R + αRn inflation in higher-dimensional space-times

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.