The luminosity-redshift relation in brane-worlds: I. Analytical results

The luminosity distance – redshift relation is analytically given for generalized Randall-Sundrum type II brane-world models containing Weyl fluid either as dark radiation or as a radiation field from the brane. The derived expressions contain both elementary functions and elliptic integrals of the first and second kind. First we derive the relation for models with the Randall-Sundrum fine-tuning. Then we generalize the method for models with cosmological constant. The most interesting models contain small amounts of Weyl fluid, expected to be in good accordance with supernova data. The derived analytical results are suitable for testing brane-world models with Weyl fluid when future supernova data at higher redshifts will be available. PACS Codes: 98.62.Py, 98.80.Jk, 11.25.-w