Holographic Ricci dark energy in Nonconservative Unimodular Gravity

The structure of unimodular gravity (UG) is invariant to a subclass of diffeomorphism, the transverse diffeomorphism, due to the unimodular condition ($\sqrt{-g}=\epsilon=cte$). Consequently, there is a freedom to define how the conservation laws of the energy-momentum tensor in unimodular gravity in the cosmological context. One of the main characteristics of the complete system of equations that describe cosmological dynamics in UG is that they form an underdetermined system if the usual conservation law of the energy-momentum tensor is not used in your structure, that is, it is necessary to insert extra information into the system to solve the complete set of equations. In this article, we propose the construction of a background cosmological model based on the description of a holographic dark energy component with a cutoff of the order of Ricci scalar in non-conservative UG. Although this choice is indeed a new addition of information to the cosmological system, the complete set of equations remains underdetermined, however, the new feature of this cosmological model is the appearance of an interaction between matter and dark energy. Indeed, this is a well-known characteristic of cosmological models in which we have holographic dark energy density. Consequently, we propose an ansatz to the interaction term $Q=\beta H \rho_{m}$, and obtain the cosmological parameters of our model. We found a viable universe model with similar characteristics to the $\Lambda \mathrm{CDM}$ model. We performed statistical analysis of the background model using the "Cosmic Chronometer" (CC) data for $H(z)$, and obtain as a result using Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC) as model selection criteria that $\Lambda \mathrm{CDM}$ prevails as the best model. However, the proposed model is competitive when compared to the cosmological model $\omega\mathrm{CDM}$.