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 the resulting late time cosmic history is very close to the concordance LCDM model, the new unified framework embodies a more complete past cosmic evolution than the standard cosmology.
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…
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 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…
We study gravitational waves generated during the inflationary epoch in presence of a decaying cosmological parameter on a 5D geometrical background which is Riemann flat. Two examples are considered, one with a constant cosmological parameter and the second with a decreasing one.
In this work I discuss the dynamical and thermodynamical equivalence between a general k-essence scalar field cosmology and an arbitrary cosmological model with a decaying vacuum, thus generalizing the approach proposed by Maia and Lima [Phys. Rev. D {\bf 65}, 083513 (2002)]. The formalism obtained is quite general and holds for any non-canonical scalar field model. As a special case I derive a Dirac-Born-Infeld (DBI) model with an exponential potential and constant speed of sound, and show that it is equivalent to a cosmological model with decay law $Λ(H) = 3βH^2$.
We develop an stochastic approach to study gravitational waves produced during the inflationary epoch under the presence of a decaying cosmological parameter, on a 5D geometrical background which is Riemann flat. We obtain that the squared tensor metric fluctuations depend strongly on the cosmological parameter $Λ(t)$ and we finally illustrate the formalism with an example of a decaying $Λ(t)$.
We consider General Relativity with matter and radiation, one of these fluids being coupled to vacuum. We find that Universe dynamics starts by an inflation phase if the coupled fluid has a negative energy density at early time. Then, there is always a finite scale factor singularity but when vacuum and matter are coupled and matter density behaves like a negative radiation density. Moreover, the convergence to the LCDM model is clearly easier to reach when vacuum is coupled to matter rather than to radiation. Two classes of theories are studied to illustrate these results.
We study a model that the entropy per particle in the universe is constant. The sources for the entropy are the particle creation and a lambda decaying term. We find exact solutions for the Einstein field equations and show the compatibilty of the model with respect to the age and the acceleration of the universe.
The thermodynamic behavior of vacuum decaying cosmologies is investigated within a manifestly covariant formulation. Such a process corresponds to a continuous irreversible energy flow from the vacuum component to the created matter constituents. It is shown that if the specific entropy per particle remains constant during the process, the equilibrium relations are preserved. In particular, if the vacuum decays into photons, the energy density $ρ$ and average number density of photons $n$ scale with the temperature as $ρ\sim T^{4}$ and $n \sim T^{3}$. The temperature law is determined and a ge…
Recent developments in string compactifications demonstrate obstructions to the simplest constructions of low energy cosmologies with positive vacuum energy. The existence of obstacles to creating scale-separated de Sitter solutions indicates a UV/IR puzzle for embedding cosmological vacua in a unitary theory of quantum gravity. Motivated by this puzzle, we propose an embedding of positive energy Friedmann-Lemaitre-Robertson-Walker cosmology within string theory. Our proposal involves confining 4D gravity on a brane which mediates the decay from a non-supersymmetric false AdS5 vacuum to a true…
In this work we study the evolution of matter-density perturbations for an arbitrary $Λ(t)$ model, and specialize our analysis to the particular phenomenological law $Λ= Λ_0 + 3βH^2$. We study the evolution of the cosmic star formation rate in this particular dark energy scenario and, by constraining the $β$ parameter using both the age of the universe and the cosmic star formation rate curve, we show that it leads to a reasonable physical model for $β\lesssim 0.1$.
A model of a cloud formed by massive strings is used as a source of LRS Bianchi type II with time decaying vacuum energy density $Λ$. To construct string cosmological models we have used the energy-momentum tensor for such string as formulated by Letelier (1983). The high nonlinear field equations have been solved for two types of strings, (i) Massive string and (ii) Nambu string. The expansion $θ$ in the model is assumed to be proportional to the shear $σ$. This condition leads to $A=βB^{m}$, where $A$ and $B$ are the metric coefficients, $m$ is a constant and $β$ is an integrating constant. …
Decaying vacuum models are a class of models that incorporate the vacuum energy density as a time-evolving entity that has the potential to explain the entire evolutionary history of the universe in a single framework. A general solution to the Friedmann equation can be obtained by considering vacuum energy density as a function of the Hubble parameter. We have obtained the asymptotic solution by choosing the appropriate equation of state for matter and radiation. Finite boundaries in the early and late de Sitter epoch could be defined by considering the evolution of primordial perturbation wa…
Introducing a variable cosmological function $Λ(t)$ in a geometrical manner from a 5D Riemann-flat metric, we investigate the possibility of having a geometrical criterion to choose a suitable cosmological function $Λ(t)$ for every 4D dynamical hypersurface capable of generate phantom cosmologies.
We propose a large class of nonsingular cosmologies of arbitrary spatial curvature whose cosmic history is determined by a primeval dynamical $Λ(t)$-term. For all values of the curvature, the models evolve between two extreme de Sitter phases driven by the relic time-varying vacuum energy density. The transition from inflation to the radiation phase is universal and points to a natural solution of the graceful exit problem regardless of the values of the curvature parameter. The flat case recovers the scenario recently discussed in the literature (Perico et al., Phys. Rev. D88, 063531, 2013). …
We investigate cosmological solutions of Brans-Dicke theory with both the vacuum energy density and the gravitational constant decaying linearly with the Hubble parameter. A particular class of them, with constant deceleration factor, sheds light on the cosmological constant problems, leading to a presently small vacuum term, and to a constant ratio between the vacuum and matter energy densities. By fixing the only free parameter of these solutions, we obtain cosmological parameters in accordance with observations of both the relative matter density and the universe age. In addition, we have t…
Properties of unstable false vacuum states are analyzed from the point of view of the quantum theory of unstable states. Some of false vacuum states survive up to times when their survival probability has a non-exponential form. At times much latter than the transition time, when contributions to the survival probability of its exponential and non-exponential parts are comparable, the survival probability as a function of time t has an inverse power-like form. We show that at this time region the instantaneous energy of the false vacuum states tends to the energy of the true vacuum state as $1…
We investigate a cosmological model in which dark energy identified with the vacuum energy which is running and decaying. In this model vacuum is metastable and decays into a bare (true) vacuum. This decaying process has a quantum nature and is described by tools of the quantum decay theory of unstable systems. We have found formulas for an asymptotic behavior of the energy density of dark energy in the form of a series of inverse powers of the cosmological time. We investigate the dynamics of FRW models using dynamical system methods as well as searching for exact solutions. From dynamical an…
We consider a nonsingular deflationary cosmological model with decaying vacuum energy density in universes of arbitrary spatial curvature. Irrespective of the value of $k$, the models are characterized by an arbitrary time scale $H_I^{-1}$ which determines the initial temperature of the universe and the largest value of the vacuum energy density, the slow decay of which generates all the presently observed matter-energy of the universe. If $H_I^{-1}$ is of the order of the Planck time, the models begin with the Planck temperature and the present day value of the cosmological constant satisfies…
Decaying vacuum cosmological models evolving smoothly between two extreme (very early and late time) de Sitter phases are capable to solve or at least to alleviate some cosmological puzzles, among them: (i) the singularity, (ii) horizon, (iii) graceful-exit from inflation, and (iv) the baryogenesis problem. Our basic aim here is to discuss how the coincidence problem based on a large class of running vacuum cosmologies evolving from de Sitter to de Sitter can also be mollified. It is also argued that even the cosmological constant problem become less severe provided that the characteristic sca…
Bianchi type $VI_{0}$ massive string cosmological models using the technique given by Letelier (1983) with magnetic field are investigated. To get the deterministic models, we assume that the expansion ($θ$) in the model is proportional to the shear ($σ$) and also the fluid obeys the barotropic equation of state. It was found that vacuum energy density $Λ\propto \frac{1}{t^{2}}$ which matches with natural units. The behaviour of the models from physical and geometrical aspects in presence and absence of magnetic field is also discussed.
We extend the results of a previous paper where a model of interacting dark energy, with a cosmological term decaying linearly with the Hubble parameter, is tested against the observed mass power spectrum. In spite of the agreement with observations of type Ia supernovas, baryonic acoustic oscillations and the cosmic microwave background, we had shown previously that no good concordance is achieved if we include the mass power spectrum. However, our analysis was based on the ad hoc assumption that the interacting cosmological term is strictly homogeneous. Now we perform a more complete analysi…
Bianchi type V viscous fluid cosmological model for barotropic fluid distribution with varying cosmological term $Λ$ is investigated. We have examined a cosmological scenario proposing a variation law for Hubble parameter $H$ in the background of homogeneous, anisotropic Bianchi type V space-time. The model isotropizes asymptotically and the presence of shear viscosity accelerates the isotropization. The model describes a unified expansion history of the universe indicating initial decelerating expansion and late time accelerating phase. Cosmological consequences of the model are also discusse…
We study the gravitational collapse of a dust dark matter star in a $Λ$-background. We consider two distinct cases: First we do not have a dark matter and dark energy coupling; second, we consider that $Λ$ decay in dark particles. The approach adopted assumes a modified matter expansion rate and we have formation of a black hole, since that, we have the formation of an apparent horizon. A brief comparison of the process of the matter condensation using the gravitational collapse approach and the linear scalar perturbation theory is considered.
As an extension of $Λ$CDM, the decaying vacuum model (DV) describes the dark energy as a varying vacuum whose energy density decays linearly with the Hubble parameter in the late-times, $ρ_Λ(t) \propto H(t)$, and produces the matter component. We examine the high-$z$ cosmic age problem in the DV model, and compare it with $Λ$CDM and the Yang-Mills condensate (YMC) dark energy model. Without employing a dynamical scalar field for dark energy, these three models share a similar behavior of late-time evolution. It is found that the DV model, like YMC, can accommodate the high-$z$ quasar APM 08279…
We consider the perturbation dynamics for the cosmic baryon fluid and determine the corresponding power spectrum for a $Λ(t)$CDM model in which a cosmological term decays into dark matter linearly with the Hubble rate. The model is tested by a joint analysis of data from supernovae of type Ia (SNIa) (Constitution and Union 2.1), baryonic acoustic oscillation (BAO), the position of the first peak of the anisotropy spectrum of the cosmic microwave background (CMB) and large-scale-structure (LSS) data (SDSS DR7). While the homogeneous and isotropic background dynamics is only marginally influence…
Many have speculated about the presence of a stiff fluid in very early stage of the universe. Such a stiff fluid was first introduced by Zel'dovich. Recently the late acceleration of the universe was studied by taking bulk viscous stiff fluid as the dominant cosmic component, but the age predicted by such a model is less than the observed value. We consider a flat universe with viscous stiff fluid and decaying vacuum energy as the cosmic components and found that the model predicts a reasonable background evolution of the universe with de Sitter epoch as end phase of expansion. More over the m…
We discuss the connection among three distinct classes of models often used to explain the late cosmic acceleration: decaying cosmological term, bulk viscous pressure, and nonlinear fluids. We focus on models that are equivalent at zeroth order, in the sense they lead to the same solutions for the evolution of the scale factor. More specifically, we show explicit examples where this equivalence is manifest, which include some well know models belonging to each class, such as a power law Lambda-term, a model with constant viscosity, and the Modified Chaplygin Gas. We also obtain new analytic so…
Among the several proposals to solve the incompatibility between the observed small value of the cosmological constant and the huge value obtained by quantum field theories, we can find the idea of a decaying vacuum energy density, leading from high values at early times of universe evolution to the small value observed nowadays. In this paper we consider a variation law for the vacuum density recently proposed by Schutzhold on the basis of quantum field estimations in the curved, expanding background, characterized by a vacuum density proportional to the Hubble parameter. We show that, in the…
We suggest an alternative framework for interpreting the current state of the visible universe. Our approach is based on a dynamical ``Cosmological Constant'' and the starting point is that a decaying vacuum produces matter. As we point out, such a dynamical Lambda is not incompatible with the general requirements of general relativity. By assuming inflation and big bang nucleosynthesis we can solve for the present fractional densities of matter Omega_{m,0} and vacuum Omega_{Lambda, 0} in terms of only one parameter which we call the vacuum domination crossing redshift, z_c. We put constraints…
Locally rotationally symmetric (L.R.S.) Bianchi type II stiff fluid cosmological model is investigated. To get the deterministic model of the universe, we have assumed a condition $A=B^{m}$ between metric potentials $A,~B$ where $n$ is the constant. It is shown that the vacuum energy density $Λ$ is positive and proportional to $\frac{1}{t^{2}}$. The values of deceleration parameter $q$, matter-energy density $Ω_{m}$ and dark-energy density $Ω_Λ$ are found to be in good agreement with the values obtain from 5-years WMAP observations. the predicted value of the jerk parameter agrees with the SNL…
Probing the Perturbative Reheating History of Decaying Oscillatory Inflation with ACT Constraints
College of Physics and Electronic Engineering, Chengdu Normal University(成都师范学院物理与电子信息学院);Department of Physics, Xinzhou Normal University(忻州师范学院物理系);School of Mathematics and Physics, University of South China(南华大学数学与物理学院)
We study cosmological perturbations in the context of an interacting dark energy model, in which the cosmological term decays linearly with the Hubble parameter, with concomitant matter production. A previous joint analysis of the redshift-distance relation for type Ia supernovas, baryonic acoustic oscillations, and the position of the first peak in the anisotropy spectrum of the cosmic microwave background has led to acceptable values for the cosmological parameters. Here we present our analysis of small perturbations, under the assumption that the cosmological term, and therefore the matter …
Using a formalism recently introduced we study the decaying of the cosmological parameter during the early evolution of an universe, whose evolution is governed by a vacuum equation of state. We use a stochastic approach in a nonperturbative treatment of the inflaton field from a Noncompact Kaluza-Klein (NKK) theory, to study the evolution of energy density fluctuations in the early universe.
We propose a possible resolution to the cosmological constant problem through a scenario in which the universe is composed of three components: matter, radiation (CMB) and vacuum energy such that vacuum energy is not constant and is decaying into the matter component. Matter in this scenario consists of baryonic matter and primordial black holes (PBHs) as the dark matter. Local equilibrium condition between PBHs and CMB confines the mass and the radius of PBHs. The mechanism accounting for the decaying process is nothing but the absorption of vacuum energy modes by the PBHs up to a wavelength …
A low matter density decaying vacuum cosmology is proposed on the assumption that the universe's radius is a complex quantity \hat{R} if it is regarded as having a zero energy-momentum tensor. But we find that when the radius is real, it contains matter. Using the Einstein-Hilbert action principle, the physical scale factor R(t) =|\hat{R}| is obtained as equal to (R_0^{2} + t^{2})^{1/2} with R_0 representing the finite radius of the universe at t=0. The resulting physical picture is roughly a theoretical justification of the old Ozer-Taha model. The new model is devoid of all cosmological prob…
A new class of LRS Bianchi type ${\rm VI}_{0}$ cosmological models with free gravitational fields and a variable cosmological term is investigated in presence of perfect fluid as well as bulk viscous fluid. To get the deterministic solution we have imposed the two different conditions over the free gravitational fields. In first case we consider the free gravitational field as magnetic type whereas in second case `gravitational wrench' of unit `pitch" is supposed to be present in free gravitational field. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass…
The conditions under which cosmologies driven by time varying cosmological terms can be described by a scalar field coupled to a perfect fluid are discussed. An algorithm to reconstruct potentials dynamically and thermodynamically analogue to given phenomenological $Λ$ models is presented. As a worked example, the deflationary cosmology, which evolves from a pure de Sitter vacuum state to a slightly modified FRW cosmology is considered. It is found that this is an example of nonsingular warm inflation with an asymptotic exponential potential. Differences with respect to other scalar field desc…
There is mounting observational evidence that the expansion of our Universe is undergoing a late-time acceleration. Among many proposals to describe this phenomenon, the cosmological constant seems to be the simplest and the most natural explanation. However, despite its observational successes, such a possibility exacerbates the well known cosmological constant problem, requiring a natural explanation for its small, but nonzero, value. In this paper we consider a cosmological scenario driven by a varying cosmological term, in which the vacuum energy density decays linearly with the Hubble par…
A $Λ$CDM model with dark matter that decays into inert relativistic energy on a timescale longer than the Hubble time will produce an expansion history that can be misinterpreted as stable dark matter with time-varying dark energy. We calculate the corresponding spurious equation of state parameter, $\widetilde w_ϕ$, as a function of redshift, and show that the evolution of $\widetilde w_ϕ$ depends strongly on the assumed value of the dark matter density, erroneously taken to scale as $a^{-3}$. Depending on the latter, one can obtain models that mimic quintessence ($\widetilde w_ϕ> -1$), phant…
Realizations of scale invariance are studied in the context of a gravitational theory where the action (in the first order formalism) is of the form $S = \int L_{1} Φd^{4}x$ + $\int L_{2}\sqrt{-g}d^{4}x$ where $Φ$ is a density built out of degrees of freedom, the "measure fields" independent of $g_{μν}$ and matter fields appearing in $L_{1}$, $L_{2}$. If $L_{1}$ contains the curvature, scalar potential $V(ϕ)$ and kinetic term for $ϕ$, $L_{2}$ another potential for $ϕ$, $U(ϕ)$, then the true vacuum state has zero energy density, when theory is analyzed in the conformal Einstein frame (CEF), whe…
We investigate observational constraints from present and future supernova data on a large class of decaying vacuum cosmologies. In such scenarios the present value of the vacuum energy density is quantified by a positive $β$ parameter smaller than unity. By assuming a Gaussian prior on the matter density parameter ($Ω_{\rm{m}} = 0.35 \pm 0.07$) we find $Ω_{\rm{m}} = 0.34^{+0.14}_{-0.12}$ and $β= 0.62^{+0.12}_{-0.24}$ (95% c.l.) as the best fit values for the present data. We show that, while the current data cannot provide restrictive constraints on the $Ω_{\rm{m}} - β$ plane, the future SNe …
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.
Quantum physics at scales large compared to the Planck scale is described in the framework of classical space-time geometries. A criterion for selecting these backgrounds out of quantized gravity is proposed. It leads to an instability of the black-hole geometry, as experienced by motion across the horizon, against emission of Hawking quanta. A phenomenological treatment of the evaporation process perceived by external observers who do not cross the event horizon is presented. Evaporation occurs within a topologically trivial ``achronon" geometrical background devoid of horizons and singularit…
We study a uniform and isotropic cosmology with a decaying vacuum energy density, in the realm of a model with a time varying gravitational "constant". We show that, for late times, such a cosmology is in accordance with the observed values of the cosmological parameters. In particular, we can obtain the observed ratio between the matter density and the total energy density, with no necessity of any fine tuning.
The possibility that the vacuum energy density $ρ_Λ$ is, indeed, varying in time, has been investigated lately from the running vacuum models perspective. Motivated by such models, in the present work, we relate the decaying vacuum energy $ρ_Λ(t)$ with a scalar field $ϕ$. We derive the equations of motion from such a premise and implement the first-order formalism in order to obtain analytical solutions to the cosmological parameters. We show that those are in agreement with recent Planck observational data. We discuss the physical consequences of having $ρ_Λ(t)$ related to $ϕ$.
We consider phase transitions and their contributions to vacuum energy in the manifestly local theory of vacuum energy sequestering. We demonstrate that the absence of instabilities imposes constraints on the couplings of gravitating and non-gravitating sectors, which can be satisfied in a large class of models. We further show by explicit construction that the vacuum energy contributions to the effective cosmological constant in the descendant vacua are generically strongly suppressed by the ratios of spacetime volumes of parent and descendant geometries. This means that the cosmological cons…
According to the standard model of cosmology, the early universe has been dominated by radiation or non-relativistic matter in several eras of its history. However, many cosmological calculations involving particle processes are commonly done using Minkowskian results for them, although, for more precise treatment, quantum field theory in curved spacetime is needed. This paper aims to fill this gap by presenting decay rates for matter and radiation dominated universes in this more precise treatment. We provide a study of the average decay rates for a process where a conformally coupled massive…
We analyse three cosmological scenarios with interaction in the dark sector, which are particular cases of a general expression for the energy flux from vacuum to matter. In the first case the interaction leads to a transition from an unstable de Sitter phase to a radiation dominated universe, avoiding in this way the initial singularity. In the second case the interaction gives rise to a slow-roll power-law inflation. Finally, the third scenario is a concordance model for the late-time universe, with the vacuum term decaying into cold dark matter. We identify the physics behind these forms of…
In the present mainstream cosmology, matter and spacetime emerged from a singularity and evolved through four distinct periods: early inflation, radiation, dark matter and late-time inflation (driven by dark energy). During the radiation and dark matter dominated stages, the universe is decelerating while the early and late-time inflations are accelerating stages. A possible connection between the accelerating periods remains unknown, and, even more intriguing, the best dark energy candidate powering the present accelerating stage (Lambda-vacuum) is plagued with the cosmological constant and c…
We present a short introduction to a non-standard cosmological scenario motivated by the duality symmetries of string theory, in which the big bang singularity is replaced with a "big bounce" at high but finite curvature. The bouncing epoch is prepared by a long (possibly infinitely extended) phase of cosmic evolution, starting from an initial state asymptotically approaching the string perturbative vacuum.
Toy models for the Hubble rate or the scalar field potential have been used to analyze the amplification of scalar perturbations through a smooth transition from inflation to the radiation era. We use a Hubble rate that arises consistently from a decaying vacuum cosmology, which evolves smoothly from nearly de Sitter inflation to radiation domination. We find exact solutions for super-horizon perturbations (scalar and tensor), and for sub-horizon perturbations in the vacuum- and radiation-dominated eras. The standard conserved quantity for super-horizon scalar perturbations is exactly constant…
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…
A mechanism is introduced to reduce a large cosmological constant to a sufficiently small value consistent with observational upper limit. The basic ingradient in this mechanism is a distinction which has been made between the two unit systems used on cosmology and particle physics. We have used a conformal invariant gravitational model to define a particular conformal frame in terms of the large scale properties of the universe. It is then argued that the contributions of mass scales in particle physics to the vacuum energy density should be considered in a different conformal frame. In this …
We demonstrate that in a vacuum-energy-dominated expansion phase, surprisingly neither the decay of matter nor matter-antimatter annihilation into relativistic particles can ever cause radiation to once again dominate over matter in the future history of the universe.