Confronting the Hubble diagram of gamma-ray bursts with Cardassian cosmology

We construct the Hubble diagram of gamma-ray bursts (GRBs) with redshifts reaching up to z similar to 6, by using five luminosity versus luminosity indicator relations calibrated with the Cardassian cosmology. This model has a major interesting feature: despite being matter dominated and. at, it can explain the present accelerated expansion of the universe. This is the first study of this class of models using high redshift GRBs. We have performed a. squared statistical analysis of the GRBs calibrated with the Cardassian model, and also combined them with both the current cosmic microwave background and baryonic acoustic oscillation data. Our results show consistency between the current observational data and the model predictions; in particular, the best fit parameters obtained from that chi(2) analysis are in agreement with those obtained from previous investigations. The influence of these best fit parameters on the redshift at which the universe would start to follow the Cardassian expansion, i.e., z(card), and on both the redshift at which the universe supposedly had started to accelerate, i.e., z(acc), and the age-redshift relation, H(0)t(0), are also discussed. Our results also show that the universe, from the point of view of GRBs, had undergone a transition to acceleration at a redshift z approximate to 0.2-0.7, which agrees with the type Ia supernovae results. One important point that we notice is that despite the statistical analysis being performed with a model that does not need any vacuum energy, we found that the results attained using this cosmological model are compatible with those obtained with the concordance cosmology (Lambda-CDM; CDM: cold dark matter), as far as GRBs are concerned. Hence, after confronting the Cardassian scenario with the GRB Hubble diagram, our main conclusion is that GRBs should indeed be considered a tool complementary to several other observational studies for doing precision cosmology.