$R+\alpha R^n$ Inflation in higher-dimensional Space-times

Understand

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.