Running vacuum interacting with dark matter or with running gravitational coupling. Phenomenological implications

The cosmological term, $\Lambda$, in Einstein's equations is an essential ingredient of the `concordance' $\Lambda$CDM model of cosmology. In this mini-review presentation, we assess the possibility that $\Lambda$ 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 $\Lambda$CDM. The `running vacuum models' (RVM's) are characterized by the vacuum energy density, $\rho_{\rm vac}$, being a series of (even) powers of the Hubble rate and its time derivatives. Here we describe the technical quantum field theoretical origin of the RVM structure in FLRW spacetime, which goes well-beyond the original semi-qualitative renormalization group arguments. In particular, we compute the renormalized energy-momentum tensor using the adiabatic regularization procedure and show that it leads to the RVM form. In other words, we find that the renormalized vacuum energy density, $\rho_{vac}(H)$ evolves as a (constant) additive term plus a leading dynamical components ${\cal O}(H^2)$. There are also ${\cal O}(H^4)$ contributions, which can be relevant for the early universe. Remarkably enough, the renormalized $\rho_{\rm vac}(H)$ does not exhibit dangerous terms proportional to the quartic power of the masses ($\sim m^4$) of the fields. It is well-known that these terms have been the main source of trouble since they are responsible for the extreme fine tuning and ultimately for the cosmological constant problem. In this context, the current $\rho_{vac}(H)$ is dominated by a constant term, as it should be, but it acquires a mild dynamical component $\sim \nu H^2$ ($|\nu|\ll1$) which makes the RVM to mimic quintessence.Comment: 21 pages, slightly extended discussion. References added and others updated. Invited talk in the 16th Marcel-Grossmann virtual Conference (MG16), parallel session DM1: Interacting Dark Matte

Cosmological constant and equation of state of the quantum vacuum

Recent studies of quantum field theory in FLRW spacetime suggest that the cause of the speeding up of the universe is the quantum vacuum, no need of ad hoc quintessence fields. Appropriate renormalization of the energy-momentum tensor shows that the vacuum energy density is a smooth function of the Hubble rate and its derivatives: $\rho_{\rm vac}=\rho_{\rm vac}(H, \dot{H},\ddot{H},...)$. This is because in QFT the quantum scaling of $\rho_{\rm vac}$ 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 $\delta\rho_{\rm vac}\sim {\cal O}(H^2)$. In this scenario, no fine tuning is needed at all. What we call the `cosmological constant' $\Lambda$ is just the nearly sustained value of $8\pi G(H)\rho_{\rm vac}(H)$ around (any) given epoch, where $G(H)$ is the running gravitational coupling. In the very early universe, higher (even) powers $\rho_{\rm vac}\sim{\cal O}(H^N)$ ($N=4,6,..$) triggered fast inflation during a short period in which $H=$const, no need of ad hoc inflatons. In that period, the equation of state (EoS) of the vacuum is very close to $w_{\rm vac}=-1$, but this ceases to be true during the FLRW era. Amazingly, the quantum vacuum acts as a formidable cosmic chameleon: it subsequently adopts the EoS of matter during the relativistic ($w_{\rm vac}=1/3$) and non-relativistic ($w_{\rm vac}=0$) epochs, and in the late universe it mimics quintessence, $w_{\rm vac}\gtrsim-1$, only to tend again to $-1$ in the remote future. In the transit, the quantum vacuum helps to solve the $H_0$ and $\sigma_8$ tensions.Comment: Extended discussion, references adde

Running vacuum in the Universe: phenomenological status in light of the latest observations, and its impact on the σ8\sigma_8 and H0H_0 tensions

A substantial body of phenomenological and theoretical work over the last few years strengthens the possibility that the vacuum energy density (VED) of the universe is dynamical, and in particular that it adopts the `running vacuum model' (RVM) form, in which the VED evolves mildly as $\delta \rho_{\rm vac}(H)\sim \nu_{\rm eff} m_{\rm Pl}^2{\cal O}\left(H^2\right)$, where $H$ is the Hubble rate and $\nu_{\rm eff}$ is a (small) free parameter. This dynamical scenario is grounded on recent studies of quantum field theory (QFT) in curved spacetime and also on string theory. It turns out that what we call the `cosmological constant', $\Lambda$, is no longer a rigid parameter but the nearly sustained value of $8\pi G(H)\rho_{\rm vac}(H)$ around (any) given epoch $H(t)$, where $G(H)$ is the gravitational coupling, which can also be very mildly running (logarithmically). Of particular interest is the possibility suggested in past works that such a running may help to cure the cosmological tensions afflicting the $\Lambda$CDM. In the current study, we reanalyze it in full and we find it becomes further buttressed. Using the modern cosmological data, namely a compilation of the latest $SNIa+BAO+$H(z)$+LSS+CMB$ observations, we probe to which extent the RVM provides a quality fit better than the concordance $\Lambda$CDM model, paying particular emphasis on its impact on the $\sigma_8$ and $H_0$ tensions. We utilize the Einstein-Boltzmann system solver $CLASS$ and the Monte Carlo sampler $MontePython$ for the statistical analysis, as well as the statistical $DIC$ criterion to compare the running vacuum against the rigid vacuum ($\nu_{\rm eff} = 0$). We show that with a tiny amount of vacuum dynamics ($|\nu_{\rm eff}|\ll 1$) the global fit can improve significantly with respect to the $\Lambda$CDM and the mentioned tensions may subside to inconspicuous levels.Comment: LaTeX, 44 pages, 11 Tables and 4 Figure

The Cosmological Constant Problem and Running Vacuum in the Expanding Universe

It is well-known that quantum field theory (QFT) induces a huge value of the cosmological constant, $\Lambda$, 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 $\rho_{\rm vac}$ 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 adiabatic renormalization within QFT in curved spacetime we find that $\rho_{\rm vac}(H)$ acquires a dynamical component ${\cal O}(H^2)$ caused by the quantum matter effects. There are also ${\cal O}(H^n)$ ($n=4,6,..$) contributions, some of which may trigger inflation in the early universe. Remarkably, the evolution of the adiabatically renormalized $\rho_{\rm vac}(H)$ is not affected by dangerous terms proportional to the quartic power of the masses ($\sim m^4$) of the fields. Traditionally, these terms have been the main source of trouble as they are responsible for the extreme fine tuning feature of the cosmological constant problem. In the context under study, however, the late time $\rho_{\rm vac}(H)$ around $H_0$ is given by a dominant term ($\rho_{\rm vac}^0$) plus the aforementioned mild dynamical component $\propto \nu (H^2-H_0^2)$ (with $|\nu|\ll1$), which makes the RVM to mimic quintessence. Finally, on the phenomenological side we show that the RVM may be instrumental in alleviating some of the most challenging problems (so-called `tensions') afflicting nowadays the observational consistency of the `concordance' $\Lambda$CDM model, such as the $H_0$ and $\sigma_8$ tensions.Comment: Matches the published version in Phil.Trans.Roy.Soc.Lond.A (2022