An Observational Test of Two-field Inflation

TL;DR

This work establishes a model-independent framework for relating adiabatic and isocurvature perturbations from two-field slow-roll inflation to late-time observables. By introducing transfer functions and rotating to the adiabatic/entropy basis, the authors derive how horizon-crossing slow-roll parameters and the cross-correlation angle $\Delta$ fix the scale-dependence and correlations of the final spectra, including a generalized tensor-scalar consistency relation $\left({P_T}/{P_{\cal R}}\right) \simeq -8 n_T \sin^2\Delta$. They provide explicit expressions for the final spectral tilts $n_{\cal R}$, $n_{\cal S}$, and $n_{\cal C}$ in terms of the four slow-roll parameters and $\Delta$, and discuss model-dependent relations for special cases such as decoupled fields and curvaton scenarios. The framework clarifies how many observables can constrain two-field inflation and how to break degeneracies with gravitational-wave data, while also outlining limitations when more than two light fields are present. Overall, the paper offers a concrete method to test two-field inflation against observations and to reconstruct horizon-exit perturbations from late-time measurements.

Abstract

We study adiabatic and isocurvature perturbation spectra produced by a period of cosmological inflation driven by two scalar fields. We show that there exists a model-independent consistency condition for all two-field models of slow-roll inflation, despite allowing for model-dependent linear processing of curvature and isocurvature perturbations during and after inflation on super-horizon scales. The scale-dependence of all spectra are determined solely in terms of slow-roll parameters during inflation and the dimensionless cross-correlation between curvature and isocurvature perturbations. We present additional model-dependent consistency relations that may be derived in specific two-field models, such as the curvaton scenario.