In this work we first used the data points of low-redshift Hubble diagrams for Pantheons, quasars, and GRBs to put constraints on the present value of cosmographic parameters in an independent cosmography approach. To do this, we used different combinations of data samples including Pantheon, Pantheon + quasars, Pantheon + GRB, finally Pantheon + quasars + GRB. In the context of a cosmography approach, we obtained the best-fit values of cosmographic parameters as well as their confidence regions up to 3 − σ uncertainties for different combinations of data samples. Our results showed that the best-fit value of the deceleration parameter q0 varies in the range of −0.844 to −0.702 and the best fit of jerk parameter j0 varies in the range of 1.60 to 2.61 for different combinations of data samples. Note that here we used the Hubble diagrams of quasars and GRBs, respectively, derived in Lusso & Risaliti (2016a) and Demianski et al. (2017a). In the calibration procedure to form the Hubble diagrams of both quasars and GRBs, they have used the SNIa data at low redshifts. Their results for quasars and GRBs samples are consistent with that of the SNIa samples at the low-redshift universe. Hence we adopted their calibrations and used their Hubble diagrams for quasars and GRBs. In the case of concordance ΛCDM cosmology, our results are also compatible with recent work in Lusso et al. (2019). They confirmed the presence of a tension between Λ cosmology and the best-fit cosmographic parameters ∼4σ with SnIa+quasars, at ∼2σ with SnIa+GRBs, and at  4σ with the whole SnIa+quasars+GRB data set (Lusso et al. 2019). Furthermore, we studied some relevant DE parameterizations as well as the concordance ΛCDM cosmology using the Hubble diagrams of Pantheons, quasars, and GRB observations in the context of a cosmography approach. The DE parameterizations studied in our analysis are wCDM, CPL, and Pade parameterizations. First, using the different combinations of data samples and in the context of the MCMC algorithm, we calculate the χ2 function of the distance modulus to find the best-fit values and also the 1 − σ uncertainty of cosmological parameters for each DE parameterization. Using the chain of data obtained for cosmological parameters, we found the best-fit values and the 1 − σ confidence region of the cosmographic parameters of DE parameterizations. Comparing the results for DE models with those obtained for the model-independent approach leads us to conclude that the model is in better (worse) agreement with Hubble diagrams of Pantheons, quasars, and GRBs. In the first stage, using the solely Pantheon sample, we found that the wCDM model is the most compatible model with the result of model-independent constraints and on the other hand the concordance ΛCDM model is the worst model. In the second step, by combining the GRB data to the Pantheon sample, we obtained disappointing results for the ΛCDM model. In this case the q0 parameter of the ΛCDM has a 3.8 − σ tension with that of the model-independent cosmography approach. Moreover, the j0 parameter of ΛCDM cosmology has roughly 5 − σ tension with that of the model-independent approach. These results will be more complicated when we see the results of other DE models and parameterizations that we studied in this work. We observed that wCDM, CPL, and Pade parameterizations are in better agreement with the results of the model-independent cosmography approach rather than the concordance model. In the third and fourth steps, using the combinations Pantheon+quasars and Pantheon+GRB+quasars data points, we obtained the same results again, supporting our results in previous steps. So we conclude that the concordance ΛCDM cosmology has much tension with observations of quasars and GRBs at higher redshift. Note that the DE parameterizations studied in this work are in better agreement with Hubble diagrams of high-redshift quasars and GRB observations. Finally, we reconstructed the Hubble parameter using the best-fit value of cosmographic parameters for both model-independent approaches, the ΛCDM model, and DE parameterizations. We observed that for different data sample combinations, the evolution of reconstructed H(z) in a concordance ΛCDM model has a maximum deviation from the confidence region compared to different DE parameterizations. Upon this result, we can conclude that among the different cosmological models studied in this work, the ΛCDM has the minimum compatibility with the predictions of a model-independent approach and thus it is falsified by a cosmography approach. The large value of tensions (between 3σ to 6σ for different data combinations) that we observed between the cosmographic parameters of ΛCDM and those we obtained in the model-independent approach support this claim again that we should explore other alternatives for standard ΛCDM cosmology. We observed that other DE parameterizations in this study cannot be refuted in the context of a cosmography approach. Our results for ΛCDM cosmology are in agreement with the results of recent work (Yang et al. 2019; Khadka & Ratra 2020), which were obtained using a different approach and different data sets. Although in the literature it has been thoroughly affirmed that the ΛCDM describes the evolution of the universe until recent times, our conclusion confirms the result of Benetti & Capozziello (2019) that show large tensions emerge at higher redshifts for ΛCDM. Our analysis can be extended by considering other cosmic observations in the context of a cosmography approach.
Citation: Lusso et al. (2019)
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Citation: Demianski et al. (2017a)
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Citation: Yang et al. 2019
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Citation: Benetti & Capozziello (2019)
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