitational waves. He also participated in the Balzan cosmology programme (Oxford Univ. and JHU) and the Elusives/invisiblesPlus project (H2020-MSCA-RISE G.A. N.690575).