We investigate the matter density perturbation $δ_m$ and power spectrum $P(k)$ in the running vacuum model (RVM) with the cosmological constant being a function of the Hubble parameter, given by $Λ= Λ_0 + 6 σH H_0+ 3νH^2$, in which the linear and quadratic terms of $H$ would originate from the QCD vacuum condensation and cosmological renormalization group, respectively. Taking the dark energy perturbation into consideration, we derive the evolution equation for $δ_m$ and find a specific scale $d_{cr}=2 π/k_{cr}$, which divides the evolution of the universe into the sub and super-interaction regimes, corresponding to $k \ll k_{cr}$ and $k \gg k_{cr}$, respectively. For the former, the evolution of $δ_m$ has the same behavior as that in the $Λ$CDM model, while for the latter, the growth of $δ_m$ is frozen (greatly enhanced) when $ν+ σ>(<)0$ due to the couplings between radiation, matter and dark energy. It is clear that the observational data rule out the cases with $ν<0$ and $ν+ σ<0$, while the allowed window for the model parameters is extremely narrow with $ν, |σ| \lesssim \mathcal{O}(10^{-7})$.
We study a special running vacuum model (RVM) with $Λ= 3 αH^2+3βH_0^4 H^{-2}+Λ_0$, where $α$, $β$ and $Λ_0$ are the model parameters and $H$ is the Hubble one. This RVM has non-analytic background solutions for the energy densities of matter and radiation, which can only be evaluated numerically. From the analysis of the CMB power spectrum and baryon acoustic oscillation along with the prior of $α>0$ to avoid having a negative dark energy density, we find that $α<2.83\times 10^{-4}$ and $β=(-0.2^{+3.9}_{-4.5})\times 10^{-4}$ (95$\%$ C.L.). We show that the RVM fits the cosmological data compar…
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 $\dot H$, 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 a running vacu…
We investigate the power spectra of the CMB temperature and matter density in the running vacuum model (RVM) with the time-dependent cosmological constant of $Λ= 3 νH^2 + Λ_0$, where $H$ is the Hubble parameter. In this model, dark energy decreases in time and decays to both matter and radiation. By using the Markov chain Monte Carlo method, we constrain the model parameter $ν$ as well as the cosmological observables. Explicitly, we obtain $ν\leq 1.54 \times 10^{-4}$ (68\% confidence level) in the RVM with the best-fit $χ^2_{\mathrm{RVM}} = 13968.8$, which is slightly smaller than $χ^2_{Λ\math…
Brans-Dicke (BD) cosmology is reconsidered from an approach in which the model can be formulated in $Λ$CDM form, but at the expense of replacing the rigid cosmological constant $Λ$ with a dynamical quasivacuum component which depends on a small parameter $ε$. The product of $ε$ times the BD-parameter $ω_{\rm BD}$ becomes exactly determined in terms of the ordinary cosmological parameters. The GR limit is recovered for $ω_{\rm BD}\to\infty$ when $ε\to 0$. We solve the background cosmology of the model as well as the perturbations equations. When fitted to the cosmological data, we find that the…
We present an analysis of the Brans-Dicke cosmological model with a cosmological constant and cold dark matter (BD-$Λ$CDM). We find that the BD-$Λ$CDM is favored by the overall cosmological data (SNIa+BAO+$H(z)$+LSS+CMB) when it is compared with the standard model of cosmology. The BD-$Λ$CDM model can be viewed from the GR perspective as a Running Vacuum Model (RVM) with a time evolving vacuum energy density. Due to this fact and also to its time evolving effective gravitational coupling, the model can alleviate the $σ_8$ and the $H_0$ tensions at a time. We also present the results for differ…
The cosmological term, $Λ$, in Einstein's equations is an essential ingredient of the `concordance' $Λ$CDM model of cosmology. In this mini-review presentation, we assess the possibility that $Λ$ can be a dynamical quantity, more specifically a `running quantity' in quantum field theory in curved spacetime. A great deal of phenomenological works have shown in the last few years that this option (sometimes accompanied with a running gravitational coupling) may cure some of the tensions afflicting the $Λ$CDM. The `running vacuum models' (RVM's) are characterized by the vacuum energy density, $ρ_…
Relaxing the $σ_8$-tension through running vacuum in the Universe
最近的研究表明，运行真空模型（RVMs）比协调的$Λ$ CDM模型更能拟合宇宙学观测，从而支持了动力学暗能量（DE）的可能性.除了宇宙微波背景（CMB）的各向异性，最重要的数据集包括：i）重子声学振荡（BAO），ii）直接大尺度结构（LSS）形成数据。分析主要集中在CMB上，并且BAO+LSS输入不足，通常无法捕获动态DE特征，而现有的少数研究解释了已知的CMB+BAO+LSS数据的丰富性（特别参见Solà，Gómez-Valent \& de Cruz Pérez 2015，2017; and Zhao et al. 2017）确实收敛到了一个显著的结论，即动力学DE很可能在$3-4σ$ c.l.的当前宇宙学观测中被编码。一个决定性因素是$Λ$和数据之间持久的$σ_8$ -张力。因为这个问题显然是紧迫的，我们致力于这项工作来解释如何以及为什么在膨胀的宇宙中运行真空成功地放松现有的$σ_8$紧张和描述的LSS形成数据显着优于$Λ$ CDM。
In this work we study different types of dark energy (DE) models in the framework of the cosmographic approach, with emphasis on the Running Vacuum models (RVMs). We assess their viability using different information criteria and compare them with the so-called Ghost DE models (GDEs) as well as with the concordance $Λ$CDM model. We use the Hubble diagrams for Pantheon SnIa, quasars (QSOs), gamma-ray bursts (GRBs) as well as the data on baryonic acoustic oscillations (BAOs) in four different combinations. Upon minimizing the $χ^2$ function of the distance modulus in the context of the Markov Ch…
We investigate observational constraints on the running vacuum model (RVM) of $Λ=3ν(H^{2}+K/a^2)+c_0$ in the spatially curved universe, where $ν$ is the model parameter, $K$ corresponds to the spatial curvature constant, and $c_{0}$ is a constant defined by the boundary conditions. As $\dotΛ \ne 0$, there are energy exchanges between vacuum, matter and radiation in RVM. We study the "geometrical degeneracy" of RVM on the CMB power spectra. By fitting the cosmological data, we find that the values of $χ^2$ in RVM and $Λ$CDM are similar to each other for the non-flat universe. Explicitly, we obt…
In this work we shall provide a model-independent general calculation of the running of the spectral index for vacuum $F(R)$ gravities. We shall exploit the functional form of the spectral index and of the tensor-to-scalar ratio in order to present a general $n_s-r$ relation for vacuum $F(R)$ gravity theories. As we show, viable $F(R)$ gravity theories can be classified to two classes of models regarding their prediction for the running spectral index. The $R^2$-attractor models predict a running of the spectral index in the range $-10^{-3}<a_s<-10^{-4}$, which classifies them in the same univ…
Theoretically, the running of the cosmological constant in the IR region is not ruled out. On the other hand, from the QFT viewpoint, the energy released due to the variation of the cosmological constant in the late universe cannot go to the matter sector. For this reason, the phenomenological bounds on such a running are not sufficiently restrictive. The situation can be different in the early universe when the gravitational field was sufficiently strong to provide an efficient creation of particles from the vacuum. We develop a framework for systematically exploring this ossibility. It is su…
The cosmological term, $Λ$, was introduced $104$ years ago by Einstein in his gravitational field equations. Whether $Λ$ is a rigid quantity or a dynamical variable in cosmology has been a matter of debate for many years, especially after the introduction of the general notion of dark energy (DE). $Λ$ is associated to the vacuum energy density, $ρ_{\rm vac}$, and one may expect that it evolves slowly with the cosmological expansion. Herein we present a devoted study testing this possibility using the promising class of running vacuum models (RVM's). We use a large string $SNIa+BAO+H(z)+LSS+CMB…
The $Λ$-term in Einstein's equations is a fundamental building block of the `concordance' $Λ$CDM model of cosmology. Even though the model is not free of fundamental problems, they have not been circumvented by any alternative dark energy proposal either. Here we stick to the $Λ$-term, but we contend that it can be a `running quantity' in quantum field theory (QFT) in curved spacetime. A plethora of phenomenological works have shown that this option can be highly competitive with the $Λ$CDM with a rigid cosmological term. The, so-called, `running vacuum models' (RVM's) are characterized by the…
Recent studies of quantum field theory in FLRW spacetime suggest that the cause of the speeding up of the universe is the running vacuum (RV). Appropriate renormalization of the energy-momentum tensor shows that the vacuum energy density is a smooth function of the Hubble rate and its derivatives: $ρ_{\rm vac}=ρ_{\rm vac}(H, \dot{H},\ddot{H},...)$. This is because in QFT the quantum scaling of $ρ_{\rm vac}$ with the renormalization point turns into cosmic evolution with $H$. As a result, any two nearby points of the cosmic expansion during the standard FLRW epoch are smoothly related through $…
We perform a comparative study of different types of dynamical dark energy models (DDES) using the cosmographic method. Among the models being examined herein we have the Running Vacuum models (RVMs), which have demonstrated considerable ability to fit the overall cosmological data at a level comparable to the standard cosmological model, $Λ$CDM, and capable of alleviating the $σ_8$ and $H_0$ tensions. At the same time we address a variety of Holographic dark energy models (HDEs) with different options for the time (redshift)-varying model parameter $c=c(z)$. We deal with the HDEs under the do…
We study particle production and the corresponding entropy increase in the context of cosmology with dynamical vacuum. We focus on the particular form that has been called "running vacuum model" (RVM), which is known to furnish a successful description of the overall current observations at a competitive level with the concordance $Λ$CDM model. It also provides an elegant global explanation of the cosmic history from a non-singular initial state in the very early universe up to our days and further into the final de Sitter era. The model has no horizon problem and provides an alternative expla…
We study the effects of vacuum energy perturbations on the evolution of the dark matter growth rate in a decomposed Chaplygin gas model with interacting dark matter and vacuum energy. We consider two different cases: (i) geodesic dark matter with homogeneous vacuum, and (ii) a covariant ansatz for vacuum density perturbations. In the latter case, we show that the vacuum perturbations are very tiny as compared to dark matter perturbations on sub-horizon scales. In spite of that, depending on the value of the Chaplygin gas parameter α, vacuum perturbations suppress or enhance the dark matter gro…
Inflationary cosmology proposes that the early Universe undergoes accelerated expansion, driven, in simple scenarios, by a single scalar field, or inflaton. The form of the inflaton potential determines the initial spectra of density perturbations and gravitational waves. We show that constraints on the duration of inflation together with the BICEP3/Keck bounds on the gravitational wave background imply that higher derivatives of the potential are nontrivial with a confidence of 99%. Such terms contribute to the scale-dependence, or running, of the density perturbation spectrum. We clarify the…
It is well-known that quantum field theory (QFT) induces a huge value of the cosmological constant, $Λ$, which is outrageously inconsistent with cosmological observations. We review here some aspects of this fundamental theoretical conundrum (`the cosmological constant problem') and strongly argue in favor of the possibility that the cosmic vacuum density $ρ_{\rm vac}$ may be mildly evolving with the expansion rate $H$. Such a `running vacuum model' (RVM) proposal predicts an effective dynamical dark energy without postulating new ad hoc fields (quintessence and the like). Using the method of …
