New Insights into Cosmological Integrals and Their Asymptotic Behavior

Recent research by Paolo Benincasa and Francisco Vazão, titled "The Asymptotic Structure of Cosmological Integrals," provides a comprehensive analysis of the asymptotic behavior of perturbative contributions to observables in various power-law Friedmann-Robertson-Walker (FRW) cosmologies. The authors focus on scalar toy models, including conformally-coupled and massless scalars across different dimensions, which can be defined through generalized cosmological polytopes.

The study reveals that the perturbative contributions can be expressed as integrals of canonical functions associated with these polytopes and weighted graphs. A significant finding is that the asymptotic behavior of these integrals is determined by a specific class of geometric structures known as nestohedra, which exist in the graph-weight space. This relationship holds true at both tree and loop levels of perturbation theory.

Furthermore, the authors demonstrate how singularities in cosmological processes, represented by graphs, can be linked to their subgraphs. This connection allows for a detailed understanding of potential divergence directions in both infrared and ultraviolet regimes, as well as the degree of divergence associated with these integrals. The implications of this research extend to the application of sector decomposition for extracting leading and subleading divergences, enhancing the understanding of cosmological observables.

This work is pivotal for advancing theoretical frameworks in cosmology and high-energy physics, potentially influencing future research directions in these fields. The findings can aid in refining models that describe the universe's evolution and the fundamental forces at play.

The full paper can be accessed at arXiv:2402.06558.