Integral reduction in cosmology

Cosmic inflation is an hypothesis that predicts a near-exponential expansion of the universe in the first instants of its life. We can regard inflation as a “cosmological” particle accelerator where we can test new physics at higher energies than those accessible with experiments on earth. Indeed, a central challenge in cosmology is to extract fundamental physics from inflationary correlations. To accomplish this ambitious goal, innovative techniques for computing these correlations are needed. In this thesis, I consider the wavefunction of the universe, whose squared modulus provides the probability distribution for computing inflationary correlations. I focus on a class of scalar toy models in FRW cosmology and, drawing inspiration from integral reduction techniques for 1-loop flat-space amplitudes, I develop a systematic way to perform integral reduction for the wavefunction of the universe at tree-level and 1-loop. Here, the integral basis is determined by the singularity structure of a given process and the coefficients are determined by the wavefunction factorization conditions near singularities.