Extra dimensions present a new flatness problem

TL;DR

This paper addresses whether large extra dimensions inexorably reproduce four-dimensional Lorentz invariance or if a genuine flatness problem emerges in the bulk. It develops the inequivalence principle, showing that higher-dimensional Lorentz violation can persist in the dimensionally reduced theory due to bulk curvature lacking $SO(3,1)$ isometry, and that inflation cannot universally restore symmetry without compromising the warp factor. The authors argue that a new flatness problem arises for warped noncompact and large compact extra dimensions, challenging standard inflationary resolutions. They also outline observational avenues, such as time-delayed signals across species, to constrain bulk Lorentz-violating signatures, highlighting the role of upcoming experiments in probing extra-dimensional physics.

Abstract

There is no known fundamental reason to demand as a cosmological initial condition that the bulk possess an SO(3,1) isometry. On the contrary, one expects bulk curvature terms that violate the SO(3,1) isometry at early epochs, leading to a violation of Lorentz invariance on our brane. Demanding that the Lorentz noninvariant terms are small leads to a new ``flatness'' problem, not solved by the usual formulation of inflation. Furthermore, unlike in four dimensions, the Lorentz violations induced from the bulk curvature cannot always be removed as the infrared cutoff is taken arbitrarily large. This means that the equivalence principle in higher dimensions does not guarantee the equivalence principle in dimensionally reduced theories. Near-future experiments are expected to severely constrain these Lorentz-violating ``signatures'' of extra dimensions.