Tropical Geometry for the Cosmological Collider

Abstract

Inflation may have occurred at energies up to 10^16 GeV, far beyond the reach of any terrestrial collider. The "cosmological collider" program seeks to extract the mass spectrum and spin content of particles present during inflation from non-Gaussian correlators. Forthcoming large-scale structure surveys target the critical f_NL ~ O(1) threshold, and future 21 cm observations could in principle approach the gravitational floor at f_NL ~ O(0.01). However, isolating these primordial signals places a premium on robust theoretical templates. Significant progress has been made in computing certain tree-level models, but important physical scenarios require going beyond tree level. Whenever the heavy particle coupled to the inflaton carries a conserved quantum number, such as gauge charge or fermion number, the leading contribution to the bispectrum first arises at one loop. This makes loop-level computations essential rather than a mere perturbative refinement. In this talk, I 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 present results for the one-loop bubble bispectrum generated by the derivative portal (d phi)^2 sigma^2 at fully general kinematics and masses, as well as the one-loop triangle diagram. I compare the resulting templates with CMB data. We expect these methods to be applicable to a broad range of cosmological models.