The dynamics of vacuum, gravity and matter: Implications on the fundamental constants

The possibility that the vacuum energy density (VED), $\rho_{\rm vac}$, could be time dependent in the expanding Universe is intuitively more reasonable than just a rigid cosmological constant for the entire cosmic history. The dynamics of $\rho_{\rm vac}=\rho_{\rm vac}(H)$ as a function of the Hubble rate, $H(t)$, most likely contributes to alleviate cosmological problems and tensions, having also implications on the so-called fundamental `constants' of Nature, which should be slowly drifting with the cosmic expansion owing to the fluctuations of the quantum vacuum. This includes the gravitational `constant' $G$, but also the gauge and Yukawa couplings as well as the particle masses themselves (both of dark matter and baryonic matter). The subtle exchange of energy involved is the basis for the ``micro and macro connection''. Herein, I discuss not only this connection as a possibility but show that it is in fact a generic prediction of QFT in cosmological spacetime which is fully compatible with general covariance. This fact has not been pointed out until recently when an appropriate renormalization framework for the VED has been found which is free from the usual conundrums associated with the cosmological constant problem.Comment: Extended discussion, typos corrected, references adde

Friedmann cosmology with decaying vacuum density in Brans-Dicke theory

In this paper, we study Friedmann cosmology with time-varying vacuum energy density in the context of Brans-Dicke theory. We consider an isotropic and homogeneous flat space, filled with a matter-dominated perfect fluid and a dynamical cosmological term Λ(t), obeying the equation of state of the vacuum. As the exact nature of a possible time-varying vacuum is yet to be found, we explore Λ(t) given by the phenomenological law Λ(t)=λ+σH, where λ and σ are positive constants. We solve the model and then focus on two different cases ΛH1 and ΛH2 by assuming Λ=λ and Λ=σH, respectively. Notice that ΛH1 is the analog of the standard ΛCDM, but within the Brans-Dicke cosmology. We find the analytical solution of the main cosmological functions such as the Hubble parameter, the scale factor, deceleration and equation of state parameters for these models. In order to test the viability of the cosmological scenarios, we perform two sets of joint observational analyses of the recent Type Ia supernova data (Pantheon), observational measurements of Hubble parameter data, Baryon acoustic oscillation/Cosmic microwave background data and Local Hubble constant for each model. For the sake of comparison, the same data analysis is performed for the ΛCDM model. Each model shows a transition from decelerated phase to accelerated phase and can be viewed as an effective quintessence behavior. Using the model selection criteria AIC and BIC to distinguish from existing dark energy models, we find that the Brans-Dicke analog of the Λ-cosmology (i.e. our model ΛH1) performs at a level comparable to the standard ΛCDM, whereas ΛH2 is less favoured

Entropic-force dark energy reconsidered

We reconsider the entropic-force model in which both kinds of Hubble terms, ˙ H and H 2 , appear in the effective dark energy (DE) density affecting the evolution of the main cosmological functions, namely, the scale factor, deceleration parameter, matter density, and growth of linear matter perturbations. However, we find that the entropic-force model is not viable at the background and perturbation levels due to the fact that the entropic formulation does not add a constant term in the Friedmann equations. On the other hand, if on mere phenomenological grounds we replace the ˙ H dependence of the effective DE density with a linear term H without including a constant additive term, we find that the transition from deceleration to acceleration becomes possible, but the recent structure formation data strongly disfavor this cosmological scenario. Finally, we briefly compare the entropic-force models with some related DE models (based on dynamical vacuum energy) which overcome these difficulties and are compatible with the present observations

Cosmological constant vis-à-vis dynamical vacuum: Bold challenging the ΛCDM

Next year we will celebrate 100 years of the cosmological term, Λ, in Einstein's gravitational field equations, also 50 years since the cosmological constant problem was first formulated by Zeldovich, and almost about two decades of the observational evidence that a nonvanishing, positive, Λ-term could be the simplest phenomenological explanation for the observed acceleration of the Universe. This mixed state of affairs already shows that we do not currently understand the theoretical nature of Λ. In particular, we are still facing the crucial question whether Λ is truly a fundamental constant or a mildly evolving dynamical variable. At this point the matter should be settled once more empirically and, amazingly enough, the wealth of observational data at our disposal can presently shed true light on it. In this short review, I summarize the situation of some of these studies. It turns out that the Λ = const. hypothesis, despite being the simplest, may well not be the most favored one when we put it in hard-fought competition with specific dynamical models of the vacuum energy. Recently, it has been shown that the overall fit to the cosmological observables SNIa+BAO+H(z)+LSS+BBN+CMB do favor the class of 'running' vacuum models (RVM's)¿ in which Λ = Λ(H) is a function of the Hubble rate ¿ against the 'concordance' ΛCDM model. The support is at an unprecedented level of ∼4σ and is backed up with Akaike and Bayesian criteria leading to compelling evidence in favor of the RVM option and other related dynamical vacuum models. I also address the implications of this framework on the possible time evolution of the fundamental constants of Natur

Relaxing the σ8-tension through running vacuum in the Universe

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 ΛCDM 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 studies accounting for the wealth of known CMB+BAO+LSS data (see in particular Sol\`a, G\'omez-Valent \& de Cruz P\'erez 2015, 2017; and Zhao et al. 2017) do converge to the remarkable conclusion that dynamical DE might well be encoded in the current cosmological observations at a 3−4σ c.l. A decisive factor is the persistent σ8-tension between the ΛCDM and the data. Because the issue is obviously pressing, we devote this work to explain how and why running vacuum in the expanding universe successfully relaxes the existing σ8-tension and describes the LSS formation data significantly better than the ΛCDM

Running vacuum in quantum field theory in curved spacetime: renormalizing ρvac without ∼m4 terms

The Λ-term in Einstein's equations is a fundamental building block of the 'concordance' ΛCDM 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 space time. A plethora of phenomenological works have shown that this option can be highly competitive with the ΛCDM with a rigid cosmological term. The, so-called, 'running vacuum models' (RVM's) are characterized by the vacuum energy density, ρvac, being a series of (even) powers of the Hubble parameter and its time derivatives. Such theoretical form has been motivated by general renormalization group arguments, which look plausible. Here we dwell further upon the origin of the RVM structure within QFT in FLRW spacetime. We compute the renormalized energy-momentum tensor with the help of the adiabatic regularization procedure and find that it leads essentially to the RVM form. This means that ρvac(H) evolves as a constant term plus dynamical components O(H2) and O(H4), the latter being relevant for the early universe only. However, the renormalized ρvac(H) does not carry dangerous terms proportional to the quartic power of the masses (∼m4) of the fields, these terms being a well-known source of exceedingly large contributions. At present, ρvac(H) is dominated by the additive constant term accompanied by a mild dynamical component ∼νH2 (|ν|≪1), which mimics quintessence

Hubble expansion and structure formation in time varying vacuum models

We investigate the properties of the FLRW flat cosmological models in which the vacuum energy density evolves with time, Λ ( t ) . Using different versions of the Λ ( t ) model, namely, quantum field vacuum, power series vacuum and power law vacuum, we find that the main cosmological functions such as the scale factor of the Universe, the Hubble expansion rate H , and the energy densities are defined analytically. Performing a joint likelihood analysis of the recent supernovae type Ia data, the cosmic microwave background shift parameter and the baryonic acoustic oscillations traced by the Sloan Digital Sky Survey galaxies, we put tight constraints on the main cosmological parameters of the Λ ( t ) scenarios. Furthermore, we study the linear matter fluctuation field of the above vacuum models. We find that the patterns of the power series vacuum Λ = n 1 H + n 2 H 2 predict stronger small scale dynamics, which implies a faster growth rate of perturbations with respect to the other two vacuum cases (quantum field and power law), despite the fact that all the cosmological models share the same equation of state parameter. In the case of the quantum field vacuum Λ = n 0 + n 2 H 2 , the corresponding matter fluctuation field resembles that of the traditional Λ cosmology. The power law vacuum ( Λ ∝ a − n ) mimics the classical quintessence cosmology, the best fit being tilted in the phantom phase. In this framework, we compare the observed growth rate of clustering measured from the optical galaxies with those predicted by the current Λ ( t ) models. Performing a Kolmogorov-Smirnov statistical test we show that the cosmological models which contain a constant vacuum ( Λ CDM ), quantum field vacuum, and power law vacuum provide growth rates that match well with the observed growth rate. However, this is not the case for the power series vacuum models (in particular, the frequently adduced Λ ∝ H model) in which clusters form at significantly earlier times ( z ≥ 4 ) with respect to all other models ( z ∼ 2 ). Finally, we derived the theoretically predicted dark matter halo mass function and the corresponding distribution of cluster-size halos for all the models studied. Their expected redshift distribution indicates that it will be difficult to distinguish the closely resembling models (constant vacuum, quantum field, and power law vacuum), using realistic future x-ray surveys of cluster abundances. However, cluster surveys based on the Sunayev-Zeldovich detection method give some hope to distinguish the closely resembling models at high redshifts

Quantum anomalies in string-inspired running vacuum universe: Inflation and axion dark matter

In this letter, we elaborate further on a Cosmological 'Running-Vacuum' type model for the Universe, suggested previously by the authors [1], [2], within the context of a string-inspired effective theory in the presence of a Kalb-Ramond (KR) gravitational axion field which descends from the antisymmetric tensor of the massless gravitational string multiplet. In the presence of this field, which has anomalous CP violating interactions with the gravitons, primordial gravitational waves induce gravitational anomalies, which in turn are responsible for the appearance of H^2 and H^4 contributions to the vacuum energy density, these terms being characteristic of generic 'running-vacuum-model (RVM) type', where H is the Hubble parameter. In this work we prove in detail the appearance of the H^4 terms due to gravitational-anomaly-induced condensates in the energy density of the primordial Universe, which can self-consistently induce inflation, and subsequent exit from it, according to the generic features of RVM. We also argue in favour of the robustness of our results, which were derived within an effective low-energy field theory approach, against Ultra Violet completion of the theory. During the radiation and matter-dominated eras, gravitational anomalies cancel, as required for the consistency of the quantum matter/radiation field theory. However, chiral and QCD-axion-type anomalies survive and have important consequences for both cosmic magnetogenesis and axionic dark matter in the Universe. Finally, the stringy RVM scenario presented here predicts quintessence-like dynamical dark energy for the current Universe, which is compatible with the existing fitting analyses of such model against observations

Running vacuum in the Universe and the time variation of the fundamental constants of Nature

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 (RVMs) of the cosmic evolution. Recently, compelling evidence has been provided that these models are able to fit the main cosmological data (SNIa+BAO+H(z)+LSS+BBN+CMB) significantly better than the concordance ΛCDM model. Specifically, the vacuum parameters of the RVM (i.e. those responsible for the dynamics of the vacuum energy) prove to be nonzero at a confidence level ≳3σ. Here we use such remarkable status of the RVMs to make definite predictions on the cosmic time variation of the fundamental constants. It turns out that the predicted variations are close to the present observational limits. Furthermore, we find that the time evolution of the dark matter particle masses should be crucially involved in the total mass variation of our Universe. A positive measurement of this kind of effects could be interpreted as strong support to the 'micro-macro connection' (viz. the dynamical feedback between the evolution of the cosmological parameters and the time variation of the fundamental constants of the microscopic world), previously proposed by two of us (HF and JS)