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 (CMB) shift parameter and the Baryonic Acoustic Oscillations (BAOs) traced by the Sloan Digital Sky Survey (SDSS) galaxies, we put tight constraints on the main cosmological parameters of the $Λ(t)$ scenarios. Furthermore, we study the linear matter fluctuation field and the growth rate of clustering of the above vacuum models. 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.
We show that the energy density of the superhorizon modes released in a non-Bunch-Davies vacuum can be arbitrarily large during inflation and it decreases like ln(a)/a^4 in the subsequent radiation dominated era. This may constitute a dark radiation component which can sufficiently alter the early cosmological evolution to alleviate the Hubble tension.
We study scalar field fluctuations of the inflaton field in an early inflationary universe on an effective 4D Schwarzschild-de Sitter (SdS) metric, which is obtained after make a planar coordinate transformation on a 5D Ricci-flat Schwarzschild-de Sitter (SdS) static metric. We obtain the important result that the spectrum of fluctuations at zeroth order is independent of the scalar field mass $M$ on Schwarzschild scales, while on cosmological scales it exhibits a mass dependence. However, in the first-order expansion, the spectrum depends of the inflaton mass and the amplitude is linear with …
The decaying vacuum model (DV), treating dark energy as a varying vacuum, has been studied well recently. The vacuum energy decays linearly with the Hubble parameter in the late-times, $ρ_Λ(t) \propto H(t)$, and produces the additional matter component. We constrain the parameters of the DV model using the recent data-sets from supernovae, gamma-ray bursts, baryon acoustic oscillations, CMB, the Hubble rate and x-rays in galaxy clusters. It is found that the best fit of matter density contrast $Ω_m$ in the DV model is much lager than that in $Λ$CDM model. We give the confidence contours in the…
We consider an ultra-light scalar field with a mass comparable to (or lighter than) the Hubble parameter of the present universe, and calculate the time evolution of the energy-momentum tensor of the vacuum fluctuations generated during and before inflation until the late-time radiation-dominated and matter-dominated universe. The equation of state changes from $w=1/3$ in the early universe to $w=-1$ at present, and it can give a candidate for the dark energy that we observe today. It then oscillates between $w=-1$ and $1$ with the amplitude of the energy density decaying as $a^{-3}$. If the f…
In this work, we investigated the electroweak vacuum instability during or after inflation. In the inflationary Universe, i.e., de Sitter space, the vacuum field fluctuations $\left< {δϕ}^{ 2 } \right>$ enlarge in proportion to the Hubble scale $H^{2}$. Therefore, the large inflationary vacuum fluctuations of the Higgs field $\left< {δϕ}^{ 2 } \right>$ are potentially catastrophic to trigger the vacuum transition to the negative-energy Planck-scale vacuum state and cause an immediate collapse of the Universe. However, the vacuum field fluctuations $\left< {δϕ}^{ 2 } \right>$, i.e., the vacuum …
We study the dynamics of the FLRW flat cosmological models in which the vacuum energy density varies with time, $Λ(t)$. In particular, we investigate the dynamical properties of a generalized vacuum model and we find that under certain conditions the vacuum term in the radiation era varies as $Λ(z) \propto (1+z)^{4}$, while in the matter era we have $Λ(z)\propto (1+z)^{3}$ up to $z\simeq 3$ and $Λ(z)=Λ$ for $z\le 3$. The confirmation of such a behavior would be of paramount importance because it could provide a solution to the cosmic coincidence problem as well as to the fine tuning problem, w…
We study the dynamics of the standard model Higgs field in the inflationary cosmology. Since metastability of our vacuum is indicated by the current experimental data of the Higgs boson and top quark, inflation models with a large Hubble parameter may have a problem: In such models, the Higgs field rolls down towards the unwanted true vacuum due to the large fluctuation in the inflationary background. However, this problem can be relaxed by supposing an additional mass term for the Higgs field generated during and after inflation. We point out that it does not have to be larger than the Hubble…
The abundance of the QCD axion is known to be suppressed if the Hubble parameter during inflation, $H_{\rm inf}$, is lower than the QCD scale, and if the inflation lasts sufficiently long. We show that the tight upper bound on the inflation scale can be significantly relaxed if the eternal old inflation is driven by the standard-model Higgs field trapped in a false vacuum at large field values. Specifically, $H_{\rm inf}$ can be larger than $100\,$GeV if the false vacuum is located above the intermediate scale. We also discuss the slow-roll inflation after the tunneling from the false vacuum t…
In the context of Finsler-Randers theory we consider, for a first time, the cosmological scenario of the varying vacuum. In particular, we assume the existence of a cosmological fluid source described by an ideal fluid and the varying vacuum terms. We determine the cosmological history of this model by performing a detailed study on the dynamics of the field equations. We determine the limit of General Relativity, while we find new eras in the cosmological history provided by the geometrodynamical terms provided by the Finsler-Randers theory.
We demonstrate that creation of dark-matter particles at a constant rate implies the existence of a cosmological term that decays linearly with the Hubble rate. We discuss the cosmological model that arises in this context and test it against observations of the first acoustic peak in the cosmic microwave background (CMB) anisotropy spectrum, the Hubble diagram for supernovas of type Ia (SNIa), the distance scale of baryonic acoustic oscillations (BAO) and the distribution of large scale structures (LSS). We show that a good concordance is obtained, albeit with a higher value of the present ma…
Taking the Planck cosmic microwave background data and the more direct Hubble constant measurement data as unaffected by systematic offsets, the values of the Hubble constant $H_0$ interpreted within the $Λ$CDM cosmological constant and cold dark matter cosmological model are in $\sim 3.3 σ$ tension. We show that the Parker vacuum metamorphosis model, physically motivated by quantum gravitational effects and with the same number of parameters as $Λ$CDM, can remove the $H_0$ tension, and can give an improved fit to data (up to $Δχ^2=-7.5$). It also ameliorates tensions with weak lensing data an…
The dynamics of interacting dark matter-dark energy models is characterized through an interaction rate function quantifying the energy flow between these dark sectors. In most of the interaction functions, the expansion rate Hubble function is considered and sometimes it is argued that, as the interaction function is a local property, the inclusion of the Hubble function may influence the overall dynamics. This is the starting point of the present article where we consider a very simple interacting cosmic scenario between vacuum energy and the cold dark matter characterized by various interac…
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…
We present a novel scenario, in which light ($\sim$ few \rm{eV}) dark fermions (sterile neutrinos) interact with a scalar field like in mass varying neutrino dark energy theories. As the $\rm{eV}$ sterile states naturally become non-relativistic before the Matter Radiation Equality (MRE), we show that the neutrino-scalar fluid develops strong perturbative instability followed by the formation of neutrino-nuggets and the early dark energy behaviour disappears around MRE. The stability of the nugget is achieved when the Fermi pressure balances the attractive scalar force and we numerically find …
We investigate the virialization of cosmic structures in the framework of flat FLRW 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, $Λ=Λ(H)$. A particularly well motivated model of this type is the so-called quantum field vacuum, in which $Λ(H)$ is a quadratic function, $Λ(H)=n_0+n_2\…
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…
In this work we investigate the holographic dark energy models with slowly time-varying model parameter defined based on the current Hubble horizon length scale. While the previous studies on the three popular holographic dark energy models defined based on the future event horizon, Ricci scale and Granda-Oliveros IR cutoffs showed that these models cannot fit the observational data [1], in this work we show that the holographic dark energy models with time-varying model parameter defined on the current Hubble radius are well favored by observations. Using the standard $χ^2$ minimization in th…
We examine the decay vacuum model with a parameter $ε$ that indicates the vacuum energy decay rate. By constraining this model with cosmic microwave background radiation, baryon acoustic oscillation, type Ia supernovae and 30 H(z) cosmic chronometer data points, we find that $ε=-0.0003\pm0.00024$ with the best fitted $χ^{2}$ value slightly smaller than that in the $Λ$CDM model. A negative value of $ε$ suggesting dark matter energy decay into vacuum energy. We also obtain the Hubble constant $H_{0}=68.05\pm0.56$ that can alleviate the current $H_{0}$ tension between the local observation by the…
The recently suggested Festina-Lente (FL) bound provides a lower bound on the masses of ${\rm U(1)}$ charged particles in terms of the positive vacuum energy. Since the charged particle masses in the Standard Model (SM) are generated by the Higgs mechanism, the FL bound provides a testbed of consistent Higgs potentials in the current dark energy-dominated universe as well as during inflation. We study the implications of the FL bound on the UV behavior of the Higgs potential for a miniscule vacuum energy, as in the current universe. We also present values of the Hubble parameter and the Higgs …
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…
We consider an open universe created by bubble nucleation, and study possible effects of an "ancestor vacuum" (de Sitter space in which bubble nucleation occurred) on the present universe. We compute vacuum expectation values of energy-momentum tensor for a minimally coupled scalar field, carefully taking into account the effect of the ancestor vacuum by the Euclidean prescription. In the study of the time evolution, an important role is played by the so-called supercurvature mode, which is non-normalizable on a spatial slice of open universe and decays in time most slowly. We point out that v…
In this year, in which we celebrate 100 years of the cosmological term, $Λ$, in Einstein's gravitational field equations, we are still facing the crucial question whether $Λ$ is truly a fundamental constant or a mildly evolving dynamical variable. After many theoretical attempts to understand the meaning of $Λ$, and in view of the enhanced accuracy of the cosmological observations, it seems now mandatory that this issue should be first settled empirically before further theoretical speculations on its ultimate nature. In this work, we summarize the situation of some of these studies. Devoted a…
We explore a model introduced by Cyr-Racine, Ge, and Knox (arXiv:2107.13000(2)) that resolves the Hubble tension by invoking a ``mirror world" dark sector with energy density a fixed fraction of the ``ordinary" sector of Lambda-CDM. Although it reconciles cosmic microwave background and large-scale structure observations with local measurements of the Hubble constant, the model requires a value of the primordial Helium mass fraction that is discrepant with observations and with the predictions of Big Bang Nucleosynthesis (BBN). We consider a variant of the model with standard Helium mass fract…
We consider the vacuum energy of massive quantum fields in an expanding universe. We define a conserved renormalized energy-momentum tensor by means of a comoving cutoff regularization. Using exact solutions for de Sitter space-time, we show that in a certain range of mass and renormalization scales there is a contribution to the vacuum energy density that scales as nonrelativistic matter and that such a contribution becomes dominant at late times. By means of the WKB approximation, we find that these results can be extended to arbitrary Robertson-Walker geometries. We study the range of param…
We propose a novel cosmological scenario with the space-time emerging from a pure initial de Sitter stage and subsequently evolving into the radiation, matter and dark energy dominated epochs, thereby avoiding the initial singularity and providing a complete description of the expansion history and a natural solution to the horizon problem. The model is based on a dynamical vacuum energy density which evolves as a power series of the Hubble rate. The transit from the inflation into the standard radiation epoch is universal, giving a clue for a successful description of the graceful exit. Since…
We show that the entropy of cosmological perturbations originating as quantum vacuum fluctuations in the very early universe, including the contribution of the leading nonlinear interactions, can be viewed as momentum space entanglement entropy between sub- and super-Hubble modes. The interactions between these modes causes decoherence of the super-Hubble fluctuations which, in turn, leads to a non-vanishing entropy of the reduced density matrix corresponding to the super-Hubble inhomogeneities. In particular, applying this to inflationary cosmology reveals that the entanglement entropy produc…
The thermodynamic behavior of a decaying vacuum cosmology describing the entire cosmological history evolving between two extreme (early and late time) de Sitter eras is investigated. The thermal evolution from the early de Sitter to the radiation phase is discussed in detail. The temperature evolution law and the increasing entropy function are analytically determined. The entropy of the effectively massless particles is initially zero but evolves continuously to the present day maximum value within the current Hubble radius, $S_0 \sim 10^{88}$ in natural units. By using the Gibbons-Hawking t…
We constrain the neutrino mass in the scenario of vacuum energy interacting with cold dark matter by using current cosmological observations. To avoid the large-scale instability problem in interacting dark energy models, we employ the parameterized post-Friedmann (PPF) approach to do the calculation of perturbation evolution, for the $Q=βHρ_{\rm c}$ and $Q=βHρ_Λ$ models. The current observational data sets used in this work include Planck (cosmic microwave background), BSH (baryon acoustic oscillations, type Ia supernovae, and Hubble constant), and LSS (redshift space distortions and weak len…
Standard Model Higgs Peaks: a Note on the Vacuum Instability during Inflation
Università degli Studi di Padova（帕多瓦大学）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；National Technical University of Athens（雅典国立技术大学）；Université de Genève（日内瓦大学）
We explore the bounds that can be placed on interactions between cold dark matter and vacuum energy, with equation of state $w=-1$, using state-of-the-art cosmological observations. We consider linear perturbations about a simple background model where the energy transfer per Hubble time, $Q/H$, is a general linear function of the dark matter density, $ρ_c$, and vacuum energy, $V$. We explain the parameter degeneracies found when fitting cosmic microwave background (CMB) anisotropies alone, and show how these are broken by the addition of supernovae data, baryon acoustic oscillations (BAO) and…
In this work I reason that in expanding space only those quantum modes contribute to the measured vacuum energy that do not transcend the observable volume. Since all quantised field modes have various observable consequences, when a gravitational horizon causally confines an observer to a finite volume quantised modes should be restricted to the observable patch to remain consistent with gravity. Within the observable patch of Friedmann-Lemaitre-Robertson-Walker (FLRW) space the vacuum expectation value of the energy-momentum tensor can be expressed as a sum over discrete field modes. Friedma…
We discuss the issue of setting appropriate initial conditions for inflation. Specifically, we consider natural inflation model and discuss the fine tuning required for setting almost homogeneous initial conditions over a region of order several times the Hubble size which is orders of magnitude larger than any relevant correlation length for field fluctuations. We then propose to use the special propagating front solutions of reaction-diffusion equations for localized field domains of smaller sizes. Due to very small velocities of these propagating fronts we find that the inflaton field in su…
Our current measurements of the Standard Model parameters imply that the Higgs field resides in a metastable electroweak vacuum, where the vacuum can decay to a lower ground state, with cataclysmic repercussions for our Universe. According to our observations, no such event has happened in the observable universe, in spite of the various energetic processes that could have triggered it. This work serves as an overview of a method that uses the metastability of the false vacuum during cosmological inflation to provide constraints on the Higgs curvature coupling $ξ$. Considering also the effects…
Varying fundamental constants (VFC) [e.g., the fine-structure constant, $α_{\rm EM}$] can arise in numerous extended cosmologies. Through their effect on the decoupling of baryons and photons during last scattering and reionisation, these models can be directly constrained using measurements of the cosmic microwave background (CMB) temperature and polarization anisotropies. Previous investigations focused mainly on time-independent changes to the values of fundamental constants. Here we generalize to time-dependent variations. Instead of directly studying various VFC parameterizations, we perf…
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…
In this paper, we investigate the observational constraints on the scenario of vacuum energy interacting with cold dark matter. We consider eight typical interaction forms in such an interacting vacuum energy scenario. The observational data used in this work to constrain these models include the JLA sample of type Ia supernovae observation, the Planck 2015 distance priors data of cosmic microwave background anisotropies observation, the baryon acoustic oscillations data, and the Hubble constant direct measurement. We find that the current observational data almost equally favor these interact…
Holographic dark energy (HDE) describes the vacuum energy in a cosmic IR region whose total energy saturates the limit of avoiding the collapse into a black hole. HDE predicts that the dark energy equation of the state transiting from greater than the $-1$ regime to less than $-1$, accelerating the Universe slower at the early stage and faster at the late stage. We propose the HDE as a new {\it physical} resolution to the Hubble constant discrepancy between the cosmic microwave background (CMB) and local measurements. With Planck CMB and galaxy baryon acoustic oscillation (BAO) data, we fit th…
We propose a new model of Early Dark Energy (EDE) as a solution to the Hubble tension in cosmology, the apparent discrepancy between local measurements of the Hubble constant $H_0\simeq 74$ km s$^{-1}$ Mpc$^{-1}$ and $H_0\simeq 67$ km s$^{-1}$ Mpc$^{-1}$ inferred from the Cosmic Microwave Background (CMB). In Chain EDE, the Universe undergoes a series of first order phase transitions, starting at a high energy vacuum in a potential, and tunneling down through a chain of every lower energy metastable minima. As in all EDE models, the contribution of the vacuum energy to the total energy density…
We generalize the ultraviolet sector of gravitation via a Born-Infeld action using lessons from massive gravity. The theory contains all of the elementary symmetric polynomials and is treated in the Palatini formalism. We show how the connection can be solved algebraically to be the Levi-Civita connection of an effective metric. The non-linearity of the algebraic equations yields several branches, one of which always reduces to General Relativity at low curvatures. We explore in detail a {\it minimal} version of the theory, for which we study solutions in the presence of a perfect fluid with s…
We investigate a spatially flat Friedmann-Lemaître-Robertson-Walker cosmology in which a decaying vacuum term causes matter production at late times. Assuming a decay proportional to the Hubble rate, the ratio of the background energy densities of dark matter and dark energy changes with the cosmic scale factor as $a^{-3/2}$. The intrinsically non-adiabatic two-component perturbation dynamics of this model is reduced to a single second-order equation. Perturbations of the vacuum term are shown to be negligible on scales that are relevant for structure formation. On larger scales, dark-energy p…
The sequestering mechanism has been proposed as a remedy to the old cosmological constant problem of the non-gravitating vacuum energy in the matter sector. Here it is shown that an extension of this global constraint mechanism arises naturally from an averaging condition for residual cosmological constants produced in different patches of the Universe. The new mechanism naturally yields the small observed value that gives rise to cosmic acceleration at late times, hence, addressing the new cosmological constant problem. Hereby the halo model picture is adopted with all matter content ultimate…
Recently there have been claims on model-independent evidence of dynamical dark energy. Herein we consider a fairly general class of cosmological models with a time-evolving cosmological term of the form $Λ(H)=C_0+C_H H^2+C_{\dot{H}} \dot{H}$, where $H$ is the Hubble rate. These models are well motivated from the theoretical point of view since they can be related to the general form of the effective action of quantum field theory in curved spacetime. Consistency with matter conservation can be achieved by letting the Newtonian coupling $G$ change very slowly with the expansion. We solve these…
An expanding universe is not expected to have a static vacuum energy density. The so-called cosmological constant $Λ$ should be an approximation, certainly a good one for a fraction of a Hubble time, but it is most likely a temporary description of a true dynamical vacuum energy variable that is evolving from the inflationary epoch to the present day. We can compare the evolving vacuum energy with a Casimir device where the parallel plates slowly move apart ("expand"). The total vacuum energy density cannot be measured, only the effect associated to the presence of the plates, and then also th…
The integrated Sachs-Wolfe (ISW) effect is an important implication for dark energy. In this paper, we have calculated the power spectrum of the ISW effect in the time varying vacuum cosmological model, where the model parameter $β=4.407$ is obtained by the observational constraint of the growth rate. It's found that the source of the ISW effect is not only affected by the different evolutions of the Hubble function $H(a)$ and the dimensionless matter density $Ω_m(a)$, but also by the different growth function $D_+(a)$, all of which are changed due to the presence of matter production term in …
We consider the observational aspects of the value of dark energy density from quantum vacuum fluctuations based initially on the Gurzadyan-Xue model. We reduce the Djorgovski-Gurzadyan integral equation to a differential equation for the co-moving horizon and then, by means of the obtained explicit form for the luminosity distance, we construct the Hubble diagram for two classes of observational samples. For supernova and gamma-ray burst data we show that this approach provides viable predictions for distances up to $z \simeq 9$, quantitatively at least as good as those provided by the lambda…
We review the dynamics of spectator scalar fields non-minimally coupled to gravity in the post-inflationary Universe, with particular emphasis on scenarios where the end of inflation is followed by a period of kination. In this context, the evolution of the Ricci scalar can lead to the spontaneous breaking of discrete or continuous symmetries through tachyonic instabilities. These Hubble-induced phase transitions may cause the amplification of field fluctuations, the formation of transient topological defects, and an efficient energy transfer into relativistic degrees of freedom. We analyze th…
