Planck data has not found the smoking gun of non-Gaussianity that would have necessitated consideration of inflationary models beyond the simplest canonical single field scenarios. This raises the important question of what these results do imply for
more general models, and in particular, multi-field inflation. In this paper we revisit four ways in which two-field scenarios can behave differently from single field models; two-field slow-roll dynamics, curvaton-type behaviour, inflation ending on an inhomogeneous hypersurface and modulated reheating. We study the constraints that Planck data puts on these classes of behaviour, focusing on the latter two which have been least studied in the recent literature. We show that these latter classes are almost equivalent, and extend their previous analyses by accounting for arbitrary evolution of the isocurvature mode which, in particular, places important limits on the Gaussian curvature of the reheating hypersurface. In general, however, we find that Planck bispectrum results only constrain certain regions of parameter space, leading us to conclude that inflation sourced by more than one scalar field remains an important possibility.
We compute the covariant three-point function near horizon-crossing for a system of slowly-rolling scalar fields during an inflationary epoch, allowing for an arbitrary field-space metric. We show explicitly how to compute its subsequent evolution us
ing a covariantized version of the separate universe or delta-N expansion, which must be augmented by terms measuring curvature of the field-space manifold, and give the nonlinear gauge transformation to the comoving curvature perturbation. Nonlinearities induced by the field-space curvature terms are a new and potentially significant source of non-Gaussianity. We show how inflationary models with non-minimal coupling to the spacetime Ricci scalar can be accommodated within this framework. This yields a simple toolkit allowing the bispectrum to be computed in models with non-negligible field-space curvature.
We study the dependence of turbulent transport coefficients, such as the components of the $alpha$ tensor ($alpha_{ij}$) and the turbulent magnetic diffusivity tensor ($eta_{ij}$), on shear and magnetic Reynolds number in the presence of helical forc
ing. We use three-dimensional direct numerical simulations with periodic boundary conditions and measure the turbulent transport coefficients using the kinematic test field method. In all cases the magnetic Prandtl number is taken as unity. We find that with increasing shear the diagonal components of $alpha_{ij}$ quench, whereas those of $eta_{ij}$ increase. The antisymmetric parts of both tensors increase with increasing shear. We also propose a simple expression for the turbulent pumping velocity (or $gamma$ effect). This pumping velocity is proportional to the kinetic helicity of the turbulence and the vorticity of the mean flow. For negative helicity, i.e. for a positive trace of $alpha_{ij}$, it points in the direction of the mean vorticity, i.e. perpendicular to the plane of the shear flow. Our simulations support this expression for low shear and magnetic Reynolds number. The transport coefficients depend on the wavenumber of the mean flow in a Lorentzian fashion, just as for non-shearing turbulence.
