Curvature and Isocurvature Perturbations in multi-field Gauss-Bonnet inflation

Abstract

We study cosmological perturbations in multi-field inflation in which the scalar fields couple to the Gauss-Bonnet terms through a general coupling function $f(ϕ^a)$. We derive the complete quadratic action for the field perturbations in spatially flat gauge and find that, besides corrections to the kinetic, gradient and mass matrices, the Gauss-Bonnet coupling induces an antisymmetric velocity coupling that vanishes in Einstein gravity. Decomposing the field perturbations into curvature and isocurvature modes, we show that the effective mass of the curvature perturbation and the non-derivative mixing mass vanish identically, $\mathcal{M}_{\mathcal{R}}^2 = \mathcal{M}_{\rm mix}^2 =0$ which are justified by the Weinberg's adiabatic mode. We then compute the curvature power spectrum in two limits. First, when the isocurvature mode is heavy, it can be integrated over all scales. This yields an effective single-field theory of the curvature perturbation with a modified sound speed. Second, when the gradient of the coupling function is aligned with the background trajectory ($f_N =0$), the derivative mixings disappear and the superhorizon transfer of isocurvature into curvature perturbations is governed by the turn rate, which is modified by the Gauss-Bonnet corrections. We also present the tensor power spectrum and the tensor-to-scalar ratio at linear order in the coupling.