Primordial Power Spectrum of Five Dimensional Uniform Inflation

Five dimensional (5D) uniform inflation describes a de Sitter (or approximate) solution of 5D Einstein equations, with cosmological constant and a 5D Planck scale $M_* \sim 10^9$ GeV. During the inflationary period all dimensions (compact and non-compact) expand exponentially in terms of the 5D proper time. This set-up requires about 40 $e$-folds to expand the fifth dimension from the fundamental length to the micron size. At the end of 5D inflation (or at any given moment during the inflationary phase) one can interpret the solution in terms of 4D fields using 4D Planck units from the relation $M_p^2 = 2 \pi R M_*^3$, which amounts going to the 4D Einstein frame. This implies that if the compactification radius $R$ expands $N$ $e$-folds, then the 3D space would expand $3N/2$ $e$-folds as a result of a uniform 5D inflation. We reexamine the primordial power spectrum predicted by this model and show that it is consistent with Planck's measurements of the comic microwave background. The best-fit to Planck data corresponds to $R \sim 10~\mu$m. A departure of the angular power spectrum predicted by 4D cosmology is visible at multipole moment $\ell \sim 7$.