Abstract : In this paper a cosmological solution of polynomial type H \approx ( t + const . ) ^ { -1 } for the causal thermodynamical approach of Isarel-Stewart , found in [ ] , is constrained using the joint of the latest measurements of the Hubble parameter ( OHD ) and Type Ia Supernovae ( SNIa ) .
Since the expansion described by this solution does not present a transition from a decelerated phase to an accelerated one , both phases can be well modeled connecting both phases by requiring the continuity of the Hubble parameter at z = z _ { t } , the accelerated-decelerated transition redshift .
Our best fit constrains the main free parameters of the model to be A _ { 1 } = 1.58 ^ { +0.08 } _ { -0.07 } ( A _ { 2 } = 0.84 ^ { +0.02 } _ { -0.02 } ) for the accelerated ( decelerated ) phase .
For both phases we obtain q = -0.37 ^ { +0.03 } _ { -0.03 } ( 0.19 ^ { +0.03 } _ { -0.03 } ) and \omega _ { eff } = -0.58 ^ { +0.02 } _ { -0.02 } ( -0.21 ^ { +0.02 } _ { -0.02 } ) for the deceleration parameter and the effective equation of state , respectively .
Comparing our model and LCDM statistically through the Akaike information criterion and the Bayesian information criterion we obtain that the LCDM model is preferred by the OHD+SNIa data .
Finally , it is shown that the constrained parameters values satisfy the criterion for a consistent fluid description of a dissipative dark matter component , but with a high value of the speed of sound within the fluid , which is a drawback for a consistent description of the structure formation .
We briefly discuss the possibilities to overcome this problem with a non-linear generalization of the causal linear thermodynamics of bulk viscosity and also with the inclusion of some form of dark energy .