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Multi-field Conformal Cosmological Attractors

We describe a broad class of multi-field inflationary models with spontaneously broken conformal invariance. It generalizes the recently discovered class of cosmological attractors with a single inflaton field. In the new multi-field theories, just as in the previously studied single-field models, the moduli space has a boundary (Kahler cone) in terms of the original homogeneous conformal variables. Upon spontaneous breaking of the conformal invariance and switching to the Einstein frame, this boundary moves to infinity in terms of the canonically normalized inflaton field. This results in the exponential stretching and flattening of scalar potentials in the vicinity of the boundary of the moduli space, which makes even very steep potentials perfectly suitable for the slow-roll inflation. These theories, just like their single-field versions, typically lead to inflationary perturbations with n_s =1-2/N and r = 12/N^2, where N is the number of e-foldings.