Cosmological implications of hybrid metric-Palatini $f(\mathcal{R},\mathcal{R}_{μν}\mathcal{R}^{μν})$ gravity

Abstract: The hybrid metric-Palatini gravity with Lagrangian density $L =R+f(\mathcal{R},\mathcal{R}{\mu\nu}\mathcal{R}^{\mu\nu})$ is considered, where $R$ is the metric Ricci scalar and $\mathcal{R}{\mu\nu}$ is the Palatini Ricci tensor. Contrary to the standard hybrid metric-Palatini theory, because of the term $\mathcal{R}_{\mu\nu}\mathcal{R}^{\mu\nu}$ in the action, the model can not be analytically transformed to a scalar-tensor theory. However, on top of a maximally symmetric space-times like the FRW universe, there is a way to solve for a metric compatible connection which we will follow in this paper. The cosmological implications of the resulting model will then be fully considered. The best fit values of the model and cosmological parameters will be obtained by confronting the model with the recent observational data on the Hubble parameter. We will see that the observational data can be explained very good in this model, but, significant deviations from the standard $\Lambda$CDM model could be seen in derivatives of the Hubble parameter $q$, $j$ and $s$. We will perform a statefinder analysis for the model and show that its behavior differs from that of the $\Lambda$CDM model. Also, we will consider the recently proposed $Om$ diagnostics to categorize the dark energy type of the model and obtain the $\omega$-varying alternative of the model that mimics the Hubble flow.