Holographic Ricci dark energy has been proposed ago has faced with problems of future singularity. In the present work we consider the Ricci dark energy with an additive constant in it's 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 dark energy 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.

Earlier studies have shown that, in a two component model of the universe with dark matter and the running vacuum energy which is phenomenologically a combination of H 2 andḢ, produces either eternal deceleration or acceleration in the absence of a bare constant in the density of the running vacuum. In this paper we have shown that, in the interaction scenario, where the interaction between matter and vacuum is introduced through a phenomenological term, the two component model is capable of causing a transition from a prior decelerated to a later accelerated epoch without a bare constant in the running vacuum density. On contrasting the model with the cosmological data, we have found that the interaction coupling constant, is small enough, for a slow decay of the running vacuum. The model is subjected to dynamical system analysis which revealed that the end de Sitter phase of the model is a stable one. We did an analysis on the thermal behavior of the system, which shows that the entropy is bounded at the end stage so that the system is behaving like an ordinary macroscopic system. Apart from these we have also performed the state finder diagnostic analysis which implies the quintessence nature of running vacuum and confirms that the model will approach the standard ΛCDM in the future arXiv:1807.00483v3 [gr-qc]

Holographic Ricci dark energy evolving through its interaction with dark matter is a natural choice for the running vacuum energy model. We have analyzed the relative significance of two versions of this model in the light of SNIa, CMB, BAO and Hubble data sets using the method Bayesian inferences. The first one, model 1, is the running holographic Ricci dark energy (rhrde) having a constant additive term in its density form and the second is one, model 2, having no additive constant, instead the interaction of rhrde with dark matter is accounted through a phenomenological coupling term. The Bayes factor of these models in comparison with the standard ΛCDM have been obtained by calculating the likelihood of each model for four different data combinations, SNIa(307)+CMB+BAO, SNIa(307)+CMB+BAO+Hubble data, SNIa(580)+CMB+BAO and SNIa(580)+CMB+BAO+Hubble data. Suitable flat priors for the model parameters has been assumed for calculating the likelihood in both cases. Our analysis shows that, according to the Jeffreys scale, the evidence for ΛCDM against both model 1 and model 2 is very strong as the Bayes factor of both models are much less than one for all the data combinations.

The holographic Ricci dark energy (HRDE) can be treated as a running vacuum due to its analogy in the energy density, which is a combination of [Formula: see text] and [Formula: see text], the model can predict either eternal acceleration or eternal deceleration. In the earlier works, we have shown that the presence of additive constant in the energy density or by considering possible interaction between dark sectors through a phenomenological term, the model can predict a transition from a prior decelerated to a late accelerated epoch. This paper analyzes the cosmic evolution of HRDE as running vacuum with a nonlinear interaction (NLI) between dark sectors in a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. We consider three possible NLI forms which give analytically feasible solutions. We have constrained the model using the Type1a Supernova(Pantheon) + CMB(Planck 2018) + BAO(SDSS) data and evaluated the best estimated values of all the model parameters. We have analyzed the evolution of the Hubble parameter and deceleration parameter of all three cases. We perform state finder analysis of the model, which implies the quintessence nature of the model and found that it is distinguishably different from the standard [Formula: see text]CDM model. The dynamical system analysis of all three cases confirms the evolution of the universe from an unstable prior matter-dominated era to a stable end de Sitter phase.

The holographic Ricci dark energy can be treated as a running vacuum due to its analogy in the energy density, which is a combination of H and Ḣ, the model can predict either eternal acceleration or eternal deceleration. In the earlier works, we have shown that the presence of additive constant in the energy density or by considering possible interaction between dark sectors through a phenomenological term, the model can predict a transition from a prior decelerated to a late accelerated epoch. This paper analyses the cosmic evolution of holographic Ricci dark energy as running vacuum with a nonlinear interaction between dark sectors in a flat FLRW universe. We consider three possible nonlinear interaction forms which give analytically feasible solutions. We have constrained the model using the Type1a Supernova(Pantheon)+CMB(Planck 2018)+BAO(SDSS) data and evaluated the best-estimated values of all the model parameters. We have analyzed the evolution of the Hubble parameter and deceleration parameter of all three cases. We perform state finder analysis of the model, which implies the quintessence nature of the model and found that it is distinguishably different from the standard ΛCDM model. The dynamical system analysis of all three cases confirms the evolution of the universe from an unstable prior matter-dominated era to a stable end de Sitter phase.