Despite the enormous significance of the Higgs potential in the context of the standard model of electroweak interactions and in grand unified theories, its ultimate origin is fundamentally unknown and must be introduced by hand in accordance with the underlying gauge symmetry and the requirement of renormalizability. Here we propose a more physical motivation for the structure of the Higgs potential, which we derive from a generalized Brans–Dicke (BD) theory containing two interacting scalar fields. One of these fields is coupled to curvature as in the BD formulation, whereas the other is coupled to gravity both derivatively and non-derivatively through the curvature scalar and the Ricci tensor. By requiring that the cosmological solutions of the model are consistent with observations, we show that the effective scalar field potential adopts the Higgs potential form with a mildly time-evolving vacuum expectation value. This residual vacuum dynamics could be responsible for the possible time variation of the fundamental constants, and is reminiscent of former Bjorken's ideas on the cosmological constant problem.

Despite the fact that a rigid -term is a fundamental building block of the concordance ΛCDM model, we show that a large class of cosmological scenarios with dynamical vacuum energy density together with a dynamical gravitational coupling G or a possible non‐conservation of matter, are capable of seriously challenging the traditional phenomenological success of the ΛCDM. In this paper, we discuss these “running vacuum models” (RVMs), in which consists of a nonvanishing constant term and a series of powers of the Hubble rate. Such generic structure is potentially linked to the quantum field theoretical description of the expanding universe. By performing an overall fit to the cosmological observables SN Ia+BAO+H(z)+LSS+BBN+CMB (in which the WMAP9, Planck 2013, and Planck 2015 data are taken into account), we find that the class of RVMs appears significantly more favored than the ΛCDM, namely, at an unprecedented level of . Furthermore, the Akaike and Bayesian information criteria confirm that the dynamical RVMs are strongly preferred compared to the conventional rigid -picture of the cosmic evolution.

Perhaps the deepest mystery of our accelerating Universe in expansion is the existence of a tiny and rigid cosmological constant, Λ. Its size is many orders of magnitude below the expected one in the standard model of particle physics. However, an expanding Universe is not expected to have a static vacuum energy density. We should rather observe a mildly dynamical behavior δΛ(t)∼ R∼ H^2(t) with the expansion rate H. At the same time, it is natural to think that the huge value of the primeval vacuum energy (presumably connected to some grand unified theory) was responsible for the initial inflationary phase. In the traditional inflaton models such phase is inserted by hand in the early epoch of the cosmic evolution, and it is assumed to match the concordance ΛCDM regime during the radiation epoch. Here, instead, we consider a class of dynamical vacuum models which incorporate into a single vacuum structure Λ̅(H) the rapid stage of inflation, followed by the radiation and cold matter epochs, until achieving our dark energy Universe. The early behavior of the model bares resemblance with Starobinsky's inflation and ptovides a solution to the large entropy problem. It is compatible with the latest cosmological data on Hubble expansion and structure formation, and presents distinctive observational features that can be tested in the near future.

We derive for the first time the growth index of matter perturbations of the Friedmann-Lemaitre-Robertson-Walker (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 Lambda(0), there is also an H-2 dependence in the functional form of the vacuum, namely, Lambda(H) = Lambda(0) + 3 nu(H-2 - H-0(2)). Since vertical bar nu vertical bar << 1, 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 the perturbation level, we find that the growth index of the running vacuum cosmological model is gamma (Lambda H) approximate to 6+3 nu/11-12 nu, and thus it nicely extends analytically the result of the Lambda CDM model, gamma(Lambda) approximate to 6/11.

In quantum haplodynamics (QHD) the weak bosons, quarks and leptons are bound states of fundamental constituents, denoted as haplons. The confinement scale of the associated gauge group SU(2)_h is of the order of $\Lambda_h\simeq 0.3$ TeV. One scalar state has zero haplon number and is the resonance observed at the LHC. In addition, there exist new bound states of haplons with no counterpart in the SM, having a mass of the order of 0.5 TeV up to a few TeV. In particular, a neutral scalar state with haplon number 4 is stable and can provide the dark matter in the universe. The QHD, QCD and QED couplings can unify at the Planck scale. If this scale changes slowly with cosmic time, all of the fundamental couplings, the masses of the nucleons and of the DM particles, including the cosmological term (or vacuum energy density), will evolve with time. This could explain the dark energy of the universe.

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 simplified. In this work we examine in detail some of these issues and suggest that a general class of models with a dynamical vacuum energy density could explain the persistent phantom anomaly, despite there is no trace of real phantom behavior in them. The spurious or "mirage" effect is caused by an attempt to describe them as if the DE would be caused by fundamental phantom scalar fields. Remarkably, the effective DE behavior can also appear as quintessence in transit to phantom, or vice versa.

We review selected results for Higgs boson production at Linear Colliders in the framework of the general Two-Higgs-Doublet Model (2HDM). We concentrate on the analysis of i) the pairwise production of neutral Higgs bosons (hA,HA); and ii) the neutral Higgs boson-strahlung modes (hZ, HZ). We identify sizable production rates, in the range of 10-100 fb for center-of-mass energies of 0.5 TeV, alongside with large quantum effects (up to 50 %), which we can fundamentally track down to the enhancement power of the triple-Higgs self-interactions. This constitutes a telltale signature of the 2HDM, with no counterpart in e.g. the Minimal Supersymmetric Standard Model (MSSM). We compare these results with several complementary double and triple Higgs-boson production mechanisms at order O(\alpha^3_{ew})-O(\alpha^4_{ew} and spotlight a characteristic phenomenological profile which could eventually be highly distinctive of a non-supersymmetric two-Higgs-doublet structure.

In an expanding universe, the vacuum energy density ρΛ is expected to be a dynamical quantity. In quantum field theory in curved spacetime, ρΛ should exhibit a slow evolution, determined by the expansion rate of the universe H. Recent measurements on the time variation of the fine-structure constant and of the proton–electron mass ratio suggest that the basic quantities of the standard model, such as the QCD scale parameter ΛQCD, may not be conserved in the course of the cosmological evolution. The masses of the nucleons mN and of the atomic nuclei would also be affected. Matter is not conserved in such a universe. These measurements can be interpreted as a leakage of matter into vacuum or vice versa. We point out that the amount of leakage necessary to explain the measured value of could be of the same order of magnitude as the observationally allowed value of , with a possible contribution from the dark matter particles. The dark energy in our universe could be the dynamical vacuum energy in interaction with ordinary baryonic matter as well as with dark matter.

The experimental evidence that the equation of state (EoS) of the dark energy (DE) could be evolving with time, suggests that the Λ‐term in the gravity action should rather be an effective quantity Λeff(t) involving new dynamical terms X(t). Remarkably, a class of these ΛXCDM models could be the clue for solving the old cosmological constant problem, including the cosmic coincidence problem. We propose a permanent (i.e. not just a late‐time) modification of gravity which is able to account for these problems, and without affecting the standard cosmological evolution of the universe.

We revisit the production of a single Higgs boson from direct \gamma \gamma -scattering at a photon collider. We compute the total cross section \sigma(\gamma \gamma \to h) (for h=h0, H0, A0), and the strength of the effective g_{h \gamma \gamma} coupling normalized to the Standard Model (SM), for both the general Two-Higgs-Doublet Model (2HDM) and the Minimal Supersymmetric Standard Model (MSSM). In both cases the predicted production rates for the CP-even (odd) states render up to 10^4 (10^3) events per 500 \invfb of integrated luminosity, in full consistency with all the theoretical and phenomenological constraints. Depending on the channel the maximum rates can be larger or smaller than the SM expectations, but in most of the parameter space they should be well measurable. We analyze how these departures depend on the dynamics underlying each of the models, supersymmetric and non-supersymmetric, and highlight the possible distinctive phenomenological signatures. We demonstrate that this process could be extremely helpful to discern non-supersymmetric Higgs bosons from supersymmetric ones. Furthermore, in the MSSM case, we show that \gamma\gamma-physics could decisively help to overcome the serious impasse afflicting Higgs boson physics at the infamous "LHC wedge".

The idea that the cosmological term, Lambda, should be a time dependent quantity in cosmology is a most natural one. It is difficult to conceive an expanding universe with a strictly constant vacuum energy density, namely one that has remained immutable since the origin of time. A smoothly evolving vacuum energy density that inherits its time-dependence from cosmological functions, such as the Hubble rate or the scale factor, is not only a qualitatively more plausible and intuitive idea, but is also suggested by fundamental physics, in particular by quantum field theory (QFT) in curved space-time. To implement this notion, is not strictly necessary to resort to ad hoc scalar fields, as usually done in the literature (e.g. in quintessence formulations and the like). A "running" Lambda term can be expected on very similar grounds as one expects (and observes) the running of couplings and masses with a physical energy scale in QFT. Furthermore, the experimental evidence that the equation of state of the dark energy could be evolving with time/redshift (including the possibility that it might currently behave phantom-like) suggests that a time-variable Lambda term (possibly accompanied by a variable Newton's gravitational coupling G=G(t)) could account in a natural way for all these features. Remarkably enough, a class of these models (the "new cosmon") could even be the clue for solving the old cosmological constant problem, including the coincidence problem.

We investigate the virialization of cosmic structures in the framework of flat Friedmann-Lemaitre-Robertson-Walker cosmological models, in which the vacuum energy density evolves with time. In particular, our analysis focuses on the study of spherical matter perturbations, as they decouple from the background expansion, "turn around,'' and finally collapse. We generalize the spherical collapse model in the case when the vacuum energy is a running function of the Hubble rate, Lambda = Lambda(H). A particularly well-motivated model of this type is the so-called quantum field vacuum, in which Lambda(H) is a quadratic function, Lambda(H) = n(0) + n(2)H(2), with n(0) not equal 0. This model was previously studied by our team using the latest high quality cosmological data to constrain its free parameters, as well as the predicted cluster formation rate. It turns out that the corresponding Hubble expansion history resembles that of the traditional Lambda CDM cosmology. We use this Lambda(t)CDM framework to illustrate the fact that the properties of the spherical collapse model (virial density, collapse factor, etc.) depend on the choice of the considered vacuum energy (homogeneous or clustered). In particular, if the distribution of the vacuum energy is clustered, then, under specific conditions, we can produce more concentrated structures with respect to the homogeneous vacuum energy case.

Cosmologies with running cosmological term ρΛ and gravitational Newton's coupling G may naturally be expected if the evolution of the universe can ultimately be derived from the first principles of quantum field theory or string theory. For example, if matter is conserved and the vacuum energy density varies quadratically with the expansion rate as ρΛ(H) = n0 + n2 H2, with n0 ≠ 0 (a possibility that has been advocated in the literature within the QFT framework), it can be shown that G must vary logarithmically (hence very slowly) with H. In this paper, we derive the general cosmological perturbation equations for models with variable G and ρΛ in which the fluctuations δG and δρΛ are explicitly included. We demonstrate that if matter is covariantly conserved, the late growth of matter density perturbations is independent of the wavenumber k. Furthermore, if ρΛ is negligible at high redshifts and G varies slowly, we find that these cosmologies produce a matter power spectrum with the same shape as that of the ΛCDM model, thus predicting the same basic features on structure formation. Despite this shape indistinguishability, the free parameters of the variable G and ρΛ models can still be effectively constrained from the observational bounds on the spectrum amplitude.

We analyze some generic properties of the dark energy (DE) perturbations, in the case of a self-conserved DE fluid. We also apply a simple test (the "F-test") to compare a model to the data on large scale structure (LSS) under the assumption of negligible DE perturbations. We exemplify our discussions by means of the LXCDM model, showing that it provides a viable solution to the cosmological coincidence problem.

We present a one-loop analysis of the pairwise production of neutral Higgs bosons (h0A0, H0A0) at linear colliders, such as the ILC and CLIC, within the general Two-Higgs-Doublet Model (2HDM). We single out sizable radiative corrections, which can well reach the level of 50 % and may be either positive (typically for \sqrt{s} \sim 0.5 TeV) and negative (for \sqrt{s} of 1 TeV and above). These large quantum effects, obtained in full agreement with the current phenomenological bounds and the stringent theoretical constraints on the parameter space of the model, can be traced back to the enhancement capabilities of the triple-Higgs self-interactions -- a trademark feature of the 2HDM, with no counterpart in e.g. the Minimal Supersymmetric Standard Model. In the most favorable scenarios, the Higgs-pair cross sections may be boosted up to barely 30 fb at the fiducial center-of-mass energy of 500 GeV -- amounting to a few thousand events per 500 inverse femtobarn of integrated luminosity. We also compare these results with several complementary double and triple Higgs-boson production mechanisms at order \alpha^3_{ew} and leading \alpha^4_{ew}, and we spotlight a plethora of potentially distinctive signatures of a Two-Higgs-Doublet structure of non-supersymmetric nature.

The pairwise production of neutral Higgs bosons (h(0)A(0), H(0)A(0)) is analyzed in the context of the future linear colliders, such as the ILC and CLIC, within the general two-Higgs-doublet model (2HDM). The corresponding cross sections are computed at the one-loop level, including the full set of contributions at order O(alpha(3)(ew)) together with the leading O(alpha(4)(ew)) terms, in full compliance with the current phenomenological bounds and the stringent theoretical constraints inherent to the consistency of the model. We uncover regions across the 2HDM parameter space, mainly for low tan beta similar to 1 and moderate-and negative-values of the relevant lambda(5) parameter, wherein the radiative corrections to the Higgs-pair production cross section, sigma(e(+)e(-) -> A(0)h(0)/A(0)H(0)), can comfortably reach vertical bar delta sigma vertical bar/sigma similar to 50%. This behavior can be traced back to the enhancement capabilities of the trilinear Higgs self-interactions-a trademark feature of the 2HDM, with no counterpart in the minimal supersymmetric standard model (MSSM). The corrections are strongly dependent on the actual value of lambda(5) as well as on the Higgs mass spectrum. Interestingly enough, the quantum effects are positive for energies around root s similar or equal to 500 GeV, thereby producing a significant enhancement in the expected number of events precisely around the fiducial startup energy of the ILC. The Higgs-pair production rates can be substantial, typically a few tens of femtobarn, therefore amounting to a few thousand events per 500 fb(-1) of integrated luminosity. In contrast, the corrections are negative in the highest energy range (viz. root s similar to 1 TeV and above). We conclude that a precise measurement of the 2H final states could carry unambiguous footprints of an extended (nonsupersymmetric) Higgs sector. Finally, to better assess the scope of these effects, we compare the exclusive pairwise production of Higgs bosons with the inclusive gauge boson fusion channels leading to 2H + X final states, and also with the exclusive triple Higgs boson production. We find that these multiparticle final states can be highly complementary in the overall Higgs bosons search strategy.

Inclusive Higgs boson pair production through the mechanism of gauge boson fusion e+e−→V∗V∗→hh+X (V=W±,Z) in the general Two-Higgs-Doublet Model (2HDM), with h=h0,H0,A0,H±, is analyzed at O(αew4) in the linear colliders ILC and CLIC. This kind of processes is highly sensitive to the trilinear (3H) Higgs boson self-interactions and hence can be a true keystone in the reconstruction of the Higgs potential. For example, in the ILC at 1 TeV, the most favorable scenarios yield cross-sections up to roughly 1 pb, thus entailing 105 events per 100 fb−1 of integrated luminosity, whilst remaining fully consistent with the perturbativity and unitarity bounds on the 3H couplings, the electroweak precision data and the constraints from B(b→sγ). Comparing with other competing mechanisms, we conclude that the Higgs boson-pair events could be the dominant signature for Higgs-boson production in the TeV-class linear colliders for a wide region of the 2HDM parameter space, with no counterpart in the Minimal Supersymmetric Standard Model (MSSM). Owing to the extremely clean environment of these colliders, inclusive 2H events should allow a comfortable tagging and might therefore open privileged new vistas into the structure of the Higgs potential.

We investigate the properties of the FLRW flat cosmological models in which the vacuum energy density evolves with time, $\ensuremath{\Lambda}(t)$. Using different versions of the $\ensuremath{\Lambda}(t)$ 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 $\ensuremath{\Lambda}(t)$ scenarios. Furthermore, we study the linear matter fluctuation field of the above vacuum models. We find that the patterns of the power series vacuum $\ensuremath{\Lambda}={n}_{1}H+{n}_{2}{H}^{2}$ 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 $\ensuremath{\Lambda}={n}_{0}+{n}_{2}{H}^{2}$, the corresponding matter fluctuation field resembles that of the traditional $\ensuremath{\Lambda}$ cosmology. The power law vacuum ($\ensuremath{\Lambda}\ensuremath{\propto}{a}^{\ensuremath{-}n}$) 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 $\ensuremath{\Lambda}(t)$ models. Performing a Kolmogorov-Smirnov statistical test we show that the cosmological models which contain a constant vacuum ($\ensuremath{\Lambda}\mathrm{CDM}$), 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 $\ensuremath{\Lambda}\ensuremath{\propto}H$ model) in which clusters form at significantly earlier times ($z\ensuremath{\ge}4$) with respect to all other models ($z\ensuremath{\sim}2$). 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.

While there is plentiful evidence in all fronts of experimental cosmology for the existence of a nonvanishing dark energy (DE) density rho(D) in the Universe, we are still far away from having a fundamental understanding of its ultimate nature and of its current value, not even of the puzzling fact that rho(D) is so close to the matter energy density rho(M) at the present time (i.e. the so-called "cosmic coincidence" problem). The resolution of some of these cosmic conundrums suggests that the DE must have some (mild) dynamical behavior at the present time. In this paper, we examine some general properties of the simultaneous set of matter and DE perturbations (delta rho(M),delta rho(D)) for a multicomponent DE fluid. Next we put these properties to the test within the context of a nontrivial model of dynamical DE (the Lambda XCDM model) which has been previously studied in the literature. By requiring that the coupled system of perturbation equations for delta rho(M) and delta rho(D) has a smooth solution throughout the entire cosmological evolution, that the matter power spectrum is consistent with the data on structure formation, and that the "coincidence ratio" r=rho(D)/rho(M) stays bounded and not unnaturally high, we are able to determine a well-defined region of the parameter space where the model can solve the cosmic coincidence problem in full compatibility with all known cosmological data.

Despite the many outstanding cosmological observations leading to a strong evidence for a non-vanishing cosmological constant (CC) term Λ in the gravitational field equations, the theoretical status of this quantity seems to be lagging well behind the observational successes. It thus seems timely to revisit some fundamental aspects of the CC term in Quantum Field Theory (QFT). We emphasize that, in curved space–time, nothing a priori prevents this term from potentially having a mild running behavior associated to quantum effects. Remarkably, this could be the very origin of the dynamical nature of the Dark Energy, in contrast to many other popular options considered in the literature. In discussing this possibility, we also address some recent criticisms concerning the possibility of such running. Our conclusion is that, while there is no comprehensive proof of the CC running, there is no proof of the non-running either. The problem can be solved only through a deeper understanding of the vacuum contributions of massive quantum fields on a curved space–time background. We suggest that such investigations are at the heart of one of the most important endeavors of fundamental theoretical cosmology in the years to come.