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

TL;DR

This paper extends Starobinsky's inflation model to higher-dimensional space-times with compactified extra dimensions, deriving conditions for consistent inflation and showing that predictions closely match the original four-dimensional model.

Contribution

It generalizes Starobinsky's inflation to higher dimensions, establishing constraints on curvature and fluxes, and demonstrates a consistent single-field inflation model with similar CMB predictions.

Findings

Stable flat direction in 4D EFT under specific constraints

Inflation predictions nearly identical to original Starobinsky model

Conditions relate curvature power and flux rank as n=p=D/2

Abstract

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.