Scalar-induced gravitational waves from spectator fields

Gravitational waves produced during inflation could carry information about fields that were present in the very early Universe in addition to the inflaton. In this thesis we study the contribution of a set of N massless spectator scalar fields, namely fields that do not drive inflation but can nevertheless source tensor perturbations through gravity. We first compute the leading contribution of these fields to the primordial gravitational- wave spectrum in an exact de Sitter background. The calculation requires a prescrip- tion for regulating the contribution of high-momentum modes, which we implement through a physical cutoff controlled by a parameter γ. We recover the known leading behavior and show analytically that, for large γ, the sourced tensor spectrum grows as γ 3 . We then extend the calculation by one gravitational order within the scalar–tensor interactions considered in this work. The corrections split into contributions with different dependence on the number of spectator fields: four connected terms scale as N , while two factorized terms scale as N 2 . After reducing the time dependence analytically and evaluating the remaining momentum integrals numerically, we find that these corrections grow approximately as γ 7 , corresponding to an additional factor γ 4 relative to the leading result. The factorized terms also develop a logarithmic dependence on the time elapsed after horizon crossing. These results show that the perturbative expansion becomes increasingly sensitive both to the cutoff scale and to the number of spectator fields. At the same time, the strong dependence on the regulating prescription indicates that the isolated sourced contribution should not be interpreted as a regulator-independent observable by itself.