Phenomenology, astrophysics, and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity

We recently proposed a solution to the hierarchy problem not relying on low-energy supersymmetry or technicolor. Instead, the problem is nullified by bringing quantum gravity down to the TeV scale. This is accomplished by the presence of $n>~2$ new dimensions of submillimeter size, with the SM fields localized on a 3-brane in the higher dimensional space. In this paper we systematically study the experimental viability of this scenario. Constraints arise both from strong quantum gravitational effects at the TeV scale, and more importantly from the production of massless higher dimensional gravitons with TeV suppressed couplings. Theories with $n>\mathrm{}2\mathrm{}$ are safe due mainly to the infrared softness of higher dimensional gravity. For $n=2,$ the six dimensional Planck scale must be pushed above $\sim 30\mathrm{TeV}$ to avoid cooling SN 1987A and distortions of the diffuse photon background. Nevertheless, the particular implementation of our framework within type I string theory can evade all constraints, for any $n>~2,$ with string scale $m_s\sim 1\mathrm{TeV}.$ We also explore novel phenomena resulting from the existence of new states propagating in the higher dimensional space. The Peccei-Quinn solution to the strong $\mathrm{CP}$ problem is revived with a weak scale axion in the bulk. Gauge fields in the bulk can mediate repulsive forces $\sim {10}^6–{10}^8$ times stronger than gravity at submillimeter distances, as well as help stabilize the proton. Higher-dimensional gravitons produced on our brane and captured on a different “fat” brane can provide a natural dark matter candidate.