Abstract
Three general cases of dynamical interacting dark energy models (\(\mathcal{D}\)-class) are investigated in the context of Brans-Dicke cosmology. Some of important cosmological quantities are calculated for every cases as a function of redshift parameter. The most important part of this paper deals with fitting models with two different expansion history: (\(\mbox{SNIa}+ \mbox{BAO}_{A}+\mathit{Omh}^{2}\) and \(\mbox{SNIa}+ \mbox{BAO}_{A}+H(z)\)) and with two different sets of data for Hubble parameter. This provides a remarkable feature to could analytically see the effects of each analyses and each data sets on final results. The best fitted values of parameters according to these analyses and data points, \(\chi_{\mathit{tot}}^{2}/\mathit{dof}\), AIC and BIC are reported. By these diagnostic tools we found that some of these models have no chance against \(\varLambda \)CDM, even without need to study the structure formation, and could be ruled out. While some (e.g. \(\mathcal{BD-D}C2\) and \(\mathcal{BD-D}A^{*}\)) render the best fit quality, i.e. the value of AIC and BIC and figures shows that they fit perfectly with overall data and reveals a strong evidence in favor of these two models against \(\varLambda \)CDM.
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Notes
One may defines \(\rho _{c}^{(0)}=3H _{0}^{2}\phi _{0}\varsigma \) and hence Eq. (8) reduced to \(\varOmega _{m}^{(0)}=\frac{u_{0}}{1+u_{0}}\) which is fixed for the present time with no dependence to free parameters of models that will be explained in Sects. 3.1, 3.2, 3.3 and thus it is not preferred here.
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Acknowledgements
We would like to express sincere gratitude to Joan Solà for constructive comments and discussion. E. Karimkhani would also like to thank Adrià Gómez-Valent for sharing his knowledge on data fitting procedure.
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Karimkhani, E., Khoadam-Mohammadi, A. Hubble-rate-dependent dark energy in Brans-Dicke cosmology. Astrophys Space Sci 364, 177 (2019). https://doi.org/10.1007/s10509-019-3662-5
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DOI: https://doi.org/10.1007/s10509-019-3662-5