Field-space surprises in multi-field preheatingI will discuss preheating in multi-field models of inflation with a curved field-space manifold, focusing on two well-studied families of models.The first includes Higgs inflation and models where the fields couple non-minimally to gravity. I will describe both analytical progress as well as recent lattice simulations that have been used to capture significant nonlinear effects like backreaction and rescattering. I will show how we can extract the effective equation of state and typical time-scales for the onset of thermalization, quantities that could affect the usual mapping between predictions for primordial perturbation spectra and measurements of anisotropies in the cosmic microwave background radiation. For large values of the nonminimal coupling constants, efficient particle production gives rise to nearly instantaneous preheating.In the case of two-field generalizations of $\alpha$-attractor models with a highly curved hyperbolic field-space manifold, analytical progress can be made for preheating using the WKB approximation and Floquet analysis. I will show the emergence of a simple scaling behavior of the Floquet exponents for large values of the field-space curvature, that enables a quick estimation of the reheating efficiency for any large value of the field-space curvature. In this regime one can observe and explain universal preheating features that arise for different values of the potential steepness. For highly curved field-space manifolds preheating is essentially instantaneous.

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