This paper proposes a way that the early-universe inflaton could change the complex phases of Standard Model interactions and leave a measurable signal in the pattern of primordial fluctuations. The authors study a modular-invariant extension of the Standard Model in which a complex scalar field called the modulus (τ) plays the role of the inflaton. If τ changes in time during inflation, the phases of the Yukawa couplings (the numbers that set fermion masses and mixings) also change. That time dependence acts like an effective chemical potential for Standard Model fermions and can produce a distinctive one-loop “cosmological collider” signal in the three-point correlation of curvature perturbations (the bispectrum). The paper gives detailed formulas for Dirac fermions with such chemical potentials in a de Sitter inflationary background.

Concretely, the authors embed the Standard Model in a framework with modular symmetry so that Yukawa couplings become functions of τ. They consider the case where the real part of τ is rolling during inflation. A convenient choice of field basis makes the time dependence appear as a coupling of ∂τ to particle currents, which is equivalent to introducing chemical potentials µ for left- and right-handed fermion components. The modulus motion also affects the Higgs field: a chemical-potential–type term reduces the Higgs effective mass squared by µ_H^2, and if this dominates the other contributions the Higgs develops a nonzero inflationary vacuum expectation value v ≈ µ_H / sqrt(2 λ_H). That Higgs value gives Standard Model fermions Dirac masses m = y v and, together with the chemical potentials, controls fermion production and propagation.

Why this matters: particle production amplified by these chemical potentials makes the fermion loop contribution to the inflaton fluctuation bispectrum larger than it would otherwise be. In simple terms, the evolving modulus biases fermion helicities, increasing the number of certain fermion modes. Those modes can propagate far and leave oscillatory signatures in the bispectrum that are characteristic of heavy particles present during inflation. The authors compute these one-loop effects and give precise expressions for fermion propagators and loop corrections in de Sitter space. They argue that next‑generation cosmological measurements could be sensitive to sub‑Planckian values of the modulus decay constant f, a parameter that controls how strongly τ affects Standard Model fields.