Avoiding an Empty Universe in RS I Models and Large-N Gauge Theories

Many proposed solutions to the hierarchy problem rely on dimensional transmutation in asymptotically free gauge theories, and these theories often have dual descriptions in terms of a warped extra dimension. Gravitational calculations show that the confining phase transition in Randall-Sundrum models is first-order and parametrically slower than the rate expected in large-N gauge theories. This is dangerous because it leads to an empty universe problem. We argue that this rate suppression arises from approximate conformal symmetry. Though this empty universe problem cannot be solved by using the radion for low-scale inflation, we argue that if the radion potential is asymptotically free, another instanton for the RS phase transition can proceed as $e^{-N^2}$. We also discuss the existence of light magnetic monopoles ($\sim 100$ TeV) as a possible signature of such a phase transition.