Gaussian Warp Factor: Towards a Probabilistic Interpretation of Braneworlds

Abstract

We investigate Gaussian warped five-dimensional thick braneworlds. Identification of the graviton's wave function (squared) in the extra-dimension with a probability distribution function leads to a straightforward probabilistic interpretation of braneworlds. The extra-coordinate $y$ is regarded as a Gaussian-distributed random variable. Hence, all of the field variables and operators which depend on $y$ are, also, randomly distributed. Four-dimensional measurable (macroscopic) quantities are identified with the corresponding averaged values over the Gaussian distribution. The present scenario represents a new phenomenological approach to smooth thick branes which can not be obtained through 'smearing out' Randall-Sundrum-like (thin) braneworlds.

8 pages, 3 eps figures. Comments on the (no)relation of our approach with Randall-Sundrum-like thick brane scenarios included. A bibliographic reference added. A misprint in Eq.(12) corrected