Krein approach is used to study the particle creation during quasi-de Sitter inflation in different background space-times. In the conventional method for calculating the created particles spectrum, the background space-time is automatically considered flat. Selecting a flat background poses two fundamental problems: First, the method of calculating is not covariant relative to the curved space-time. Second, the number of created particles becomes negative. Krein approach can be considered as a covariant method to calculate two-point functions in curved space-time. So we extend this method for particle creation during early cosmic inflation. As a new proposal, we choose the background vacuum based on the smallest number of created particles in that space-time. The calculations will show that in order to solve the above mentioned problems, the background space-time must be non-flat and the number of particles in the background must be minimum.
Recent work has shown that the addition of an appropriate covariant boundary term to the gravitational action yields a well-defined variational principle for asymptotically flat spacetimes and thus leads to a natural definition of conserved quantities at spatial infinity. Here we connect such results to other formalisms by showing explicitly i) that for spacetime dimension $d \ge 4$ the canonical form of the above-mentioned covariant action is precisely the ADM action, with the familiar ADM boundary terms and ii) that for $d=4$ the conserved quantities defined by counter-term methods agree pre…
The influence of electromagnetic fields on the creation of scalar particles from vacuum in a flat Robertson-Walker space-time is studied. The Klein Gordon equation with varying electric field and constant magnetic one is solved. The Bogoliubov transformation method is applied to calculate the pair creation probability and the number density of created particles. It is shown that the electric field amplifies the creation of scalar particles while the magnetic field minimizes it.
We extend the Gross-Perry-Yaffe approach of hot flat space instability to Minkowski space. This is done by a saddle point approximation of the partition function in a Schwarzschild wormhole background which is coincident with an eternal black hole. The appearance of an instability in the whole manifold is here interpreted as a black hole pair creation.
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.
The oft-neglected issue of the causal structure in the flat spacetime approach to Einstein's theory of gravity is considered. Consistency requires that the flat metric's null cone be respected, but this does not happen automatically. After reviewing the history of this problem, we introduce a generalized eigenvector formalism to give a kinematic description of the relation between the two null cones, based on the Segre' classification of symmetric rank 2 tensors with respect to a Lorentzian metric. Then we propose a method to enforce special relativistic causality by using the naive gauge free…
We discuss conformally covariant differential operators, which under local rescalings of the metric, δ_σg^{μν} = 2 σg^{μν}, transform according to δ_σΔ= r Δσ+ (s-r) σΔfor some r if Δis s-th order. It is shown that the flat space restrictions of their associated Green functions have forms which are strongly constrained by flat space conformal invariance. The same applies to the variation of the Green functions with respect to the metric. The general results are illustrated by finding the flat space Green function and also its first variation for previously found second order conformal different…
The discrepancy between the results of covariant and non-covariant one-loop calculations for higher-spin fields in quantum cosmology is analyzed. A detailed mode-by-mode study of perturbative quantum gravity about a flat Euclidean background bounded by two concentric 3-spheres, including non-physical degrees of freedom and ghost modes, leads to one-loop amplitudes in agreement with the covariant Schwinger-DeWitt method. This calculation provides the generalization of a previous analysis of fermionic fields and electromagnetic fields at one-loop about flat Euclidean backgrounds admitting a well…
There is great interest in the construction of brane worlds, where matter and gravity are forced to be effective only in a lower dimensional surface , the brane . How these could appear as a consequence of string theory is a crucial question and this has been widely discussed. Here we will examine a distinct scenario that appears in dynamical tension theories and where string tension is positive between two surfaces separated by a short distance and at the two surfaces themselves the string tensions become infinite, therefore producing an effective confinement of the strings and therefore of a…
A geometrical interpretation of Schrödinger's kinetic and potential energy operators is proposed, allowing for a covariant momentum space formulation of the dynamics that is relevant for the theories with the deformation of the momentum space structure. Some specific examples are discussed in the context of flat space deformations and the Euclidean Snyder (spherical momentum space) model. In this formulation the dynamics for the deformations of the flat momentum space becomes trivial, while different versions of the Snyder model turn out to be dynamically equivalent.
We present two generic classes of supersymmetric solutions of N=2, d=4 supergravity coupled to non-Abelian vector supermultiplets with a gauge group that includes an SU(2) factor. The first class consists of embeddings of the 't Hooft-Polyakov monopole and in the examples considered it has a fully regular, asymptotically flat space-time metric without event horizons. The other class of solutions consists of regular non-Abelian extreme black holes. There is a covariant attractor at the horizon of these non-Abelian black holes.
The present thesis aims at providing a unified description of radiative phase spaces in General Relativity for any value of the cosmological constant using covariant phase space methods. We start by considering generic asymptotically locally (A)dS spacetimes with leaky boundary conditions in the Starobinsky/Fefferman-Graham gauge. The boundary structure is allowed to fluctuate and plays the role of source yielding some flux of gravitational radiation at the boundary. The holographic renormalization procedure is employed to obtain finite surface charges for the whole class of boundary diffeomor…
The non-relativistic covariant framework for fields is extended to investigate fields and fluids on scale covariant curved backgrounds. The scale covariant Newton-Cartan background is constructed using the localization of spacetime symmetries of non-relativistic fields in flat space. Following this, we provide a Weyl covariant formalism which can be used to study scale invariant fluids. By considering ideal fluids as an example, we describe its thermodynamic and hydrodynamic properties and explicitly demonstrate that it satisfies the local second law of thermodynamics. As a further application…
We present a dynamical analysis of the (classical) spatially flat and negative curved Friedmann-Lameitre-Robertson-Walker (FLRW) universes evolving, (by assumption) close to the thermodynamic equilibrium, in presence of a particles creation process, described by means of a realiable phenomenological approach, based on the application to the comoving volume (i. e. spatial volume of unit comoving coordinates) of the theory for open thermodynamic systems. In particular we show how, since the particles creation phenomenon induces a negative pressure term, then the choice of a well-grounded ansatz …
Covariantization is of course required for initially flat space matter to couple consistently to GR; here I show in detail for concrete systems how it follows in the same physical way as that deriving GR itself from its initial free-field form.
We obtain a coordinate independent algorithm to determine the class of conformal Killing vectors of a locally conformally flat $n$-metric $γ$ of signature $(r,s)$ modulo conformal transformations of $γ$. This is done in terms of endomorphisms in the pseudo-orthogonal Lie algebra $\mathfrak{o}(r+1,s+1)$ up to conjugation of the its group $O(r+1,s+1)$. The explicit classification is worked out in full for the Riemannian $γ$ case ($r = 0, s = n$). As an application of this result, we prove that the set of five dimensional, $(Λ>0)$-vacuum, algebraically special metrics with non-degenerate optical …
Based on an earlier introduced new class of generalized gravity-matter models defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold, we derive an effective "Einstein-frame" theory featuring the following remarkable properties: (i) We obtain effective potential for the cosmological scalar field possessing two infinitely large flat regions which allows for a unified description of both early universe inflation as well as of present dark energy epoch; (ii) For a specific parameter range the model …
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}
We undertake a complete and covariant treatment for the quadratic Lagrangian of all of the degrees of freedom of massive gravity with a fixed flat fiducial metric for arbitrary massive gravity parameters around any isotropic self-accelerating background solution. Generically, 3 out of 4 Stuckelberg degrees of freedom propagate in addition to the usual 2 tensor degrees of freedom of general relativity. The complete kinetic structure typically is only revealed at an order in the graviton mass that is equivalently to retaining curvature terms in a locally flat expansion. These results resolve sev…
We derive the 1-loop effective action of the cubic Galileon coupled to quantum-gravitational fluctuations in a background and gauge-independent manner, employing the covariant framework of DeWitt and Vilkovisky. Although the bare action respects shift symmetry, the coupling to gravity induces an effective mass to the scalar, of the order of the cosmological constant, as a direct result of the non-flat field-space metric, the latter ensuring the field-reparametrization invariance of the formalism. Within a gauge-invariant regularization scheme, we discover novel, gravitationally induced non-Gal…
We propose a covariant prescription to compute holographic entanglement entropy and Poincare blocks (Global BMS blocks) in the context of three-dimensional Einstein gravity in flat space. We first present a prescription based on worldline methods in the probe limit, inspired by recent analog calculations in AdS/CFT. Building on this construction, we propose a full extrapolate dictionary and use it to compute holographic correlators and blocks away from the probe limit.
The main results are: 1. A manifestly covariant technique for the calculation of De Witt coefficients is elaborated; 2. The coefficients $a_3$ and $a_4$ are calculated; 3. Covariant methods for the study of the nonlocal structure of the effective action are developed. The terms of first and second order in background fields in De Witt coefficients are calculated. The summation of these terms is carried out and nonlocal covariant expression for the Green function, the heat kernel and the effective action are obtained. It is shown that in the conform-invariant case the Green function is finite. …
If inflation can occur only at the energy density V much smaller than the Planck density, which is the case for many inflationary models based on string theory, then the probability of quantum creation of a closed or an infinitely large open inflationary universe is exponentially suppressed for all known choices of the wave function of the universe. Meanwhile under certain conditions there is no exponential suppression for creation of topologically nontrivial compact flat or open inflationary universes. This suggests, contrary to the standard textbook lore, that compact flat or open universes …
Recent work has shown that the symmetries of classical gravitational scattering in asymptotically flat spacetimes include, at the linearized level, infinitesimal superrotations. These act like Virasoro generators on the celestial sphere at null infinity. However, due to the singularities in these generators, the physical status of finite superrotations has remained unclear. Here we address this issue in the context of the breaking of a cosmic string via quantum black hole pair nucleation. This process is described by a gravitational instanton known as the $C$-metric. After pair production, the…
We analyze the quantum process in which a cosmic string breaks in an anti-de Sitter (AdS) background, and a pair of charged or neutral black holes is produced at the ends of the strings. The energy to materialize and accelerate the pair comes from the strings tension. In an AdS background this is the only study done in the process of production of a pair of correlated black holes with spherical topology. The acceleration $A$ of the produced black holes is necessarily greater than (|L|/3)^(1/2), where L<0 is the cosmological constant. Only in this case the virtual pair of black holes can overco…
We explore the holographic principle in the context of asymptotically flat spacetimes. In analogy with the AdS/CFT scenario we analyse the asympotically symmetry group of this class of spacetimes, the so called Bondi-Metzner-Sachs (BMS) group. We apply the covariant entropy bound to relate bulk entropy to boundary symmetries and find a quite different picture with respect to the asymptotically AdS case. We then derive the covariant wave equations for fields carrying BMS representations to investigate the nature of the boundary degrees of freedom. We find some similarities with 't Hooft S-matri…
We continue the development of the effective covariant methods for calculating the heat kernel and the one-loop effective action in quantum field theory and quantum gravity. The status of the low-energy approximation in quantum gauge theories and quantum gravity is discussed in detail on the basis of analyzing the local Schwinger - De Witt expansion. It is argued that the low-energy limit, when defined in a covariant way, should be related to background fields with covariantly constant curvature, gauge field strength and potential. Some new approaches for calculating the low-energy heat kernel…
A flat FLRW cosmological model with perfect fluid comprising of variable Chaplygin gas has been studied in context of f(R; T) gravity with particle creation. The considered scale factors describe the accelerated expansion of universe due to the effective negative pressure produced during evolution of universe. The role of particle creation pressure on the cosmological parameters have been discussed in detail. By considering well accepted values of free parameters, the late time expansion of the universe with energy conditions have also been studied. The state-finder diagnostic for the consider…
The flat inflationary dust universe with matter creation proposed by Prigogine and coworkers is generalized and its dynamical properties are reexamined. It is shown that the starting point of these models depends critically on a dimensionless parameter $Σ$, closely related to the matter creation rate $ψ$. For $Σ$ bigger or smaller than unity flat universes can emerge, respectively, either like a Big-Bang FRW singularity or as a Minkowski space-time at $t=-\infty$. The case $Σ=1$ corresponds to a de Sitter-type solution, a fixed point in the phase diagram of the system, supported by the matter …
Exact construction of superstring field theory in some background fields is very important. We construct the low energy NS-NS sector of superstring field action in the pp-wave background with the flux of NS-NS antisymmetric tensor field (NS-NS pp-wave) without gauge fixing up to the second-order where the action is world-sheet BRST invariant. Here we use the word "covariant" in a invariant theory for a symmetric transformation of the pp-wave background which is not the Lorentz transformation in the flat background. Moreover we prove the exact correspondence between this low energy action and t…
Using the existence of a covariant conserved quantity on large perturbation scales in a spatially flat perfect fluid or scalar field universe, we present a general formula for gauge-invariantly defined comoving energy density perturbations which encodes the entire linear perturbation dynamics in a closed time integral. On this basis we discuss perturbation modes in different cosmological epochs.
We use the Brans-Dicke theory from the framework of General Relativity (Einstein frame), but now the total energy momentum tensor fulfills the following condition $\rm <[\{1}ϕT^{μνM}+T^{μν}(ϕ)>]_{;ν}=0$. We take as a first model the flat FRW metric and with the law of variation for Hubble's parameter proposal by Berman \cite{Berman}, we find solutions to the Einstein field equations by the cases: inflation ($γ=-1$), radiation ($γ=\{1}{3}$), stiff matter ($γ=1$). For the Inflation case the scalar field grows fast and depends strongly of the constant $\rm M_{γ=-1}$ that appears in the solution, …
A thermal squeezed state representation of inflaton is constructed for a flat Friedmann-Robertson-Walker background metric and the phenomenon of particle creation is examined during the oscillatory phase of inflaton, in the semiclassical theory of gravity. An approximate solution to the semiclassical Einstein equation is obtained in thermal squeezed state formalism by perturbatively and is found obey the same power-law expansion as that of classical Einstein equation. In addition to that the solution shows oscillatory in nature except on a particular condition. It is also noted that, the coher…
A scenario for gravitational particle creation in a stiff matter dominated flat Friedmann-Robertson-Walker universe is presented. The primary creation of scalar particles is calculated using quantum field theory in curved spacetime and it is found to be strongly dependent on the scalar mass and the expansion parameter of the universe. The particle creation is most effective for a very massive scalar field and large expansion parameter. We apply the results to cosmology and calculate an upper bound for the equilibrium temperature of the secondary particles created by the scalar field decay.
Here we formulate scenario of emergent universe from particle creation mechanism in spatially flat braneworld models. We consider an isotropic and homogeneous universe in Braneworld cosmology and universe is considered as a non-equilibrium thermodynamical system with dissipation due to particle creation mechanism. Assuming the particle creation rate as a function of the Hubble parameter , we formulate emergent scenario in RS2 and DGP models of Braneworld.
The effect of the electric field on the creation of spin 1/2 particles from vacuum in the (1+1) dimensional de-Sitter space-time is studied. The Dirac equation with a constant electric field is solved by introducing an unitary transformation. Then the canonical method based on Bogoliubov transformation is applied to calculate the pair creation probability and the density of created particles both for positive or negative wave vector. By doing summation over all allowed states, the number of created particles per unit of time per unit of length and the imaginary part of the Schwinger effective …
We describe spontaneous creation of the Brane World in $AdS_{5}$ with external field. The resulting Brane World consists of a flat 4d spatially finite expanding Universe and curved expanding "regulator" branes. No negative tension branes are involved.
We present a non-singular instanton describing the creation of an open universe with a compactified extra dimension. The four dimensional section of this solution is a singular instanton of the type introduced by Hawking and Turok. The ``singularity'' is viewed in five dimensions as a smooth bubble of ``nothing'' which eats up a portion of spacetime as it expands. Flat space with a compact extra dimension is shown to be gravitationally metastable, but sufficiently long lived if the size of the extra dimension is large compared with the Planck length.
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…
We consider the diffeomorphism invariant gravity coupled with the ideal fluid in the non-standard way. The Lorentz-invariance of the graviton propagator in such a theory considered as perturbation over flat background turns out to be broken due to non-standard coupling with the ideal fluid. As a result the behavior of the propagator in the ultraviolet/infrared region indicates that some versions of such theory are (super-)renormalizable ones (with appearance of only physical transverse modes). The FRW cosmology in same cases may be different from the one in General Relativity with the possible…
A model of an emergent universe is formulated using the mechanism of particle creation. Here the universe is considered as a non-equilibrium thermodynamical system with dissipation due to particle creation mechanism. The universe is chosen as spatially flat FRW space-time and the cosmic substratum is chosen as perfect fluid with barotropic equation of state. Both first and second order deviations from equilibrium prescription is considered and it is found that the scenario of emergent universe is possible in both the cases.
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 …
We show that the standard perfect fluid paradigm is not necessarily a valid description of a curved space steady state gravitational source. Simply by virtue of not being flat, curved space geometries have to possess intrinsic length scales, and such length scales can affect the fluid structure. For modes of wavelength of order or greater than such scales eikonalized geometrical optics cannot apply and rays are not geodesic. Covariantizing thus entails not only the replacing of flat space functions by covariant ones, but also the introduction of intrinsic scales that were absent in flat space.…
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.
We propose definitions for covariance and local Lorentz invariance applicable when the speed of light $c$ is allowed to vary. They have the merit of retaining only those aspects of the usual definitions which are invariant under unit transformations, and which can therefore legitimately represent the outcome of an experiment. We then discuss some possibilities for invariant actions governing the dynamics of such theories. We consider first the classical action for matter fields and the effects of a changing $c$ upon quantization. We discover a peculiar form of quantum particle creation due to …
We investigate the possibility of gravitationally generated particle production via the mechanism of nonminimal torsion--matter coupling. An intriguing feature of this theory is that the divergence of the matter energy--momentum tensor does not vanish identically. We explore the physical and cosmological implications of the nonconservation of the energy--momentum tensor by using the formalism of irreversible thermodynamics of open systems in the presence of matter creation/annihilation. The particle creation rates, pressure, and the expression of the comoving entropy are obtained in a covarian…
Conformally-flat gravitational analogues to the Schwinger effect
Universidad Nacional de La Plata（拉普拉塔国立大学）；CONICET（阿根廷国家科学研究委员会）；Université de Tours（图尔大学）；Université d’Orléans（奥尔良大学）；Centro Atómico Bariloche（巴里洛切原子中心）；Comisión Nacional de Energía Atómica（国家原子能委员会）；Instituto Balseiro（巴尔塞罗研究所）；Universidad Nacional de Cuyo（库约国立大学）；Technische Universität München（慕尼黑工业大学）
We show that in the isentropic scenario the first order thermodynamical particle creation model gives an emergent universe solution even when the chemical potential is non-zero. However there exists no emergent universe scenario in the second order non-equilibrium theory for the particle creation model. We then point out a correspondence between the particle creation model with barotropic equation of state and the equation of state giving rise to an emergent universe without particle creation in spatially flat FRW cosmology.
It was recently found that there are classes of nonlocal gravity theories that are free of ghosts and singularities in their Newtonian limit [PRL, 108 (2012), 031101]. In these proceedings, a detailed and pedagogical derivation of a main result, the flat space propagator for an arbitrary covariant metric theory of gravitation, is presented. The result is applied to analyse f(R) models, Gauss-Bonnet theory, Weyl-squared gravity and the potentially asymptotically free nonlocal theories.
We present a covariant, supersymmetric and kappa-symmetric action for non-Abelian multiwave system (nAmW) in D=3 AdS superspace. Its flat superspace limit provides a simplest counterpart of the recently proposed action for 11 dimensional system of N nearly coincident M-waves (multiple M0-branes), which is presently known for the case of flat target superspace only.
Within the framework of adiabatic regularization, we present a simple formalism to calculate number density and renormalized energy-momentum density of spin 1/2 particles in spatially flat FLRW spacetimes using an appropriate WKB ansatz for the adiabatic expansion for the field modes. The conformal and axial anomalies thus found are in exact agreement with those obtained from other renormalization methods. This formalism can be considered as an appropriate extension of the techniques originally introduced for scalar fields, applicable to fermions in curved space.
The lecture explains the geometric basis for the recently-discovered nonholonomic mapping principle which specifies certain laws of nature in spacetimes with curvature and torsion from those in flat spacetime, thus replacing and extending Einstein's equivalence principle. An important consequence is a new action principle for determining the equation of motion of a free spinless point particle in such spacetimes. Surprisingly, this equation contains a torsion force, although the action involves only the metric. This force changes geodesic into autoparallel trajectories, which are a direct mani…
Starting from an action for discretized gravity we derive a canonical formalism that exactly reproduces the dynamics and (broken) symmetries of the covariant formalism. For linearized Regge calculus on a flat background -- which exhibits exact gauge symmetries -- we derive local and first class constraints for arbitrary triangulated Cauchy surfaces. These constraints have a clear geometric interpretation and are a first step towards obtaining anomaly--free constraint algebras for canonical lattice gravity. Taking higher order dynamics into account the symmetries of the action are broken. This …
We propose a global minimal embedding of the Schwarzschild theory in a five-dimensional flat space by using two surfaces. Covariant field equations are deduced for the gravitational forces.
