A tunneling bounce driving the decay of a metastable vacuum must respect an integral constraint dictated by simple scaling arguments that is very useful to determine key properties of the bounce. After illustrating how this works in a simple toy model, the Standard Model Higgs potential is considered, including quartic coupling running and gravitational corrections as sources of scale invariance breaking. This approach clarifies the existence of the bounce and leads to simple and accurate analytical results in an expansion in the breaking parameters. Using the so-called tunneling-potential approach (generalized for nonminimal coupling to gravity) the integral constraint and the tunneling action are extended to second order in perturbations.
The vacuum--polarization contributions of ${\cal O}(b^{n-1} \al_s^n)$ to the relation between the pole--mass $M$ of a quark and the \MS parameter $\mh (M)$ are evaluated by a straightforward method. They are found to approximate very well the exact answer, known through ${\cal O}(\al_s^2)$, thus providing a simple physical interpretation. Results are also given for the cases when the vacuum--polarization contributions are defined by the pinch technique prescription and specific background field gauges. Assuming that the terms $n \geq 3$ are also dominant, we evaluate $M_t/\hat{m}_t(M_t)$, comp…
We study in detail the effect of the finite current quark mass on chiral symmetry breaking, in the framework of truncated Coulomb gauge QCD with a linear confining quark-antiquark potential. In the chiral limit of massless current quarks, the breaking of chiral symmetry is spontaneous. But for a finite current quark mass, some dynamical symmetry breaking continues to add to the explicit breaking caused by the quark mass. Moreover, using as order parameter the mass gap, i. e. the quark mass at vanishing moment or the quark condensate, a finite quark mass transforms the chiral symmetry breaking …
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 derive simple analytical formulae for the renormalization group running of neutrino masses, leptonic mixing angles and CP phases, which allow an easy understanding of the running. Particularly for a small angle theta_13 the expressions become very compact, even when non-vanishing CP phases are present. Using these equations we investigate: (i) the influence of Dirac and Majorana phases on the evolution of all parameters, (ii) the implications of running neutrino parameters for leptogenesis, (iii) changes of the mass bounds from WMAP and neutrinoless double beta decay experiments, relevant f…
To avoid possible electroweak vacuum instability in the vector-like fermion model, we introduce a new singlet scalar to the model, which couples to the vector-like fermion, and also mixes with the Higgs boson after spontaneous symmetry breaking. We investigate the vector-like fermion predominantly coupled to the third generation quarks, and its mass is generated from the vacuum expectation value of the new scalar field in the model. In this setup, as running towards high energies, the new scalar provides positive contribution to the running of the higgs quartic coupling, and the matching on th…
We investigate the running vacuum model (RVM) in the framework of scalar field theory.This dynamical vacuum model provides an elegant global explanation of the cosmic history, namely the universe starts from a non-singular initial de Sitter vacuum stage, it passes smoothly from an early inflationary era to a radiation epoch ("graceful exit") and finally it enters the dark matter and dark energy (DE) dominated epochs, where it can explain the large entropy problem and predicts a mild dynamical evolution of the DE. Within this phenomenologically appealing context, we formulate an effective {\it …
Fully analytical results for the first two moments of the heavy-quark vacuum polarisation function at four loops in quantum chromo-dynamics are presented.
We derive for the first time the growth index of matter perturbations of the FLRW flat cosmological models in which the vacuum energy depends on redshift. A particularly well motivated model of this type is the so-called quantum field vacuum, in which apart from a leading constant term $Λ_0$ there is also a $H^{2}$-dependence in the functional form of vacuum, namely $Λ(H)=Λ_{0}+3ν(H^{2}-H^{2}_{0})$. Since $|ν|\ll1$ this form endows the vacuum energy of a mild dynamics which affects the evolution of the main cosmological observables at the background and perturbation levels. Specifically, at th…
We elaborate further on the compatibility of the "vacuumon potential" that characterises the inflationary phase of the Running Vacuum Model (RVM) with the Swampland criteria. The work is motivated by the fact that, as demonstrated recently by the authors [1-3], the RVM framework can be derived as an effective gravitational field theory stemming from underlying microscopic (critical) string theory models with gravitational anomalies, involving condensation of primordial gravitational waves. Although believed to be a classical scalar field description, not representing a fully fledged quantum fi…
Current astronomical observations are successfully explained by the present cosmological paradigm based on the concordance model ($Λ_0$CDM + Inflation). However, such a scenario is composed of a heterogeneous mix of ingredients for describing the different stages of cosmological evolution. Particularly, it does not give an unified explanation connecting the early and late time accelerating inflationary regimes which are separated by many aeons. Other challenges to the concordance model include: a singularity at early times or the emergence of the Universe from the quantum gravity regime, the "…
We generalize the previously proposed running vacuum energy model by including a term proportional to \dot{H}, in addition to the existing H^2 term. We show that the added degree of freedom is very constrained if both low redshift and high redshift data are taken into account. Best-fit models are undistinguishable from LCDM at the present time, but could be distinguished in the future with very accurate data at both low and high redshifts. We stress the formal analogy at the phenomenological level of the running vacuum models with recently proposed dark energy models based on the holographic o…
The contributions to the $g-2$ of the muon from some eighth-order (four-loop) graphs containing one-loop and two-loop vacuum polarization insertions have been evaluated analytically in QED perturbation theory, expanding the results in the ratio of the electron to muon mass ${(m_e / m_μ)}$. The results agree with the numerical evaluations and the asymptotic analytical results already existing in the literature.
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 compact, fully analytical expressions for singular parts of a class of three-loop diagrams which cannot be factorized into lower-loop integrals. As a result of the calculations we obtain the analytical expression for the three-loop effective potential of the massive O(N) ϕ^4 model presented recently by J.-M.Chung and B.K.Chung, Phys.Rev. D56, 6508 (1997).
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…
We investigate the dynamics of the FLRW flat cosmological models in which the vacuum energy varies with redshift. A particularly well motivated model of this type is the so-called quantum field vacuum, in which both kind of terms $H^{2}$ and constant appear in the effective dark energy density affecting the evolution of the main cosmological functions at the background and perturbation levels. Specifically, it turns out that the functional form of the quantum vacuum endows the vacuum energy of a mild dynamical evolution which could be observed nowadays and appears as dynamical dark energy. Int…
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_…
Including contributions of scale-dependent vacuum expectation values of Higgs scalars, we derive new one-loop formulas analytically for running quark-lepton masses at higher scales in MSSM. Apart from the gauge-coupling dependence being different from earlier formulas, the third-generation- Yukawa-coupling effects are absent in the masses of the first two generations. While predicting the masses and $\tanβ$ numerically, we also include two-loop effects.
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…
The contributions to the g-2 of the muon from some tenth-order (five-loop) graphs containing one-loop and two-loop vacuum polarization insertions have been evaluated analytically in QED perturbation theory, expanding the results in the ratio of the electron to muon mass (m_e /m_μ). Some results contain also terms known only in numerical form. Our results agree with the renormalization group results already existing in the literature.
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…
The latest results of the ATLAS and CMS experiments indicate 116 GeV \lesssim M_H \lesssim 131 GeV and 115 GeV \lesssim M_H \lesssim 127 GeV, respectively, for the mass of the Higgs boson in the standard model (SM) at the 95% confidence level. In particular, both experiments point to a preferred narrow mass range M_H \simeq (124 ... 126) GeV. We examine the impact of this preliminary result of M_H on the SM vacuum stability by using the two-loop renormalization-group equations (RGEs), and arrive at the cutoff scale Λ_VS \sim 4 \times 10^{12} GeV (for M_H = 125 GeV, M_t = 172.9 GeV and α_s(M_Z)…
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…
In previous works we have embedded the Running Vacuum Model (RVM) of Cosmology in the framework of string theory. Specifically, we considered a string-inspired Cosmology with primordial gravitational waves (GW) and gravitational anomalies, which were argued to lead, via appropriate condensation during the very-early-universe era, to dynamical inflation, of RVM type, without the need for extra inflaton fields. A crucial role for the associated slow-roll nature of the inflationary era was played by the fundamental axion field that exists in the gravitational multiplet of strings, viz. the Kalb-R…
We present a model for the Universe in which quantum anomalies are argued to play an important dual role: they are responsible for generating matter-antimatter asymmetry, but also provide time-dependent contributions to the vacuum energy density of "running-vacuum" type, which drive the Universe evolution. During the inflationary phase of a string-inspired Universe, and its subsequent exit, the existence of primordial gravitational waves induce gravitational anomalies, which couple to the Kalb-Ramond (KR)axion field of the massless gravitational string multiplet. Such anomalous CP violating in…
The equation for two reggeized gluons in the vacuum channel is generalized to take into account the running QCD coupling constant on the basis of the bootstrap condition for gluon reggeization. Both the gluon trajectory as a function of momentum and the interaction as a function of distance grow like $\log\log$ in the ultraviolet. The resulting equation depends on the confinement region. With a simple parametrization of its influence by an effective gluon mass the pomeron intercept turns out much smaller than for a fixed coupling constant (the BFKL pomeron).
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 …
In this letter, we elaborate further on a Cosmological "Running-Vacuum" type model for the Universe, suggested previously by the authors 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 …
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 have computed Wilsonian effective action in a simple model containing scalar field with quartic self-coupling which interacts via Yukawa coupling with a Dirac fermion. The model is invariant under a chiral parity operation, which can be spontaneously broken by a vev of the scalar field. We have computed explicitly Wilsonian running of relevant parameters which makes it possible to discuss in a consistent manner the issue of fine-tuning and stability of the scalar potential. This has been compared with the typical picture based on Gell-Mann-Low running. Since Wilsonian running includes autom…
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 $f(z)σ_8(z)$…
We examine, in the `t Hooft renormalization scheme, the analytic running coupling $\barα_t(Q^2)$ in QCD, using the two-loop $β$-function with positive expansion parameters $β_0$ and $β_1$. An exact integral representation is derived for this causal coupling, which is fully expressed in terms of the imaginary part of the Lambert function $W$. This integral form manifestly accounts for the universal value of the infrared limit $\barα_t(Q^2=0)= 4 π/β_0$.
Quantum loops induce an anomaly, a_mu, in the magnetic moment of the muon that can be accurately measured. Its Standard Model prediction is limited in precision by contributions from hadronic vacuum polarisation of the photon. The dominant lowest-order hadronic term can be calculated with a combination of experimental cross section data, involving e+e- annihilation to hadrons, and perturbative QCD. These are used to evaluate an energy-squared dispersion integral that strongly emphasises low photon virtualities. The dominant contribution to the integral stems from the two-pion channel that can …
We discuss a connection between gravitational-wave physics, quantum theory anomalies, right-handed (sterile) neutrinos, (spontaneous) CPT Violation and Leptogenesis, within the framework of string-inspired cosmological models. In particular, we present a scenario, according to which (primordial) gravitational waves induce gravitational anomalies during inflation. This, in turn, results in the existence of an undiluted (at the exit of inflation/beginning of radiation era) bakcground of the Kalb-Ramond (KR) axion of the massless bosonic string gravitational multiplet. The latter may violate spon…
We perform a phenomenological analysis of the observable consequences on the extended scalar sector of the SMASH (Standard Model - Axion - Seesaw - Higgs portal inflation) framework. We solve the vacuum metastability problem in a suitable region of SMASH scalar parameter spaces and discuss the one-loop correction to triple Higgs coupling $λ_{HHH}$. We also find that the correct neutrino masses and mass squared differences and baryonic asymmetry of the universe can arise from this model and consider running of the Yukawa couplings of the model. In fact, we perform a full two-loop renormalizatio…
We study a real scalar septuplet model which has a neutral component regarded as a dark matter particle candidate. The calculation of its thermal relic abundance without (with) the Sommerfeld effect suggests that the observed value corresponds to the mass of the dark matter particle $m_0 \gtrsim 8.8~(25)~\mathrm{TeV}$. Two extra quartic couplings $λ_2$ and $λ_3$ introduced in this model affect the running of other couplings, and hence the vacuum stability and the perturbativity up to the Planck scale. Therefore, the vacuum stability and the perturbativity conditions can constrain these couplin…
Using analytical methods, a nonpertubative vacuum is constructed recursively in the field theory for the open bosonic string. Evidence suggests it corresponds to the Lorentz-invariant endpoint of tachyon condensation on a D25-brane. The corresponding string field is a twisted squeezed state.
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 calculate the gravitational contributions to $ϕ^4$ theory with general $R_ξ$ gauge-fixing choice and find that the result is gauge independent. Based on weak coupling expansion of gravity and ignoring the possible higher dimensional operators from "integrating out" the impact of gravity, we study the impacts of gravitational effects on vacuum stability. New contributions to the beta function of scalar quartic coupling $\la$ by gravitational effects can modify the RGE running of $\la$ near the Planck scale. Numerical calculations show that the lower bound of higgs mass requiring absolutely v…
We report first results of an ongoing project devoted to the analytical calculation of the QCD $β$-function and the quark mass anomalous dimension at the five loop level.
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 investigate the renormalization group (RG) running of the effective potential and the pole mass in the broken symmetry phase of the $R_{ξ}$ and the $\overline{R_{ξ}}$ gauges which have different RG running for the effective potential in the symmetric phase and show that if the vacuum expectation value (VEV) is expressed as a function of the other parameters of the theory by solving the minimization condition, then the effective potential in the broken symmetry phase in both gauges satisfies the same RG equation as one in the symmetric phase of the $\overline{R_{ξ}}$ gauge. The pole masses i…
Three--loop contributions to massive QED vacuum polarization are evaluated by a combination of analytical and numerical techniques. The first three Taylor coefficients, at small $q^2$, are obtained analytically, using $d$\/--dimensional recurrence relations. Combining these with analytical input at threshold, and at large $q^2$, an accurate Padé approximation is obtained, for all $q^2$. Inserting this in the one--loop diagram for the muon anomalous magnetic moment, we find reasonable agreement with four--loop, single--electron--loop, muon--anomaly contributions, recently re--evaluated by Kinos…
I review a string-inspired cosmological model with gravitational anomalies in its early epochs, which is based on fields from the (bosonic) massless gravitational multiplet of strings, in particular gravitons and Kalb Ramond (KR), string-model independent, axions (the dilaton is assumed constant). I show how condensation of primordial gravitational waves, which are generared at the very early eras immediately after the big bang, can lead to inflation of the so called running vacuum model (RVM) type, without external inflatons. The role of the slow-roll field is played by the KR axion, but it d…
We report on recent experimental and theoretical developments in our understanding of the QCD running coupling α_s in QCD's nonperturbative regime. They allow us to analytically compute the hadron mass spectrum, with Λ_s the only input necessary to this determination. The computed spectra agrees well with experimental data.
Past analyses of the equation of state (EoS) of the Dark Energy (DE) were not incompatible with a phantom phase near our time. This has been the case in the years of WMAP observations, in combination with the remaining cosmological observables. Such situation did not completely disappear from the data collected from the Planck satellite mission. In it the EoS analysis may still be interpreted as suggesting w<-1, and so a mildly evolving DE cannot be discarded. In our opinion the usual ansatzs made on the structure of the EoS for dynamical DE models (e.g. quintessence and the like) are too simp…
The equation for two reggeized gluons with a running QCD coupling constant, proposed earlier on the basis of the bootstrap condition, is investigated by the variational technique in the vacuum channel. The pomeron intercept and slope are calculated as a function of the infrared cutoff parameter $m$ ("the gluon mass"). The intercept depends weakly on $m$ staying in the region $0.3--0.5$ for values of $m$ in the range $0.3--1.0\ GeV$. The slope goes down from $5.0\ GeV^{-2}$ to $0.08\ GeV^{-2}$ in this range. The optimal value of $m$ seems to lie in the region $0.6--0.8\ GeV$ with the intercept …
