Inhomogeneous compact extra dimensions

Abstract

We show that an inhomogeneous compact extra space possesses two necessary features --- their existence does not contradict the observable value of the cosmological constant ${\Lambda }_4$ 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 ${\Lambda }_4$. 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.

arXiv comment17 pages, 3 figures

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• Primordial Black Holes from Spatially Varying Cosmological Constant Induced by Field Fluctuations in Extra Dimensions
• Cosmology and matter induced branes
• Cosmological accumulation of conserved numbers in Kaluza-Klein theories