Constraints on theories with large extra dimensions

Recently, a number of authors have challenged the conventional assumptionthat the string scale, Planck mass, and unification scale are roughlycomparable. It has been suggested that the string scale could be as low as aTeV. In this note, we explore constraints on these scenarios. We argue that themost plausible cases have a fundamental scale of at least 10 TeV and fivedimensions of inverse size 10 MeV. We show that a radial dilaton mass in therange of proposed millimeter scale gravitational arises naturally in thesescenarios. Most other scenarios require huge values of flux and may not berealizable in M Theory. Existing precision experiments put a conservative lowerbound of 6-10 TeV on the fundamental energy scale. We note that largedimensions with bulk supersymmetry might be a natural framework forquintessence, and make some other tentative remarks about cosmology.Comment: 31 pp. latex. Minor changes, ref. problems fixe