We examine the running vacuum model with $Λ(H) = 3 νH^2 + Λ_0$, where $ν$ is the model parameter and $Λ_0$ is the cosmological constant. From the data of the cosmic microwave background radiation, weak lensing and baryon acoustic oscillation along with the time dependent Hubble parameter $H(z)$ and weighted linear growth $f (z)σ_8(z)$ measurements, we find that $ν=(1.37^{+0.72}_{-0.95})\times 10^{-4}$ with the best fitted $χ^2$ value slightly smaller than that in the $Λ$CDM model.
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…
We study the gravitational baryogenesis mechanism for generating baryon asymmetry in the context of running vacuum models. Regardless if these models can produce a viable cosmological evolution, we demonstrate that they produce a non-zero baryon-to-entropy ratio even if the universe is filled with conformal matter. This is a sound difference between the running vacuum gravitational baryogenesis and the Einstein-Hilbert one, since in the latter case, the predicted baryon-to-entropy ratio is zero. We consider two well known and most used running vacuum models and show that the resulting baryon-t…
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 cosmology, phenomenologically motivated expressions for running vacuum are commonly parametrized as linear functions $Λ(H^2)$ or $Λ(R)$. Such kind of models assume an equation of state for vacuum given by $\,\overline P_Λ=-\,\overlineρ_Λ$, relating their background pressure $\,\overline P_Λ$ and mean energy density $\,\overlineρ_Λ\equivΛ/8πG$. This equation of state requires that the dynamic for vacuum is due to the energy exchange with the material species. Most of the approaches to background level consider only the energy exchange between vacuum and the transient dominant material compon…
I review the excellent phenomenological status of a class of dynamical vacuum models in which the vacuum energy density, $ρ_Λ=ρ_Λ(H)$, as a function of the Hubble rate, evolves through its interaction with dark matter and/or through the accompanying running of the gravitational coupling $G$, including the possibility of being self-conserved with a nontrivial effective equation of state. Some of these models have been used to incorporate into a single vacuum structure the rapid stage of inflation, followed by the standard radiation and cold dark matter epochs all the way down until the dark ene…
We show that a CP-violating interaction induced by a derivative coupling between the running vacuum and a non-conserving baryon current may dynamically break CPT and trigger baryogenesis through an effective chemical potential. By assuming a non-singular class of running vacuum cosmologies which provides a complete cosmic history (from an early inflationary de Sitter stage to the present day quasi-de Sitter acceleration), it is found that an acceptable baryon asymmetry is generated for many different choices of the model parameters. It is interesting that the same ingredient (running vacuum en…
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 cosmological production of gravitational waves in a nonsingular flat cosmology powered by a "running vacuum" energy density described by $ρ_Λ\equivρ_Λ(H)$, a phenomenological expression potentially linked with the renormalization group approach in quantum field theory in curved spacetimes. The model can be interpreted as a particular case of the class recently discussed by Perico et al. (Phys. Rev. D {\bf 88}, 063531, 2013) which is termed complete in the sense that the cosmic evolution occurs between two extreme de Sitter stages (early and late time de Sitter phases). {The …
The problem of cosmological production of gravitational waves is discussed in the framework of an expanding, spatially homogeneous and isotropic FRW type Universe with time-evolving vacuum energy density. The gravitational wave equation is established and its modified time-dependent part is analytically resolved for different epochs in the case of a flat geometry. Unlike the standard $Λ$CDM cosmology (no interacting vacuum), we show that gravitational waves are produced in the radiation era even in the context of general relativity. We also show that for all values of the free parameter, the h…
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 re…
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…
Recent analyses in the literature suggest that the concordance $Λ$CDM model with rigid cosmological term, $Λ=$const., may not be the best description of the cosmic acceleration. The class of "running vacuum models", in which $Λ=Λ(H)$ evolves with the Hubble rate, has been shown to fit the string of $SNIa+BAO+H(z)+LSS+CMB$ data significantly better than the $Λ$CDM. Here we provide further evidence on the time-evolving nature of the dark energy (DE) by fitting the same cosmological data in terms of scalar fields. As a representative model we use the original Peebles & Ratra potential, $V\proptoΦ…
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_…
The thermal history of a large class of running vacuum models in which the effective cosmological term is described by a truncated power series of the Hubble rate, whose dominant term is $Λ(H) \propto H^{n+2}$, is discussed in detail. Specifically, by assuming that the ultra-relativistic particles produced by the vacuum decay emerge into space-time in such a way that its energy density $ρ_r \propto T^{4}$, the temperature evolution law and the increasing entropy function are analytically calculated. For the whole class of vacuum models explored here we findthat the primeval value of the comovi…
We describe the primeval inflationary phase of the early Universe within a quantum field theoretical (QFT) framework that can be viewed as the effective action of vacuum decay in the early times. Interestingly enough, the model accounts for the "graceful exit" of the inflationary phase into the standard radiation regime. The underlying QFT framework considered here is Supergravity (SUGRA), more specifically an existing formulation in which the Starobinsky-type inflation (de-Sitter background) emerges from the quantum corrections to the effective action after integrating out the gravitino field…
We develop a complete set of tools for CMB forecasting, simulation and estimation of primordial running bispectra, arising from a variety of curvaton and single-field (DBI) models of Inflation. We validate our pipeline using mock CMB running non-Gaussianity realizations and test it on real data by obtaining experimental constraints on the $f_{\rm NL}$ running spectral index, $n_{\rm NG}$, using WMAP 9-year data. Our final bounds (68\% C.L.) read $-0.6< n_{\rm NG}<1.4$, $-0.3< n_{\rm NG}<1.2$, $-1.1<n_{\rm NG}<0.7$ for the single-field curvaton, two-field curvaton and DBI scenarios, respectivel…
It has recently been shown that the class of running vacuum models (RVMs) has the capacity to fit the overall cosmological observations better than the concordance $Λ$CDM model, therefore supporting the possibility of dynamical dark energy (DE). Apart from the cosmic microwave background (CMB) anisotropies, the most crucial datasets involved are: i) baryonic acoustic oscillations (BAO), and ii) direct large scale structure (LSS) formation data. Analyses mainly focusing on CMB and with insufficient BAO+LSS input generally fail to capture the dynamical DE signature, whereas the few existing stud…
We constrain the spectral running by combining cosmic microwave background (CMB) data, baryon acoustic oscillation (BAO) data and the constraint from primordial black holes (PBHs). We find that the constraint from PBHs has a significant impact on the running of running of scalar spectral index, and a power-law scalar power spectrum without running is consistent with observational data once the constraint from PBHs is taken into account. In addition, from the constraints on the slow-roll parameters, the derived tensor spectral index in the single-field slow-roll inflation model is quite small, …
Despite the fact that a rigid $Λ$-term is a fundamental building block of the concordance $Λ$CDM model, we show that a large class of cosmological scenarios with dynamical vacuum energy density $ρ_Λ$ and/or gravitational coupling $G$, together with a possible non-conservation of matter, are capable of seriously challenging the traditional phenomenological success of the $Λ$CDM. In this paper, we discuss these "running vacuum models" (RVM's), in which $ρ_Λ=ρ_Λ(H)$ consists of a nonvanishing constant term and a series of powers of the Hubble rate. Such generic structure is potentially linked to …
The current vacuum energy density observed as dark energy ${ ρ}_{ \rm dark }\simeq 2.5\times10^{-47}\ {\rm GeV^{4}}$ is unacceptably small compared with any other scales. Therefore, we encounter serious fine-tuning problem and theoretical difficulty to derive the dark energy. However, the theoretically attractive scenario has been proposed and discussed in literature: In terms of the renormalization-group (RG) running of the cosmological constant, the vacuum energy density can be expressed as ${ ρ}_{ \rm vacuum }\simeq m^{2}H^{2}$ where $m$ is the mass of the scalar field and rather dynamical …
We compute the spectral index of primordial perturbations in a rainbow universe. We allow the Newton constant $G$ to run at (super-)Planckian energies and we consider both vacuum and thermal perturbations. If the rainbow metric is the one associated to a generalized Horava-Lifshitz dispersion relation, we find that only when $G$ tends asymptotically to zero can one match the observed value of the spectral index and solve the horizon problem, both for vacuum and thermal perturbations. For vacuum fluctuations the observational constraints imply that the primordial universe expansion can be both …
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…
We compute the time variation of the fundamental constants (such as the ratio of the proton mass to the electron mass, the strong coupling constant, the fine structure constant and Newton's constant) within the context of the so-called running vacuum models (RVM's) of the cosmic evolution. Recently, compelling evidence has been provided showing that these models are able to fit the main cosmological data (SNIa+BAO+H(z)+LSS+BBN+CMB) significantly better than the concordance $Λ$CDM model. Specifically, the vacuum parameters of the RVM (i.e. those responsible for the dynamics of the vacuum energy…
Recent studies suggest that dynamical dark energy (DDE) provides a better fit to the rising affluence of modern cosmological observations than the concordance model ($Λ$CDM) with a rigid cosmological constant, $Λ$. Such is the case with the running vacuum models (RVMs) and to some extent also with a simple XCDM parametrization. Apart from the cosmic microwave background (CMB) anisotropies, the most crucial datasets potentially carrying the DDE signature are: i) baryonic acoustic oscillations (BAO), and ii) direct large scale structure (LSS) formation data (i.e. the observations on $f(z)σ_8(z)$…
In this work we study a phenomenological non-gravitational interaction between dark matter and dark energy. The scenario studied in this work extends the usual interaction model proportional to the derivative of the dark component density adding to the coupling a non-linear term of the form $Q = ρ'/3(α+ βρ)$. This dark sector interaction model could be interpreted as a particular case of a running vacuum model of the type $Λ(H) = n_0 + n_1 H^2 + n_2 H^4$ in which the vacuum decays into dark matter. For a flat FRW Universe filled with dark energy, dark matter and decoupled baryonic matter and r…
As a contribution to a viable candidate for a standard model of cosmology, we here show that pre-inflationary quantum fluctuations can provide a scenario for the long-sought initial conditions for the inflaton field. Our proposal is based on the assumption that at very high energies (higher than the energy scale of inflation) the vacuum-expectation value (VeV) of the field is trapped in a false vacuum and then, due to renormalization-group (RG) running, the potential starts to flatten out toward low energy, eventually tending to a convex one which allows the field to roll down to the true vacu…
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…
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…
In this letter we present constraints on the scale-dependent "local" type primordial non-Gaussianity, which is described by non-Gaussianity's spectral index $n_{\rm NG}$, from the NRAO VLA Sky Survey and the quasar catalog of the Sloan Digital Sky Survey (SDSS) Data Release 6, together with the SDSS Data Release 12 photo-z sample. Here, we use the auto-correlation analyses of these three probes and their cross-correlation analyses with the cosmic microwave background (CMB) temperature map, and obtain the tight constraint on the spectral index: $n_{\rm NG}=0.2 ^{+0.7}_{-1.0}$ ($1\,σ$ C.L.), whi…
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 $…
Cosmological inflation predicts that the scalar spectral index "runs" with scale. Constraints on the values of the spectral runnings, $α_s\equiv \textrm{d} n_s/\textrm{d}\ln k$ and $β_s\equiv \textrm{d}α_s/\textrm{d}\ln k$, therefore provide a fundamental test of the physics of inflation. Here we study the feasibility of measuring the runnings when information from upcoming large-volume galaxy surveys is used to supplement the information provided by a CMB-S4 experiment, particularly focusing on the effect of including high-$k$, nonlinear scales. Since these measurements will be sensitive to m…
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…
By writing the running of the scalar spectral index completely in terms of the scalar index $n_s$ and the tensor-to-scalar ratio $r$ we are able to impose constraints to models of inflation which are independent of the parameters of the model in question. We write analytical expressions for the running index of Natural Inflation, two models of the type Mutated Hilltop Inflation and the Starobinsky model. The resulting formulae for the running depend exclusively on $n_s$ and/or $r$ and will keep tightening the running index further as additional conditions and observations constrain the scalar …
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…
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 …
We revisit the decoupling effects associated with heavy particles in the renormalization group running of the vacuum energy in a mass-dependent renormalization scheme. We find the running of the vacuum energy stemming from the Higgs condensate in the entire energy range and show that it behaves as expected from the simple dimensional arguments meaning that it exhibits the quadratic sensitivity to the mass of the heavy particles in the infrared regime. The consequence of such a running to the fine-tuning problem with the measured value of the Cosmological Constant is analyzed and the constraint…
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…
In previous works we have derived a Running Vacuum Model (RVM) for a string Universe, which provides an effective description of the evolution of 4-dimensional string-inspired cosmologies from inflation till the present epoch. In the context of this "stringy RVM" version, it is assumed that the early Universe is characterised by purely gravitational degrees of freedom, from the massless gravitational string multiplet, including the antisymmetric tensor field. The latter plays an important role, since its dual gives rise to a `stiff' gravitational-axion "matter", which in turn couples to the gr…
