Emil T. Akhmedov
Using properly defined Feynman propagator we obtain non--zero imaginary contribution to the scalar field effective action in even dimensional de Sitter space. Such a propagator follows from the path integral in de Sitter space and obeys composition principle proposed in arXiv:0709.2899. The obtained expression for the effective action shows particle production with the Gibbons--Hawking rate.
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In this paper we calculate the particle creation as seen by a stationary observer in 3+1 de Sitter space. This particle creation is calculated using an observer dependent geometrically based definition of time which is used to quantize a field on two different spacelike surfaces. The Bogolubov transformation relating these two quantizations is then calculated and the resulting particle creation is shown to be finite.
We present a method to semiclassically compute the pair creation rate of bosons and fermions in de Sitter spacetime. The results in the bosonic case agree with the ones in the literature. We find that for the constant electric field the fermionic and bosonic pair creation rate are the same. This analogy of bosons and fermions in the semiclassical limit is known from several flat spacetime examples.
For a spherically symmetric vacuum model with a negative cosmological constant, a complex constrained instanton is considered as the seed for the quantum pair creation of Schwarzschild-anti-de Sitter black holes. The relative creation probability is found to be the exponential of the negative of the black hole entropy. The black hole entropy is known to be one quarter of the black hole horizon area. In the absence of a general no-boundary proposal for open creation, the constrained instanton approach is used in treating both the open and closed pair creations of black holes.
We study pair creation of Kerr-Newman-anti-de Sitter and Kerr-Newman-de Sitter black holes.
On the Imaginary Part of the Effective Action in de Sitter Spacetime with Different Regularization Schemes
研究德西特时空下不同正则化方案对有效作用虚部的影响，揭示两种方法差异的根源。
When do real observers resolve de Sitter's imaginary problem?
本文探讨了现实观测者如何通过区分引力观测者与拓扑旁观者，解决德西特路径积分中的虚相问题，并通过实例证明信息承载钟表的必要性。
Following the subtraction procedure for manifolds with boundaries, we calculate by variational methods, the Schwarzschild-de Sitter and the de Sitter space energy difference. By computing the one loop approximation for TT tensors we discover the existence of an unstable mode even for the non-degenerate case. This result seems to be in agreement with the sub-maximal black hole pair creation of Bousso-Hawking. The instability can be eliminated by the boundary reduction method. Implications on a foam-like space are discussed.
The main objective of this comment is to correct the density number of created fermions by an electric field in the (1+1) dimensional de-Sitter space-time communicated by V. M. Villalba in Phys. Rev. D 52, 3742 (1995). It is shown how the positive and negative energy solutions are connected to one another by the charge conjugation. Some concluding remarks are made.
Over the years, de Sitter spacetime has been a central focus, in studies involving quantum fields, for its importance in the early and late expansion stages of the universe. While de Sitter spacetime closely mimics characteristics of the inflationary and dark energy dominated universe it does not help to understand the radiation and matter dominated expansions. In this review, we revisit some recent works, involving the author, which study gravitational particle creation beyond the de Sitter stage. Specifically, we present novel aspects of particle creation in the radiation dominated universe,…
Particle Creation and Excited-de Sitter Modes
该研究受Krein空间量子化方法启发，以激发德西特模为暴胀初始态，计算平坦Robertson-Walker时空的粒子产生，验证了其在德西特、闵氏时空远过去极限下与标准结果一致，且时空对称性更明确。
We discuss the quantum creation scenario of a Kerr-de Sitter black hole in all dimensions. We show that its relative creation probability is the exponential to the entropy of the black hole, using a topological argument. The action of the regular Euclidean instanton can be calculated in the same way.
We consider time-ordered (or Feynman) propagators between two different $α-$states of a linear de Sitter Quantum Field in the global de Sitter manifold and in the Poincaré patch. We separately examine $α-β$, In-In and In-Out propagators and find the imaginary contribution to the effective actions. The In-In propagators are real in both the Poincaré patch and in the global de Sitter manifold. On the other side the In-Out propagators at coincident points contain finite imaginary contributions in both patches in even dimensions, but they are not equivalent. In odd dimensions in both patches the i…
Using methods in the theory of semisimple Lie algebras, we can obtain all smooth solutions of the Klein-Gordon equation on the 4-dimensional de Sitter spacetime (dS^4). The mass of a Klein-Gordon scalar on dS^4 is related to an eigenvalue of the Casimir operator of so(1,4). Thus it is discrete, or quantized. Furthermore, the mass m of a Klein-Gordon scalar on dS^4 is imaginary: m^2 being proportional to -N(N+3), with N >= 0 an integer.
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 study in detail the quantum process in which a pair of black holes is created in a higher D-dimensional de Sitter (dS) background. The energy to materialize and accelerate the pair comes from the positive cosmological constant. The instantons that describe the process are obtained from the Tangherlini black hole solutions. Our pair creation rates reduce to the pair creation rate for Reissner-Nordstrom-dS solutions when D=4. Pair creation of black holes in the dS background becomes less suppressed when the dimension of the spacetime increases. The dS space is the only background in which we …
In the absence of a general no-boundary proposal for open creation, the complex constrained instanton is used as the seed for the open pair creations of black holes in the Kerr-Newman-anti-de Sitter family. The relative probability of the chargeless and nonrotating black hole pair is the exponential of the negative of the entropy, and that of the charged and (or) rotating black hole pair is the exponential of the negative of one quarter of the sum of the outer and inner black hole horizon areas.
We present an exact one-loop calculation of the tunneling process in Euclidean quantum gravity describing creation of black hole pairs in a de Sitter universe. Such processes are mediated by $S^2\times S^2$ gravitational instantons giving an imaginary contribution to the partition function. The required energy is provided by the expansion of the universe. We utilize the thermal properties of de Sitter space to describe the process as the decay of a metastable thermal state. Within the Euclidean path integral approach to gravity, we explicitly determine the spectra of the fluctuation operators,…
Action, entropy and pair creation rate of charged black holes in de Sitter space
本文计算并阐明了德西特空间中雷斯纳-诺德斯特龙黑洞壳上欧几里得作用量的解释，得出其为黑洞与宇宙学视界熵之和的负值，进而估算了任意质量电荷黑洞对产生概率，并揭示了带电德西特黑洞的衰变机制。
We show that global de Sitter space is unstable to particle creation, even for a massive free field theory with no self-interactions. The O(4,1) de Sitter invariant state is a definite phase coherent superposition of particle and anti-particle solutions in both the asymptotic past and future, and therefore is not a true vacuum state. In the closely related case of particle creation by a constant, uniform electric field, a time symmetric state analogous to the de Sitter invariant one is constructed, which is also not a stable vacuum state. We provide the general framework necessary to describe …
In the in-/out-state formalism we find the exact one-loop effective action of a massive scalar field in the global coordinates of de Sitter spaces, which is a gravity analog of the Heisenberg-Euler action in QED. The nonperturbative effective action, modulo the angular momentum sum, has an imaginary part in all even dimensions, but the imaginary part of the effective action is zero in all odd dimensions. However, in the zeta-function regularization for angular momenta, the weak-curvature expansion of the renormalized effective action vanishes in any even dimension, while the real part is finit…
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 show that the quasinormal spectrum of gravitational perturbations of Schwarzschild - de Sitter black holes contains a new branch of purely imaginary modes. These modes are not algebraically special and we showed that the sum of them form the well-known in the literature exponential asymptotic tail. When the ratio of the event horizon radius to the cosmological horizon vanishes, these quasinormal modes approach modes of empty de Sitter spacetime. Thus, the spectrum consists of the two branches: Schwarzschild branch deformed by the cosmological constant and de Sitter branch deformed by the bl…
The quasinormal modes (QNMs) of Dirac field perturbations of a Reissner-Nordström black hole in an asymptotically Anti-de Sitter spacetime are investigated. We find that both the real and imaginary parts of the fundamental quasinormal frequencies for large black holes are the linear functions of the Hawking temperature, and the slope of the lines for the real parts decreases while that for the magnitude of the imaginary parts increases as the black hole charge increases. According to the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, the fact shows that different charge presen…
In the present article we solve the Dirac equation in a de Sitter universe when a constant electric field is present. Using the Bogoliubov transformations, we compute the rate of spin 1/2 created particles by the electric field. We compare our results with the scalar case. We also analyze the behavior of the density of particles created in the limit H=0, when de Sitter background reduces to a flat space-time.
On the scalar tachyons creation in noncommutative de Sitter space-time
本研究通过求解变形Klein-Gordon方程与Bogoliubov变换，分析非对易德西特空间的标量快子产生，发现其能谱为热分布、非对易性降低有效温度，且非对易参数作用等价于标准粒子产生中的电场。
We study a massive scalar field theory in de Sitter space. Using worldline instanton approach, we calculate probability of pair production in weak-field limit. In addition to exponential factor we derive pre-exponential factor. Within this approach the vanishing probability for odd-dimensional de Sitter space gets a clear geometrical interpretation. We find leading contribution to imaginary part of two point correlator in $ϕ^3$-theory.
Non-perturbative de Sitter Jackiw-Teitelboim gravity
本文推导了德西特 Jackiw-Teitelboim 引力的亏格展开，发现其有效弦耦合为纯虚数，导致 S-矩阵展开交替符号且可 Borel-Le Roy 求和，并形式上等价于负自由度矩阵积分。
A quantum mechanical picture, relating accelerated geodesic deviation to creation of massive particles via quantum tunneling in curved background spacetimes, is presented. The effect is analogous to pair production by an electric field and leads naturally to production of massive particles in de Sitter and superluminal FRW spacetimes. The probability of particle production in de Sitter space per unit volume and time is computed in a leading semiclassical approximation and shown to coincide with the previously obtained expression.
The creation of 4d de Sitter (inflationary) boundary gluing two d5 de Sitter bulks on the classical as well as on quantum level (with account of brane QFT via corresponding trace anomaly induced effective action) is discussed. Quantum effects decrease the classical de Sitter brane radius or create new de Sitter brane with even smaller radius. It is important that brane CFT may be chosen to be dual to one of 5d de Sitter bulks, making the explicit relation of de Sitter brane-world with dS/CFT correspondence. In this way, the localization of gravity on the brane is shown. Moving (time-dependent)…
Creation of thermal distribution of particles by a black hole is independent of the detail of gravitational collapse, making the construction of the eternal horizons suffice to address the problem in asymptotically flat spacetimes. For eternal de Sitter black holes however, earlier studies have shown the existence of both thermal and non-thermal particle creation, originating from the non-trivial causal structure of these spacetimes. Keeping this in mind we consider this problem in the context of a quasistationary gravitational collapse occurring in a $(3+1)$-dimensional eternal de Sitter, set…
We study the possible types of the nucleation of vacuum bubbles. We classify vacuum bubbles in de Sitter background and present some numerical solutions. The thin-wall approximation is employed to obtain the nucleation rate and the radius of vacuum bubbles. With careful analysis we confirm that Parke's formula is also applicable to the large true vacuum bubbles. The nucleation of the false vacuum bubble in de Sitter background is also evaluated. The tunneling process in the potential with degenerate vacua is analyzed as the limiting cases of the large true vacuum bubble and false vacuum bubble…
In the three-dimensional anti-de Sitter spacetime/two-dimensional conformal field theory correspondence, we derive the imaginary-time path-integral of a non-relativistic particle in the anti-de Sitter bulk space, which is dual to the ground state, from the holographic principle. This derivation is based on (i) the author's previous argument that the holographic principle asserts that the anti-de Sitter bulk space as a holographic tensor network after classicalization has as many stochastic classicalized spin degrees of freedom as there are sites and (ii) the reinterpretation of the Euclidean a…
The quasinormal modes of the Reissner-Nordström de Sitter black hole for the massless Dirac fields are studied using the Pöshl-Teller potential approximation. We find that the magnitude of the imaginary part of the quasinormal frequencies decreases as the cosmological constant or the orbital angular momentum increases, but it increases as the charge or the overtone number increases. An interesting feature is that the imaginary part is almost linearly related to the real part as the cosmological constant changes for fixed charge, and the linearity becomes better as the orbital angular momentum …
We analyze the quantum process in which a cosmic string breaks in a de Sitter (dS) background, and a pair of neutral or charged black holes is produced at the ends of the string. The energy to materialize and accelerate the pair comes from the positive cosmological constant and, in addition, from the string tension. The compact saddle point solutions without conical singularities (instantons) or with conical singularities (sub-maximal instantons) that describe this process are constructed through the analytical continuation of the dS C-metric. Then, we explicitly compute the pair creation rate…
The possibility of quantum creation of a dilatonic AdS Universe is discussed.Without dilaton it is known that quantum effects lead to the annihilation of AdS Universe. We consider the role of the form for the dilatonic potential in the quantum creation of a dilatonic AdS Universe. Using the conformal anomaly for dilaton coupled scalar, the anomaly induced action and the equations of motion are obtained. The anomaly induced action is added to classical dilaton gravity action. The solutions of the full theory which correspond to quantum-corrected AdS Universe are given for number of dilatonic po…
A general form of quasi-de Sitter(dS) modes in a dynamical background is used to study the creation of particle during the inflation. Actually, by considering the general form of inflaton field equation as a function of the Hankel function index and by using the Planck 2015 constraint on spectral index, we obtain the possible new constraints for the values of coupling constant in the era with quasi-dS space-time. Then, we explicitly calculate the general form of expectation value of the created particles in terms of the Hankel function index and the conformal time. As an important result, we s…
We investigate the decay of metastable de Sitter, Minkowski and anti-de Sitter vacua catalyzed by a black hole and a cloud of strings. We apply the method to the creation of the four dimensional bubble universe in the five dimensional anti-de Sitter spacetime recently proposed by Banerjee, Danielsson, Dibitetto, Giri and Schillo. We study the bounce action for the creation and find that the bubble with very small cosmological constant, of order $Λ^{(4)}/M^2_4 \sim 10^{-120}$, is favored by the catalysis by assuming appropriate mass scales of the black hole and the cloud of strings to reproduce…
In a related paper we have obtained that the effective action for a kappa-deformed quantum field theory has a real and an imaginary part. The real part is half the sum of the kappa-deformed zero mode frequencies, while the imaginary part is proportional to the sum of the squares of the zero mode frequencies, being proportional to the inverse of kappa. Here we calculate this imaginary part for the kappa-deformed electromagnetic field confined between two perfectly conducting parallel plates. After renormalization this imaginary part gives a creation rate of kappa-deformed electromagnetic radiat…
Using the AdS/CFT correspondence, we construct the holographic dual of a tunneling instanton describing Schwinger pair creation in de Sitter space. Our approach allows us to extract the critical value of the electric field for which the potential barrier disappears, rendering the vacuum unstable. In addition, we compute the large-$λ$, large-$N_c$ corrections to the nucleation rate and we find that it agrees with previous expectations based on perturbative computations. As a by-product of this investigation, we study the causal structure of the string dual to the nucleated pair as seen by diffe…
We investigate Euclidean wormholes in Einstein gravity with a massless scalar field in de Sitter space. Euclidean wormholes are possible due to the analytic continuation of the time as well as complexification of fields, where we need to impose the classicality after the Wick-rotation to the Lorentzian signatures. For some parameters, wormholes are preferred than Hawking-Moss instantons, and hence wormholes can be more fundamental than Hawking-Moss type instantons. Euclidean wormholes can be interpreted in three ways: (1) classical big bounce, (2) either tunneling from a small to a large unive…
We compute the imaginary part of scalar four-point functions in the AdS/CFT correspondence relevant to N=4 super Yang-Mills theory. Unitarity of the AdS supergravity demands that the imaginary parts of the correlation functions factorize into products of lower-point functions. We include the exchange diagrams for scalars as well as gravitons and find explicit expressions for the imaginary parts of these correlators. In momentum space these expressions contain only rational functions and logarithms of the kinematic invariants, in such a manner that the correlator is not a free-field result. The…
Making use of the symmetries of anti-de Sitter space-time, we derive an analytic expression for the bispinor of parallel transport, from which we construct in closed form the vacuum Feynman Green's function of the Dirac field on this background. Using the imaginary time anti-periodicity property of the thermal Feynman Green's function, we calculate the thermal expectation values of the fermion condensate and stress-energy tensor and highlight the effect of quantum corrections as compared to relativistic kinetic theory results.
The method of adiabatic invariants for time dependent Hamiltonians is applied to a massive scalar field in a de Sitter space-time. The scalar field ground state, its Fock space and coherent states are constructed and related to the particle states. Diverse quantities of physical interest are illustrated, such as particle creation and the way a classical probability distribution emerges for the system at late times.
Nonlocal effective action and particle creation in $D$ dimensions
本研究在弯曲时空量子场论框架下，通过计算曲率二阶精度的有效作用量虚部得到粒子产生率，推导了不同维度下的相关张量表达式并类比电磁成对产生，强调了被忽视的粒子产生阈值的重要性。
We revisit the Hamiltonian formalism for a massive scalar field and study the particle production in a de Sitter space. In the invariant-operator picture the time-dependent annihilation and creation operators are constructed in terms of a complex solution to the classical equation of motion for the field and the Gaussian wave function for each Fourier mode is found which is an exact solution to the Schrödinger equation. The in-out formalism is reformulated by the annihilation and creation operators and the Gaussian wave functions. The de Sitter radiation from the in-out formalism differs from …
In this note we consider the spontaneous creation of the brane world in five-dimensional space with nondynamical external four-form field via spherically asymmetric bounce solution. We argue that spherically asymmetric bounce suggests several inequivalent directions of the time arrow upon the analytic continuation to the space-time with Lorentzian signature. It it shown that S-branes in the imaginary time emerge naturally upon the particular continuation.
In the very early universe, a generalized Schwinger effect can create pairs from both electrical and gravitational fields. The expectation value of fermionic current induced by these newly created pairs has been recently computed in de Sitter spacetime. I will discuss different limiting cases of this result and some of its possible physical interpretations.
We discuss the role of conformal matter quantum effects (using large $N$ anomaly induced effective action) to creation-annihilation of an Anti-de Sitter Universe. The arbitrary GUT with conformally invariant content of fields is considered. On a purely gravitational (supersymmetric) AdS background, the quantum effects act against an (already existing) AdS Universe. The annihilation of such a Universe occurs, what is common for any conformal matter theory. On a dilaton-gravitational background, where there is dilatonic contribution to the induced effective action, the quantum creation of an AdS…
We study various bubble solutions in string/M theories obtained by double Wick rotations of (non-)extremal brane configurations. Typically, the geometry interpolates de Sitter space-time times non-compact extra-dimensional space in the near-bubble wall region and the asymptotic flat Minkowski space-time. These bubble solutions provide nice background geometries reconciling string/M theories with de Sitter space-time. For the application of these solutions to cosmology, we consider multi-bubble solutions and find landscapes of varying cosmological constant. Double Wick rotation in string/M theo…
In the No-Boundary Universe a primordial black hole is created from a constrained gravitational instanton. The black hole created is immersed in the de Sitter background with a positive cosmological constant. The constrained instanton is characterized not only by the external parameters, the mass parameter, charge and angular momentum, but also by one more internal parameter, the identification period in the imaginary time coordinate. Although the period has no effect on the black hole background, its inverse is the temperature of the no-boundary state of the perturbation modes perceived by an…
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.
We construct a four dimensional Yang-Mills theory with ${\cal N}=4$ twisted supersymmetry whose classical vacua correspond to four dimensional anti-de Sitter space. The theory utilizes a complex gauge field whose real part is a spin connection which is used to enforce local Lorentz invariance. The imaginary part of the connection can then be interpreted as a vierbein. The topological construction ensures that the partition function and classical vacua are independent of the background geometry. Additionally a supersymmetric and gauge invariant lattice construction is possible yielding a non-pe…
We set up a consistent renormalizable perturbation theory of a scalar field in a nontrivial alpha vacuum in de Sitter space. Although one representation of the effective action involves non-local interactions between anti-podal points, we show the theory leads to causal physics, and we prove a spectral theorem for the interacting two-point function. We construct the renormalized stress energy tensor and show this develops no imaginary part at leading order in the interactions, consistent with stability.
We give the generalization of the method of the space-time description of particle creation by a gravitational field for a scalar field with nonconformal coupling to the curvature. The space-time correlation function is obtained for a created pair of the quasi-particles, corresponding to a diagonal form of the instantaneous Hamiltonian. The case of an adiabatic change of the metric of homogeneous isotropic space is analyzed. We show that the created pairs of quasi-particles in de Sitter space should be interpreted as pairs of virtual particles.
Time-resolved digital quantum simulation of cosmological particle creation in a de Sitter-radiation transition
研究德西特-辐射跃迁中宇宙粒子产生，通过离散共形时间演化实现时间分辨数字量子模拟，用四量子比特单激发编码动量对，比较多种模拟方法，结果与解析基准一致，IBM 实验有残余硬件误差。
Connection of the invariant Dirac equation over the de Sitter space with irreducible representations of the de Sitter group is ascertained. The set of solutions of this equation is obtained in the form of the product of two different systems of generalized coherent states for the de Sitter group. Using these solutions the quantized Dirac field over de Sitter space is constructed and its propagator is found. It is a result of action of some de Sitter invariant spinor operator onto the spin zero propagator with an imaginary shift of a mass.
Using the Pais-Uhlenbeck Oscillator as a toy model, we outline a consistent alternative to the indefinite-metric quantization scheme that does not violate unitarity. We describe the basic mathematical structure of this method by giving an explicit construction of the Hilbert space of state vectors and the corresponding creation and annihilation operators. The latter satisfy the usual bosonic commutation relation and differ from those of the indefinite-metric theories by a sign in the definition of the creation operator. This change of sign achieves a definitization of the indefinite-metric tha…
Complex effective actions and gravitational pair creation
本文通过不同方法研究无质量标量场引起的引力有效作用虚部，探讨微扰与非微扰的区别，并参考已有研究成果。
We study the Schwinger mechanism by a uniform electric field in ${\rm dS}_2$ and ${\rm AdS}_2$ and the curvature effect on the Schwinger effect, and further propose a thermal interpretation of the Schwinger formula in terms of the Gibbons-Hawking temperature and the Unruh temperature for an accelerating charge in ${\rm dS}_2$ and an analogous expression in ${\rm AdS}_2$. The exact one-loop effective action is found in the proper-time integral in each space, which is determined by the effective mass, the Maxwell scalar, and the scalar curvature, and whose pole structure gives the imaginary part…
Sen has recently drawn attention to an exact time-dependent Boundary Conformal Field Theory with the space-time interpretation of brane creation and annihilation. An interesting limit of this BCFT is formally equivalent to an array of D-branes located in imaginary time. This raises the question: what is the meaning of D-branes in imaginary time? The answer we propose is that D-branes in imaginary time define purely closed string backgrounds. In particular we prove that the disk scattering amplitude of m closed strings off an arbitrary configuration of imaginary branes is equivalent to a sphere…
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