Enabling Polyspectra via Stochastic Realizations of Inverse Decay Curvature Perturbations in Axion Inflation

Current and upcoming galaxy-redshift surveys offer a promising path for constraining inflationary physics. These constraints are often imposed by relating correlations of the primordial curvature perturbation to the late-time galaxy correlation functions. The primordial correlators can either be computed analytically, or via realizations of the primordial curvature perturbations that are initialized on a grid and evolved numerically according to the classical equations of motion. In this work we take a hybrid approach, initializing the fields in the Bunch-Davies vacuum; and then imposing time evolution through direct numerical integration. Our method efficiently generates realizations of the inverse decay primordial curvature perturbations for axion inflation—an inflationary model in which a pseudoscalar inflaton field couples to a $U(1)$ gauge field via a Chern-Simons interaction. Depending on the choice of parameter $\xi \in \{2,2.5,3\}$, which controls gauge field particle production in this model, our method generates realizations with an average runtime of a few hours on 1 CPU core. We compute the power spectrum and bispectrum from these realizations and find a surprisingly large discrepancy between our result and previous work that used an approximation for the gauge field mode functions—up to a factor of $\sim 4$ difference for the bispectrum in the case of $\xi =2$. This new method enables not only rapid computation of higher order polyspectra, but also generation of initial conditions for large-scale structure analyses.