The likelihood of GODs' existence: Improving the SN1987a constraint on the size of large compact dimensions

The existence of compact dimensions which are accessible only to gravity represents an intriguing possible solution to the hierarchy problem. At present the strongest constraint on the existence of such compact Gravity-Only Dimensions (GODs) comes from SN1987a. Here we report on the first self-consistent simulations of the early, neutrino-emitting phase of a proto-neutron star which include energy losses due to the coupling of the Kaluza-Klein modes of the graviton which arise in a world with GODs. We compare the neutrino signals from these simulations to that from SN1987a and use a rigorous probabilistic analysis to derive improved bounds for the radii of such GODs. We find that the possibility that there are two compact extra dimensions with radii larger than 0.66 $\mu$m is excluded at the 95% confidence level---as is the possibility that there are three compact extra dimensions larger than 0.8 nm.