2024/08/29 by Paolo Benincasa, Benincasa, Paolo, Giacomo Brunello +7 · 3 citations
Earth and Planetary Sciences · Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Gravity Measurements #High Energy Physics - Theory (hep-th) #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2408.16386
openalex publication_date 2024/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Understanding the loop corrections to cosmological observables is of paramount importance for having control on the quantum consistency of a theory in an expanding universe as well as for phenomenological reasons. In the present work, we begin with a systematic study of such corrections in the context scalar toy models whose perturbative Bunch-Davies wavefunction enjoys an intrinsic definition in terms of cosmological polytopes, focusing on one-loop graphs. Owing to the underlying twisted period integral representation they admit, their combinatorial structure along with their vector space structure, emerging from polynomial ideals algebra and intersection theory, are exploited to set-up and analyse the differential equations that the two- and three-site one-loop corrections have to satisfy upon variation of the external kinematic variables. We find that, while the two-site contribution can be written in terms of multiple-polylogarithms, this is no longer true for the three-site case, for which elliptic structures appear. As a non-trivial check, we consider the scattering amplitude limit, recovering the known result in terms of polylogarithms only.