Power Spectra in Double-Field Inflation Using Renormalization-Group Techniques

A perturbative strategy for inflation described by two-inflaton fields is developed using a mathematical analogy with the renormalization-group. Two small quantities, $α$ and $λ$, corresponding to standard slow-roll parameters are defined and systematic expansions of all inflationary quantities in terms of powers of $α$ and $λ$ are found. No other slow-roll parameters are needed. To illustrate this perturbative method in the multi-field context, we adopt a simple two-inflaton model with quadratic potentials in the parameter range where both fields contribute similarly to the dynamics of inflation. The model, even though it is not a viable alternative for phenomenological description of the inflationary period, nicely illustrates subtleties of the perturbative approach. In particular, this method allows us to derive two independent gauge-invariant scalar perturbations that are conserved in the superhorizon limit, overcoming typical problems that emerge in multi-field inflation. Furthermore, it is possible to perform nonperturbative resummations that allow to study the model in a true multi-field regime. We derive tensor and scalar power spectra to the next-to-next-to-leading and next-to-leading orders, respectively, as well as their spectral indices. The hierarchy between the two scalar perturbations allows us to single out the dominant entry of the scalar power-spectrum matrix. Modifications due to the second inflaton occur already at the leading order. Finally, we explain why the quadratic two-inflaton model is not compatible with the present experimental constraints even though non-trivial corrections to scalar perturbations do emerge.