Probing bulk viscous matter-dominated models with Gamma-ray bursts

In this paper we extend the range of consistency of a constant bulk viscosity model to redshifts up to $z\sim 8.1$. In this model the dark sector of the cosmic substratum is a viscous fluid with pressure $p= -\zeta \theta$, where $\theta$ is the fluid-expansion scalar and $\zeta$ is the coefficient of bulk viscosity. Using the sample of 59 high-redshift GRBs reported by Wei (2010), we calibrate GRBs at low redshifts with the Union 2 sample of SNe Ia, avoiding then the circularity problem. Testing the constant bulk viscosity model with GRBs we found the best fit for the viscosity parameter $\tilde{\zeta}$ in the range $0<\tilde{\zeta}<3$, being so consistent with previous probes; we also determined the deceleration parameter $q_0$ and the redshift of transition to accelerated expansion. Besides we present an updated analysis of the model with CMB5-year data and CMB7-year data, as well as with the baryon acoustic peak BAO. From the statistics with CMB it turns out that the model does not describe in a feasible way the far far epoch of recombination of the universe, but is in very good concordance for epochs as far as $z\sim 8.1$ till present.