The luminosity-redshift relation in brane-worlds: II. Confrontation with experimental data
The luminosity distance - redshift relation for a wide class of generalized Randall-Sundrum type II brane-world models with Weyl fluid is compared to the presently available supernova data. We find that there is a class of spacially flat models with different amounts of matter $\Omega_{\rho}$ and Weyl fluid $\Omega_{d}$, which have a very similar fitting quality. The best-fit models are equally likely and can be regarded as extensions of the $\Lambda $CDM model, which is also included. We examine three models with different evolutionary history of the Weyl fluid, characterized by a parameter $\alpha =0,~2$ and$~3$. The first model describes a brane which had radiated energy into the bulk some time ago, but in recent times this energy exchange has ceased and only a dark radiation ($\alpha =0$) is left. In the other two models the Weyl-fluid describes a radiating brane throughout the cosmological evolution, up to our days. We find that the trought of the fitting surface extends over a wider $\Omega_{d}$-range with increasing $\alpha $, but the linear correlation of $\Omega_{d}$ and $\Omega_{\rho}$ holds all over the examined $\Omega_{d}$ range.