R+αRⁿ Inflation in higher-dimensional Space-times

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We generalise Starobinsky's model of inflation to space-times with D>4 dimensions, where D-4 dimensions are compactified on a suitable manifold. The D-dimensional action features Einstein-Hilbert gravity, a higher-order curvature term, a cosmological constant, and potential contributions from fluxes in the compact dimensions. The existence of a stable flat direction in the four-dimensional EFT implies that the power of space-time curvature, n, and the rank of the compact space fluxes, p, are constrained via n=p=D/2. Whenever these constraints are satisfied, a consistent single-field inflation model can be built into this setup, where the inflaton field is the same as in the four-dimensional Starobinsky model. The resulting predictions for the CMB observables are nearly indistinguishable from those of the latter.