We calculate the average numbers of closed, flat, and open universes spontaneously created from nothing in third quantization. The creation of universes is exponentially suppressed for large values of the kinetic energy of the inflaton, while for small kinetic energies it is exponentially favoured for closed universes over flat and open ones: For a scale of inflation less than about $2 \times 10^{16}$GeV, the ratio of the number of closed universes to either the number of flat or open universes is \begin{equation} \frac{n_{closed}}{n_{flat,open}} \gtrsim 10^{10^{10}} . \nonumber \end{equation}
The problem of cosmological particle creation for a spatially flat, homogeneous and isotropic Universes is discussed in the context of f(R) theories of gravity. Different from cosmological models based on general relativity theory, it is found that a conformal invariant metric does not forbid the creation of massless particles during the early stages (radiation era) of the Universe.
Quantum creation processes during the very rapid early expansion of the universe are believed to give rise to temperature anisotropies and polarization patterns in the CMB radiation. These have been observed by satellites such as COBE, WMAP, and PLANCK, and by bolometric instruments placed near the South Pole by the BICEP collaborations. The expected temperature anisotropies are well-confirmed. The B-mode polarization patterns in the CMB are currently under measurement jointly by the PLANCK and BICEP groups to determine the extent to which the B-modes can be attributed to gravitational waves f…
Several recent possible counterexamples to the Chronology Protection Conjecture are critically examined. The ``adapted'' Rindler vacuum state constructed by Li and Gott for a conformal scalar field in Misner space is extended to nonconformally coupled and self-interacting scalar fields. For these fields, the vacuum stress-energy always diverges on the chronology horizons. The divergence of the vacuum stress-energy on Misner space chronology horizons cannot be generally avoided by choosing a Rindler-type vacuum state.
The approximation of the renormalized stress-energy tensor of the quantized massive scalar field in Reissner-Nordström spacetime is constructed. It is achieved by functional differentiation of the first two nonvanishing terms of the Schwinger-DeWitt expansion involving the coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficients $[a_{3}]$ and $[a_{4}]$ with respect to the metric tensor. It is shown, by comparison with the existing numerical results, that inclusion of the second-order term leads to substantial improvement of the approximation of the exact stress-energy tenso…
We study the vacuum polarization of a massive scalar field $ϕ$ with arbitrary coupling to gravity in pointlike global monopole spacetime. Using Schwinger-DeWitt proper time formalism, we calculate the vacuum expectation value $<ϕ^{2}>$, when the Compton length of the quantum field is much less than the characteristic radius of the curvature of the background geometry, and we can ignore nonlocal contributions. Explicit analytic expressions are obtained for a general curvature coupling parameter, and specified to the more physical cases of minimal and conformal coupling. Comparing the leading te…
In the Friedmann equations, an infinite initial density is avoided only when the universe is spatially flat. With such equations being then valid when the scale factor $a=0$, the universe must also be in the state of vacuum when $a$ is infinitesimal. Matter creation thus largely comes from nonlinearity of the Friedmann equations at a finite $a$. For the correspondence between such an initial vacuum and the Friedmann universe, therefore, a vacuum density is suggested to be gravitationally significant only when it could also have a matter phase. The effective cosmological term is then due to suc…
In the more recent literature on cosmological evolutions of the universe the cosmic vacuum energy has become a non-renouncable ingredient. The cosmological constant $Λ$, first invented by Einstein, but later also rejected by him, presently experiences an astonishing revival. Interestingly enough it acts, like a constant vacuum energy density would also do. Namely, it has an accelerating action on cosmic dynamics without which, as it appears, presently obtained cosmological data cannot be conciliated with theory. As we are going to show in this review, however, the concept of a constant vacuum …
It is shown that the vacuum state in presence of Lorentz violation can be followed by a particle-full universe that represents the current status of the universe. In this model the modification in dispersion relation (Lorentz violation) is picked up representing the regime of quantum gravity. The result can be interpreted such that the existence of the particles is an evidence for quantum effects of gravity in the past. It is concluded that only the vacuum state is sufficient to appear the matter fields spontaneously after the process of semi-classical analysis.
We use the Bogoliubov formalism to study both, particles and gravitons creation at the reheating epoch, after a phase transition from inflation to a radiation dominated universe. The modes of the inflaton field fluctuations and the scalar fluctuations of the metric at the end of inflation are obtained by using a recently introduced formalism related to the Induced Matter theory of gravity. The interesting result is that the number of created particles is bigger than $10^{90}$ on cosmological scales. Furthermore, the number of gravitons are nearly $10^{-17}$ times smaller than the number of cre…
We consider the backreaction problem of a quantized minimally coupled massless scalar field in cosmology. The adiabatically regularized stress-energy tensor in a general Friedmann-Robertson-Walker background is approximately evaluated by using the fact that subhorizon modes evolve adiabatically and superhorizon modes are frozen. The vacuum energy density is verified to obey a new first order differential equation depending on a dimensionless parameter of order unity, which calibrates subhorizon/superhorizon division. We check the validity of the approximation by calculating the corresponding v…
In this paper we will analyse the third quantization of a model of super-group field cosmology with gauge symmetry. The effect of creation and annihilation of bosonic and fermionic universes in the multiverse will also be analysed. We will also construct a third quantized Noether's charge which will be conserved even when the number of universes is not conserved. Finally, we will construct both the third quantized BRST and the third quantized anti-BRST charges for this theory and use them to show that the creation and annihilation of universes is a unitarity process.
Among the different methods to derive particle creation, finding the quantum stress tensor expectation value gives a covariant quantity which can be used for examining the back-reaction issue. However this tensor also includes vacuum polarization in a way that depends on the vacuum chosen. Here we review different aspects of particle creation by looking at energy conservation and at the quantum stress tensor. It will be shown that in the case of general spherically symmetric black holes that have a \emph{dynamical horizon}, as occurs in a cosmological context, one cannot have pair creation on …
I propose modified set of creation and annihilation operators for the Schrödinger representation which is compatible with the Fock representation which differs from previous works. I take into account the relation between different non-unitary vacuums obtained from restricted frameworks like the relation between the Minkowski and Unruh vacuums.
For a quantum field in a curved background the choice of the vacuum state is crucial. We exhibit a vacuum state in which the expectation values of the energy and pressure allow an intuitive interpretation. We apply this general result to the de Sitter universe.
The problem of particle creation from vacuum in a flat Robertson-Walker space-time is studied. Two sets of exact solutions for the Klein Gordon equation are given. Then the canonical method based on Bogoliubov transformation is applied to calculate the pair creation probability and the density number of created particles. Some particular cosmological models such as radiation dominated universe and Milne universe are discussed. For the both cases the vacuum to vacuum transition probability is calculated and the imaginary part of the effective action is extracted.
A detector undergoing a huge acceleration measures a thermal distribution with the Unruh temperature out of the Minkowski vacuum. Though such huge accelerations occur naturally in astrophysics and gravity, one may design untraintense laser facility to detect the Unruh effect and simulate laboratory astrophysics. We derive the QED vacuum polarization and the vacuum persistence amplitude as well as the Schwinger pair creation in an accelerating frame when a constant electric field exists in the Minkowski spacetime. We advance a thermal interpretation of Schwinger pair creation in the Rindler spa…
We construct second-quantized (field) theories on coset spaces of pseudo-unitary groups U(p,q)$. The existence of degenerated quantum vacua (coherent states of zero modes) leads to a breakdown of the original pseudo-unitary symmetry. The action of some spontaneously broken symmetry transformations destabilize the vacuum and make it to radiate. We study the structure of this thermal radiation for curved phase spaces of constant curvature: complex projective spaces CP^{N-1}=SU(N)/U(N-1) and open complex balls CD^{N-1}=SU(1,N-1)/U(N-1). Positive curvature is related to generalized Fermi-Dirac (FD…
Starting with the vacuum fluctuation, it is known that gravitinos will be created just after inflation, with number density $\sim 10^{-2}M^3$ where $M$ is the mass of the inflaton. Here, we argue that creation may be expected to continue, maintaining about the same number density, until a usually much later epoch. This epoch is either the `intermediate epoch' when Hubble parameter falls below the gravitino mass, or the reheat epoch if that is earlier. We verify that such late-time creation indeed occurs if only a single chiral superfield is relevant, using the description of the helicity 1/2 g…
In the context of quantum field theories in curved spacetime, we compute the effective action of the transition amplitude from vacuum to vacuum in the presence of an external gravitational field. The imaginary part of resulted effective action determines the probability of vacuum decay via quantum tunneling process, giving the rate and spectrum of particle creations. We show that gravitational field polarizes vacuum and discretizes its spectrum for such a polarization gains gravitational energy. On the basis of gravitational vacuum polarization, we discuss the quantum origin of vacuum decay in…
An effective one-loop action built from the soliton field itself for the two-dimensional (2D) problem of soliton pair creation is proposed. The action consists of the usual mass term and a kinetic term in which the simple derivative of the soliton field is replaced by a covariant derivative. In this effective action the soliton charge is treated no longer as a topological charge but as a Noether charge. Using this effective one-loop action, the soliton-antisoliton pair production rate is calculated and one recovers Stone's exponential factor and the prefactor of Kiselev, Selivanov and Voloshin…
This paper is devoted to the construction of the renormalized quantum stress energy tensor $\left<T_μ^ν\right>_{ren}$ for a massive scalar field with arbitrary coupling to the gravitational field of a pointlike global monopole, using the Schwinger-DeWitt approximation, up to second order in the inverse mass $μ$ of the field. The given stress energy tensor is constructed by functional differentiation with respect to the metric tensor of the one-loop effective action of sufficiently massive scalar field, such that the Compton length of the quantum field is much less than the characteristic radiu…
Results on particle creation from vacuum by the gravitational field of the expanding Friedmann Universe are presented. Finite results for the density of particles and the energy density for created particles are given for different exact solutions for different regimes of the expansion of the Universe. The results are obtained as for conformal as for nonconformal particles. The hypothesis of the origination of visible matter from the decay of created from vacuum superheavy particles identified with the dark matter is discussed.
The creation of ultra-light dark particles in the late-time FLRW spacetime provides a cosmological model in accordance with precise observational tests. The matter creation backreaction implies in this context a vacuum energy density scaling linearly with the Hubble parameter H, which is consistent with the vacuum expectation value of the QCD condensate in a low-energy expanding spacetime. Both the cosmological constant and coincidence problems are alleviated in this scenario. We also explore the opposite, high energy limit of the particle creation process. We show that it leads to a non-singu…
We constructed the conformally invariant model for scalar particle creation induced by strong gravitational fields. Starting from the "usual" hydrodynamical description of the particle motion written in the Eulerian coordinates we substituted the particle number conservation law (which enters the formalism) by "the particle creation law", proportional to the square of the Weyl tensor (following the famous result by Ya.B.Zel`dovich and A. A.Starobinsky). Then, demanding the conformal invariance of the whole dynamical system, we have got both the (Weyl)-conformal gravity and the Einstein--Hilber…
A massive scalar field is quantized in the background of a cosmic string which is generalized to a static flux-carrying codimension-2 brane in the locally flat multidimensional space-time. We find that the finite energy-momentum tensor is induced in the vacuum. The dependence of the tensor components on the brane flux and tension, as well as on the coupling to the space-time curvature scalar, is comprehensively analyzed. The tensor components are holomorphic functions of space dimension, decreasing exponentially with the distance from the brane. The case of the massless quantized scalar field …
The predictions of the semiclassical description of particle creation based on QFT in classical backgrounds may be significantly modified when the source of the classical background is also quantized and backreaction is taken into account. In the cases of a stable charged particle, expanding empty (Milne) universe, and de Sitter universe with a true cosmological constant, the semiclassical particle creation is completely blocked up.
The possibility of electron-positron pair creation by an electric field is studied by using only those methods in field theory the predictions of which are confirmed experimentally. These methods include the perturbative method of quantum electrodynamics and the bases of classical electrodynamics. Such an approach includes the back reaction. It is found that the vacuum is always stable, in the sense that pair creation, if occurs, cannot be interpreted as a decay of the vacuum, but rather as a decay of the source of the electric field or as a process similar to bremsstrahlung. It is also found …
Particle production due to a quantized, massless, minimally coupled scalar field in two-dimensional flat spacetime with an accelerating mirror is investigated, with a focus on the time dependence of the process. We analyze first the classes of trajectories previously investigated by Carlitz and Willey and by Walker and Davies. We then analyze four new classes of trajectories, all of which can be expressed analytically and for which several ancillary properties can be derived analytically. The time dependence is investigated through the use of wave packets for the modes of the quantized field t…
We consider the possibility of the quantum vacuum states in f(R,T) gravity. Particularly, we study the Bogoliubov transformations associated to different vacuum states for some f(R,T) models. The method consists of fixing the f(R,T) free parameters by requiring the Bogoliubov coefficients to be minimized. In such a way, the particle production is related to the value of the Hubble parameter and also the given f(R,T) model.
Using squeezed vacuum state formalism of quantum optics, an approximate solution to the semiclassical Einstein equation is obtained in Bianchi type-I universe. The phenomena of nonclassical particle creation is also examined in the anisotropic background cosmology.
We adopt the general formalism for analyzing evolution of gaussian states of quantized fields in time-dependent backgrounds in the Schrodinger picture (presented in detail in arXiv:0708.1233 and 0708.1237) to study the example of a spatially uniform electric field background (in a time-dependent gauge) which is kept turned on for a finite duration of time. In particular, we study the \emph{time-dependent} particle content, defined in terms of the concept of instantaneous eigenstates, and describe how it captures the time evolution of the quantized field modes. The actual particle creation proc…
In this paper we analyze the third quantization of Horava-Lifshits theory of gravity without detail balance. We show that the Wheeler-DeWitt equation for Horava-Lifshits theory of gravity in minisuperspace approximation becomes the equation for time-dependent harmonic oscillator. After interpreting the scaling factor as the time, we are able to derive the third quantized wavefunction for multiverse. We also show in third quantized formalism it is possible that the universe can form from nothing. After we go on to analyze the effect of introducing interactions in the Wheeler-DeWitt equation. We…
Using the formalism of Weitzenböck induced matter theory (WIMT) we calculate the gravito-magnetic charge on a topological string which is induced through a foliation on a five-dimensional (5D) gravito-electromagnetic vacuum defined on a 5D Ricci-flat metric, which produces a symmetry breaking on an axis. We obtain the resonant result that the quantized charges are induced on the effective four-dimensional hypersurface. This quantization describes the behavior of a test gravito-electric charge in the vicinity of a point gravito-magnetic monopole, both geometrically induced from a 5D vacuum. We …
We discuss a two-step mechanism to create a new inflationary domain beyond a wormhole throat which is created by a phase transition around an evaporating black hole. The first step is creation of a false vacuum bubble with a thin-wall boundary by the thermal effects of Hawking radiation. Then this wall induces a quantum tunneling to create a wormhole-like configuration. As the space beyond the wormhole throat can expand exponentially, being filled with false vacuum energy, this may be interpreted as creation of another inflationary universe in the final stage of the black hole evaporation.
Dense enough compact objects were recently shown to lead to an exponentially fast increase of the vacuum energy density for some free scalar fields properly coupled to the spacetime curvature as a consequence of a tachyonic-like instability. Once the effect is triggered, the star energy density would be overwhelmed by the vacuum energy density in a few milliseconds. This demands that eventually geometry and field evolve to a new configuration to bring the vacuum back to a stationary regime. Here, we show that the vacuum fluctuations built up during the unstable epoch lead to particle creation …
A constant-rate creation of dark particles in the late-time FLRW spacetime provides a cosmological model in accordance with precise observational tests. The matter creation backreaction implies in this context a vacuum energy density scaling linearly with the Hubble parameter, which is consistent with the vacuum expectation value of the QCD condensate in a low-energy expanding spacetime. Both the cosmological constant and coincidence problems are alleviated in this scenario. We discuss the cosmological model that arises in this context and present a joint analysis of observations of the first …
I describe the logical basis of the method that I developed in 1962 and 1963 to define a quantum operator corresponding to the observable particle number of a quantized free scalar field in a spatially-flat isotropically expanding (and/or contracting) universe. This work also showed for the first time that particles were created from the vacuum by the curved space-time of an expanding spatially-flat FLRW universe. The same process is responsible for creating the nearly scale-invariant spectrum of quantized perturbations of the inflaton scalar field during the inflationary stage of the expansio…
Analytical approximations for $< ϕ^2 >$ of a quantized scalar field in ultrastatic asymptotically flat spacetimes are obtained. The field is assumed to be both massive and massless, with an arbitrary coupling $ξ$ to the scalar curvature, and in a zero or nonzero temperature vacuum state. The expression for $< ϕ^2 >$ is divided into low- and high-frequency parts. The expansion for the high-frequency contribution to this quantity is obtained. This expansion is analogous to the DeWitt-Schwinger one. As an example, the low-frequency contribution to $< ϕ^2 >$ is calculated on the background of the …
We discuss the possibility of quantum transitions from the string perturbative vacuum to cosmological configurations characterized by isotropic contraction and decreasing dilaton. When the dilaton potential preserves the sign of the Hubble factor throughout the evolution, such transitions can be represented as an anti-tunnelling of the Wheeler--De Witt wave function in minisuperspace or, in a third-quantization language, as the production of pairs of universes out of the vacuum.
The main topic of this talk is the Hawking effect when the black holes in question are undergoing a uniform acceleration. The semiclassical effect of the acceleration is most striking when the Hawking temperature equals the acceleration temperature. Within the usual late-time approximation, the natural black hole vacuum is then equivalent to the asymptotically empty Minkowskian vacuum, and the accelerated black hole becomes semiclassically stable against the familiar thermal evaporation. An important application of this phenomenon is found in the problem of charged black hole pair-creation.
We investigate the bubble nucleation in five dimensional spacetime catalyzed by quintessence. We especially focus on decay of a metastable Minkowski vacuum to an anti-de Sitter vacuum and study dynamics of the bubble on which four dimensional expanding universe is realized. We also discuss the trans-Planckian censorship conjecture and impose a constraint on the parameter space of the catalysis. As an application of this model, we propose an inflation mechanism and an origin of the dark energy in the context of quintessence in five dimensions.
Analytical approximations for ${< ϕ^2 >}$ and ${< T^μ_ν >}$ of a quantized scalar field in static spherically symmetric spacetimes are obtained. The field is assumed to be both massive and massless, with an arbitrary coupling $ξ$ to the scalar curvature, and in a zero temperature vacuum state. The expressions for ${< ϕ^2 >}$ and ${< T^μ_ν >}$ are divided into low- and high-frequency parts. The contributions of the high-frequency modes to these quantities are calculated for an arbitrary quantum state. As an example, the low-frequency contributions to ${< ϕ^2 >}$ and ${< T^μ_ν >}$ are calculated…
Using as dynamical variable the square of the radius of the Universe, we solve analytically the Einstein equations in the framework of Robertson-Walker models where a cosmological constant describing phenomenologically the vacuum energy decays into radiation. Emphasis is put on the computation of the entropy creation.
The constrained instanton method is used to study quantum creation of a vacuum or charged topological black hole. At the $WKB$ level, the relative creation probability is the exponential of a quarter sum of the horizon areas associated with the seed instanton.
We study the particle creation process in the Schwinger model coupled with an external classical source. One can approach the problem by taking advantage that the full quantized model is solvable and equivalent to a (massive) gauge field with a non-local effective action. Alternatively, one can also face the problem following the standard semiclassical route. This means quantizing the massless Dirac field and considering the electromagnetic field as a classical background. We evaluate the energy created by a generic, homogeneous, and time-dependent source. The results exactly match in both app…
An interesting idea is that the universe could be spontaneously created from nothing, but no rigorous proof has been given. In this paper, we present such a proof based on the analytic solutions of the Wheeler-DeWitt equation (WDWE). Explicit solutions of the WDWE for the special operator ordering factor p=-2 (or 4) show that, once a small true vacuum bubble is created by quantum fluctuations of the metastable false vacuum, it can expand exponentially no matter whether the bubble is closed, flat or open. The exponential expansion will end when the bubble becomes large and thus the early univer…
A geometric formalism is developed which allows to describe the non-linear regime of higher-spin gravity emerging on a cosmological quantum space-time in the IKKT matrix model. The vacuum solutions are Ricci-flat up to an effective vacuum energy-momentum tensor quadratic in the torsion, which arises from a Weitzenböck-type higher spin connection. Torsion is expected to be significant only at cosmic scales and around very massive objects, and could behave like dark matter. A non-linear equation for the torsion tensor is found, which encodes the Yang-Mills equations of the matrix model. The metr…
In the early sixties Leonard Parker discovered that the expansion of the universe can create particles out of the vacuum, opening a new and fruitfull field in physics. We give a historical review in the form of an interview that took place during the Conference ERE2014 (Valencia 1-5, September, 2014).
Recent determinations of the equation of state of dark energy hint that this may well be of the phantom type, i.e., $w_{de} < -1$. If confirmed by future experiments, this would strongly point to the existence of fields that violate the dominant energy condition, which are known to present serious theoretical difficulties. This paper presents an alternative to this possibility, namely, that the measured equation of state, $w_{de}$, is in reality an effective one, the equation of state of the quantum vacuum, $w_Λ = -1$, plus the negative equation of state, $w_{c}$, associated to the production …
We study the interaction of a massless quantized spinor field with the gravitational filed of N parallel static cosmic strings by using a perturbative approach. We show that the presence of more than one cosmic string gives rise to an additional contribution to the energy density of vacuum fluctuations, thereby leading to a vacuum force attraction between two parallel cosmic strings.
The effect of particle creation by nonstationary external fields is considered as a radiation effect in the expectation-value spacetime. The energy of created massless particles is calculated as the vacuum contribution in the energy-momentum tensor of the expectation value of the metric. The calculation is carried out for an arbitrary quantum field coupled to all external fields entering the general second-order equation. The result is obtained as a functional of the external fields. The paper gives a systematic derivation of this result on the basis of the nonlocal effective action. Although …
We investigated the possibility of the homogeneous and isotropic cosmological solution in Weyl geometry, which differs from the Riemannian geometry by adding the so called Weyl vector. The Weyl gravity is obtained by constructing the gravitational Lagrangian both to be quadratic in curvatures and conformal invariant. It is found that such solution may exist provided there exists the direct interaction between the Weyl vector and the matter fields. Assuming the matter Lagrangian is that of the perfect fluid, we found how such an interaction can be implemented. Due to the existence of quadratic …
The loss of time-translational invariance caused by a time-dependent external agent leads to particle creation effects in quantum field theory. This phenomenon results in ambiguities when selecting the quantum vacuum of the canonical quantization. In this work we analyze how the time evolution of the number of created particles depends on these ambiguities when external agents are spatially homogeneous. In particular, we generalize the standard quantum Vlasov equation in order to accommodate in its formulation the possibility of having different choices of vacuum, including adiabatic vacua. Th…
We consider an alternative mechanism for the production of the cosmic microwave background (CMB) radiation. It is basically due to vacuum pair creation (VPC) of vector bosons (W and Z) as a consequence of a rapid W and Z mass generation during the electroweak phase transition in the early Universe. The mechanism is as follows: after their pair crreation, the vector bosons may either annihilate directly into photons or decay into leptons and quarks which subsequently annihilate as lepton-antilepton and quark-antiquark pairs into photons. Preliminary estimates show that the number of CMB photons…
