A Modal Approach to Constrain Inflation through Numerical Bispectra

Abstract

Constraining inflationary models with high precision bispectra across broad parameter ranges is a challenging task, requiring intensive computations at all stages, first, predicting the primordial inflation bispectrum from quantum field theory, secondly, projecting this forward with transfer functions to the late universe and, finally, comparing with the bispectrum extracted from the observational data and matching mock catalogues. Here, the longstanding separable \texttt{Modal} pipeline for constraining primordial bispectrum templates using WMAP and Planck CMB data has been supplemented by the more recently developed \texttt{Primodal} code to accurately calculate bispectra numerically from inflation models, showing great potential for enhanced computational efficiency; \texttt{Primodal} exploits the in-in separability of the tree-level in-in formalism, together with a separable mode-expansion technique to bypass the need for point-by-point bispectrum calculations. Building upon this progress, we propose a bispectrum pipeline that systematically explores the parameter space of inflationary Lagrangians, numerically computing the tree-level bispectrum (and power spectrum) for each scenario and comparing with the \texttt{Modal} bispectrum decompositions obtained from the Planck 2018 data. Our pipeline identifies and excludes disfavored scenarios through this analysis, providing direct constraints on the parameter space, the sound speed and other quantities from the surviving observationally viable scenarios. This is preparatory work for a planned analysis using much higher-resolution CMB data from the Simons Observatory. To validate our pipeline, we perform a proof-of-concept analysis of the IR DBI inflation model, obtaining constraints of $c_s \geq 0.073$ for the sound speed and $β\leq 0.39$ for the parameter space, demonstrating the pipeline's accuracy and effectiveness.