Tropical Geometry for the One-Loop Cosmological Collider

Inflation may have occurred at energies up to 10^16 GeV, far beyond any terrestrial collider. The "cosmological collider" program aims to extract the mass spectrum and spin content of particles present during inflation from non-Gaussian correlators. While forthcoming large-scale structure surveys target the critical f_NL ~ O(1) threshold, and future 21cm observations could theoretically reach the gravitational floor of f_NL ~ O(0.01), extracting these primordial signals requires overcoming formidable astrophysical systematics and foregrounds. This reality makes robust theoretical templates more crucial than ever. Moreover, whenever the heavy particle carries a conserved quantum number, such as gauge charge or fermion number, the leading contribution to the bispectrum begins at one loop, making loop-level computations essential rather than a perturbative refinement. I will describe how techniques from tropical geometry, originally developed for multi-loop Feynman integrals in flat space, can be adapted to evaluate loop-level Witten diagrams in de Sitter space in complete generality for the first time. I will present results for the one-loop bubble bispectrum from the derivative portal (d phi)^2 sigma^2 at fully general kinematics and masses, and compare the resulting templates with CMB data. We also compute the triangle diagram.