Brane universes tested against astronomical data
  We discuss observational constrains coming from supernovae imposed on the behaviour of the Randall-Sundrum models. The data indicates that, under the assumption that we admit zero pressure dust matter on the brane, the cosmological constant is still needed to explain current observations. The observations from supernovae give a large value of the density parameter for brane matter $\Omega_{\lambda,0} \simeq 0.01$ as the best fit. For high redshifts $z > 1.2$, the difference between the brane model and the $\Lambda$CDM (Perlmutter) model becomes detectable observationally. From the maximum likelihood method we obtained the favored value of $\Omega_{\lambda,0} = 0.004 \pm 0.016$ for $\Omega_{k,0}=0$ and $\Omega_{\mathrm{m},0}=0.3$. This gives the limit $\Omega_{\lambda,0} < 0.02$ at $1 \sigma$ level. While the model with brane effects is preferred by the supernovae type Ia data, the model without brane fluid is still statistically admissible. For comparison the limit on brane effects which comes from CMB anisotropies and BBN is also obtained. The uncertainty in the location of the first peak gives a stronger limit $\Omega_{\lambda,0} < 1.0 \cdot 10^{-12}$, whereas from BBN we obtain that $\Omega_{\lambda,0} < 1.0 \cdot 10^{-27}$. However, both very strict limits are obtained with the assumption that brane effects do not change the physics in the pre-recombination era, while the SN Ia limit is model independent.We demonstrate that the fit to supernovae data can also be obtained if we admit the phantom matter $p = - (4/3) \varrho$ on the brane, where this matter mimics the influence of the cosmological constant. Finally, we propose to check for dark radiation and brane tension by the application of the angular diameter of galaxies minimum value test. 
Mariusz P. Dabrowski, Wlodzimierz Godlowski and Marek Szydlowski