Big extra dimensions make Λ too small

Abstract

I argue that the true quantum gravity scale cannot be much larger than the Planck length, because if it were then the quantum gravity-induced fluctuations in Λ would be insufficient to produce the observed cosmic "dark energy". If one accepts this argument, it rules out scenarios of the "large extra dimensions" type. I also point out that the relation between the lower and higher dimensional gravitational constants in a Kaluza-Klein theory is precisely what is needed in order that a black hole's entropy admit a consistent higher dimensional interpretation in terms of an underlying spatio-temporal discreteness.