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Holographic Ricci dark energy (DE) that has been proposed ago has faced problems of future singularity. In the present work, we consider the Ricci DE with an additive constant in its density as running vacuum energy. We have analytically solved the Friedmann equations and also the role played by the general conservation law followed by the cosmic components together. We have shown that the running vacuum energy status of the Ricci DE helps to remove the possible future singularity in the model. The additive constant in the density of the running vacuum played an important role, such that, without that, the model predicts either eternal deceleration or eternal acceleration. But along with the additive constant, equivalent to a cosmological constant, the model predicts a late time acceleration in the expansion of the universe, and in the far future of the evolution it tends to de Sitter universe.

The Ricci dark energy is a model inspired by the holographic dark energy models with the dark energy density being proportional to Ricci scalar curvature. Here, this model is studied in the bumblebee gravity theory. It is a gravitational theory that exhibit spontaneous Lorentz symmetry breaking. Then, the modified Friedmann equation is solved for two cases. In the first case, the coupling constant $\xi$ is equal to zero and in the second case a solution in the vacuum, where the bumblebee field becomes a constant that minimizes the potential, is considered. The coupling constant controls the interaction gravity-bumblebee.

This research focuses on exploring the dynamics of a cosmos model under the influence of Ricci dark energy within the framework of modified Lyra geometry. The modified field equations of Einstein for Lyra’s geometry are introduced, and specific solutions are obtained for a Big Rip cosmos scenario. Additionally, various physical and geometrical aspects of the cosmos are comprehensively investigated and discussed.

A derivation of the Ricci dark energy from quantum field theory of fluctuating "matter" fields in a classical gravitational background is presented. The coupling to the dark energy, the parameter α, is estimated in the framework of our formalism, and qualitatively it appears to be within observational expectations.

In this work, we develop some interesting models of cosmos exhibiting anisotropic properties in the extended scalar-tensor theory. In the first place, we consider the LRS Bianchi type I (BI) geometry filled with matter contents as magnetized bulk viscous cloud of strings. We developed analytic solutions and explore the cosmological significance of some interesting physical measures like cosmic volume, directional Hubble parameter, deceleration parameter, viscosity factor, particle energy density, shear and expansion scalars, and string tension density. Moreover, modified holographic Ricci dark energy is introduced in anisotropic scenario to discuss the dynamics of anisotropic comic models. In order to construct the exact cosmic solutions, we take hybrid law of scale factor as well as some viable ansatz for scalar field and its scalar potential. The physical viability of model parameters is discussed through graphical analysis. Physical analysis of both models show that our results are in agreement with the current observations and hence are cosmologically viable and promising.

The impact of anisotropy on the Ricci dark energy cosmologies is investigated where it is assumed that the geometry of the universe is described by Bianchi type I (BI) metric. The main goal is to determine the astrophysical constraints on the model by using the current available data as type Ia supernovae (SNIa), the Baryon Acoustic Oscillation (BAO), and the Hubble parameter $H(z)$ data. In this regard, a maximum likelihood method is applied to constrain the cosmological parameters. Combining the data, it is found out that the allowed range for the density parameter of the model stands in $-3.6\times 10^{-3}\lesssim {\mathrm{\Omega }}_{{\sigma }_0}\lesssim -2.6\times 10^{-3}$. With the help of the Supernova Legacy Survey (SNLS) sample, we estimate the possible dipole anisotropy of the Ricci dark energy model. Then, by using a standard ${\chi }^2$ minimization method, it is realized that the transition epoch from early decelerated to current accelerated expansion occurs faster in Ricci dark energy model than $\mathrm{\Lambda }$CDM model. The results indicate that the BI model for the Ricci dark energy is consistent with the observational data.