Cosmological Constraints on Theories with Large Extra Dimensions

TL;DR

This work investigates cosmological constraints on ADD-type theories with large extra dimensions, focusing on the two extra dimensions case ($n=2$) where sub-mm gravity deviations could occur. By computing the production and decay of Kaluza-Klein gravitons and their contribution to the cosmic diffuse gamma-ray background (CDG), the authors derive lower bounds on the fundamental gravity scale $M_F$ and upper bounds on the compactification radius $r_2$, depending on the assumed normalcy temperature $T_*$. The CDG bound is the strongest constraint (e.g., $M_F > 110$ TeV and $r_2 < 5.1 imes 10^{-5}$ mm for $T_*=1$ MeV), with a complementary overclosure bound ($r_2 < 0.015 h$ mm); increasing $T_*$ to $2.15$ MeV tightens the CDG bound to $M_F > 350$ TeV and $r_2 < 5.2 imes 10^{-6}$ mm. The authors also discuss potential evasion mechanisms via extra branes, but conclude that the cosmological bounds are robust in typical scenarios, making the two-dimensional ADD scenario unlikely to be probed by planned sub-mm gravity experiments.

Abstract

In theories with large extra dimensions, constraints from cosmology lead to non-trivial lower bounds on the fundamental scale M_F, corresponding to upper bounds on the radii of the compact extra dimensions. These constraints are especially relevant to the case of two extra dimensions, since only if M_F is 10 TeV or less do deviations from the standard gravitational force law become evident at distances accessible to planned sub-mm gravity experiments. By examining the graviton decay contribution to the cosmic diffuse gamma radiation, we derive, for the case of two extra dimensions, a conservative bound M_F > 110 TeV, corresponding to r_2 < 5.1 times 10^-5 mm, well beyond the reach of these experiments. We also consider the constraint coming from graviton overclosure of the universe and derive an independent bound M_F > 6.5 h^(-1/2) TeV, or r_2 < .015 h mm.