In theories with large extra dimensions, constraints from cosmology lead to nontrivial lower bounds on the gravitational scale M, 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 is 10 TeV or less do deviations from the standard gravitational force law become evident at distances accessible to planned submillimeter 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 $M>\mathrm{}110\mathrm{}\mathrm{TeV},$ corresponding to $r_2<5.1\mathrm{}\times {10}^{-5}\mathrm{mm},$ well beyond the reach of these experiments. We also consider the constraint coming from graviton overclosure of the universe and derive an independent bound $M>\mathrm{}6.5/\sqrt{h}\mathrm{TeV}$ or $r_2<0.015h\mathrm{mm}.$

• Received 26 April 1999

DOI:https://doi.org/10.1103/PhysRevD.60.085008