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Inhomogeneous compact extra dimensions

We show that an inhomogeneous compact extra space possesses two necessary features— their existence does not contradict the observable value of the cosmological constant Λ4 in pure f(R) theory, and the extra dimensions are stable relative to the "radion mode" of perturbations, the only mode considered. For a two-dimensional extra space, both analytical and numerical solutions for the metric are found, able to provide a zero or arbitrarily small Λ4. A no-go theorem has also been proved, that maximally symmetric compact extra spaces are inconsistent with 4D Minkowski space in the framework of pure f(R) gravity.