This paper studies how an extra massive field that mixes strongly with the inflaton could leave detailed fingerprints in the early universe. The authors work in an effective theory of inflationary fluctuations with one extra “isocurvature” scalar field. They compute exact predictions for the primordial bispectrum — the three-point correlation of fluctuations — when the mixing strength λ = ρ/H is treated to all orders and the sound speed is set to one.

To make the problem solvable, the authors put the mixing into the free part of the theory. That lets them resum the quadratic mixing exactly and reduce every scale‑invariant tree‑level bispectrum to a single integral over simple “leg kernels” (a Schwinger‑parameter integral in the paper). What standard perturbation theory calls single, double and triple exchange processes become contact diagrams in this resummed description. The paper works out every cubic interaction of dimension four or less in the chosen gauge and gives closed formulas for many coefficients.

The results show new, exact bispectrum shapes when mixing is strong. These shapes are genuinely different from the standard templates that data analysts usually use. In the squeezed limit — where one fluctuation has a much longer wavelength than the other two — the bispectra carry an oscillatory “cosmological collider” signal. The oscillation frequency is universal and set by a dressed mass parameter μ_eff, which includes the effect of mixing, at every exchange order.

The authors also connect to known weak‑mixing results. At small λ they recover the previously known single‑ and double‑exchange perturbative formulas exactly. They further give, for the first time, the leading triple‑exchange coefficient in closed form for any mass, expressed with hypergeometric functions (a class of well‑known special functions). In the strong‑mixing regime the paper finds the collider amplitude scales roughly like exp[π(λ − 2μ_eff)/2] across the plane of mixing and mass parameters. The authors provide code that releases the full set of shapes so templates at any chosen mixing and mass can be produced quickly.