Michael Freedman, Modjtaba Shokrian Zini
We explore the emergence of many-body physics from quantum mechanics via spontaneous symmetry breaking. To this end, we study potentials which are functionals on the space of Hamiltonians enjoying an unstable critical point corresponding to a random quantum mechanical system (the Gaussian unitary ensemble), but also less symmetrical local minima corresponding to interacting systems at the level of operators.
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We calculate the particle production rate in an expanding universe with a three-torus topology. We discuss also the complete evolution of the size of such a universe. The energy density of particles created through the nonzero modes is computed for selected masses. The unique contribution of the zero mode and its properties are also analyzed.
In the present article we analyze the phenomenon of particle creation in a cosmological anisotropic universe when a constant electric field is present. We compute, via the Bogoliubov transformations, the density number of particles created.
In this article we compute the density of Dirac particles created by a cosmological anisotropic Bianchi I universe in the presence of a constant electric field. We show that the particle distribution becomes thermal when one neglects the electric interaction.
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.
We reanalyze the problem of particle creation in a 3+1 spatially closed Robertson-Walker space-time. We compute the total number of particles produced by this non-stationary gravitational background as well as the corresponding total energy and find a slight discrepancy between our results and those recently obtained in the literature
In this article we compute the density of scalar and Dirac particles created by a cosmological anisotropic Bianchi type I universe in the presence of a time varying electric field. We show that the particle distribution becomes thermal when one neglects the electric interaction.
We study a class of three-point functions on the de Sitter universe and on the asymptotic cone. A blending of geometrical ideas and analytic methods is used to compute some remarkable integrals, on the basis of a generalized star-triangle identity living on the cone and on the complex de Sitter manifold. We discuss an application of the general results to the study of the stability of scalar particles on the Sitter universe.
We consider a scenario where our universe is taken as a three-dimensional domain wall embedded in a five-dimensional Minkowski space-time, as originally proposed by Brito and collaborators [1]. We explore the existence of a richer class of soliton solutions and their consequences for the acceleration of the universe driven by collisions of bulk particle excitations with the walls. In particular it is shown that some of these solutions should play a fundamental role throughout the expansion process.
The scalar particle production from vacuum in the presence of electric field, on the de Sitter spacetime is studied. We use perturbation methods to define the transition amplitude. We obtain that the momentum is not conserved in this process. The probability of pair production is computed by squaring the transition amplitude. Our graphical representations shows that, the probability of scalar particle production was important only in early stage of the universe, when the Hubble's constant was very large in comparison with the mass of the particle. Also we propose here a criteria of particle-an…
We study creation and time evolution of particle number asymmetry with nonequilibrium quantum field theory. We introduce a model of a neutral scalar and a complex scalar and it has CP violating and particle number violating features. Starting with an initial condition specified by density operator, we show how particle number asymmetry can be generated through interaction. We investigate the time evolution of particle number asymmetry of universe using perturbation method.
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 study the effect of the non-commutativity on the creation of scalar particles from vacuum in the anisotropic universe space-time. We derive the deformed Klein-Gordon equation up to second order in the non-commutativity parameter using the general modified field equation. Then the canonical method based on Bogoliubov transformation is applied to calculate the probability of particle creation in vacuum and the corresponding number density in the $k$ mode. We deduce that the non-commutative space-time introduces a new source of particle creation.
Quantum gravity has exciting peculiarities on the Planck scale.The effect of generalized uncertainty principle (GUP) to the entangled scalar/fermion particles' tunneling from a Schwarzschild black hole immersed in an electromagnetic Universe is investigated by the help of semi-classical tunneling method. The quantum corrected Hawking temperature of this black hole with an external parameter "a" modifies the Hawking temperature for the entangled particles.
In the present article we study the process of particle creation for Elko spinor fields as a consequence of expansion of the universe. We study the effect driven by a expanding background that is asymptotically minkowskian in the past and future. The differential equation that governs the time mode function is obtained for the conformal coupling case and, although its solution is non-analytic, within an approximation that preserves the characteristics of the terms that break the analyticity, analytic solutions are obtained. Thus, by means of the Bogolyubov transformations technique, the number…
The lack of energy conservation introduces new particle processes in curved spacetime that are forbidden in flat space. Therefore one has to be very cautious about using the results calculated in Minkowskian space in early universe applications. This is true for particle decay rates in particular, which need to be calculated using quantum field theory in curved spacetime. Previous studies are usually restricted to using minimal or conformal coupling for the decaying particle, while using a more general coupling would give deeper insight into particle decay. This paper presents the results we o…
An expanding closed universe filled with radiation can either recollapse or tunnel to the regime of unbounded expansion, if the cosmological constant is nonzero. We re-examine the question of particle creation during tunneling, with the purpose of resolving a long-standing controversy. Using a perturbative superspace model with a conformally coupled massless scalar field, which is known to give no particle production, we explicitly show that the breakdown of the semiclassical approximation and the ``catastrophic particle production'' claimed earlier in the literature are due to an inappropriat…
We investigate the radiation from an inertial scalar particle evolving in a de Sitter expanding Universe. In the context of scalar QED the process is generated by the first order term in the perturbation theory expansion of the S-matrix. The partial transition probability is obtained and analysed, and soft-photon emission is found to dominate overall. It has been argued that an inertial particle evolving in dS spacetime loses physical momentum just as a decelerated particle in Minkowski space does. It is thus expected that an inertial charge will radiate in a similar way. We investigate the ra…
It is a well known result that the scalar field is composed of two chiral particles (Floreanini-Jackiw particles) of opposite chiralities. Also, that a Siegel particle spectrum is formed by a nonmover field (a Hull's noton) and a FJ particle. In this work we show that in a scalar field spectrum, in a curved expanding universe scenario, we can find two dynamical chiral fields.
We study particle decay in de Sitter space-time as given by first order perturbation theory in an interacting quantum field theory. We show that for fields with masses above a critical mass $m_c$ there is no such thing as particle stability, so that decays forbidden in flat space-time do occur there. The lifetime of such a particle also turns out to be independent of its velocity when that lifetime is comparable with de Sitter radius. Particles with lower mass are even stranger: The masses of their decay products must obey quantification rules, and their lifetime is zero.
We investigate the fate of particle production in an expanding universe dominated by a perfect fluid with equation of state $p = αρ$. The rate of particle production, using the Bogolioubov coefficients, are determined exactly for any value of $α$ in the case of a flat universe. When the strong energy condition is satisfied, the rate of particle production decreases as time goes on, in agreement to the fact that the four-dimensional curvature decreases with the expansion; the opposite occurs when the strong energy condition is violated. In the phantomic case, the rate of particle production div…
We study the phenomenon of mass loss by a scalar charge -- a point particle that acts a source for a noninteracting scalar field -- in an expanding universe. The charge is placed on comoving world lines of two cosmological spacetimes: a de Sitter universe, and a spatially-flat, matter-dominated universe. In both cases, we find that the particle's rest mass is not a constant, but that it changes in response to the emission of monopole scalar radiation by the particle. In de Sitter spacetime, the particle radiates all of its mass within a finite proper time. In the matter-dominated cosmology, th…
The earlier developed algorithm for constructing a self-conjugate Hamiltonian in the η-representation for Dirac particles interacting with a general gravitational field is extended to the case of electromagnetic fields. This Hamiltonian is applied to the case when the gravitational field describes the spatially flat Friedmann model, and the electromagnetic field is the Coulomb potential extended to the case of this model. The analysis of atomic systems and electromagnetic forces of interaction under the conditions of spatially flat expansion of the universe has demonstrated that the system of …
The possibility of an emergent universe solution to Einstein's field equations allowing for an irreversible creation of matter at the expense of the gravitational field is shown. With the universe being chosen as spatially flat FRW spacetime together with equation of state proposed in [17], the solution exists when the ratio of the phenomenological matter creation rate to the number density times the Hubble parameter is a number $β$ of the order of unity and independent of time. The thermodynamic behaviour is also determined for this solution. Interestingly, we also find that an emergent unive…
Anisotropic particle creation from $T-$vacuum in the radiation dominated universe
本文将(1+1)维辐射主导宇宙中的$T-$真空理论扩展至(3+1)维，证明其可产生非热、瞬时的各向异性粒子，或可与早期宇宙各向异性观测比较。
Chaotic motion of particles in the spacetime of a Kerr black hole immersed in swirling universes
该研究针对浸没于涡旋宇宙中的Kerr黑洞时空下的粒子运动展开分析，借助多种动力学分析方法证实混沌存在，发现两参数可相互调节混沌发生范围，且吸引域边界存在自相似分形结构，丰富了相关物理内涵。
In the presence of a gravitational field decay rates may significantly differ from flat space equivalent. By studying mutually interacting quantum fields the decay rates can be calculated on a given spacetime. This paper presents the calculation of the transition probability for the decay of a massive scalar particle in a stiff matter dominated universe. We find that due to the precence of a gravitational field a finite correction to the transition probability is added which depends inversely on the mass. Moreover the decay rate is smaller and lifetime of the particles is longer compared to fl…
In the present paper, we solve the Dirac equation in the 2+1 dimensional exponentially expanding magnetized by uniform magnetic field and non-magnetized universes, separately. Asymptotic behaviors of the solutions are determined. Using these results we discuss the current of a Dirac particle to discuss the polarization densities and the magnetization density in the context of Gordon decomposition method. In this work we also calculate the total polarization and magnetization, to investigate that the magnetic field how can effect on the particle production. Furthermore, the electric and the mag…
In this article there are considered non-equilibrium cosmological scenarios with the assumption that scaling of particles interaction is restored in range of extra-high energies. On basis of energy-balance equation's exact solutions it is obtained the strong conclusion about fundamental unattainability of local thermodynamic equilibrium in the accelerated Universe. There are presented the results of numerical simulation of previously constructed strict mathematical model which describes thermodynamic equilibrium's establishment in the originally nonequilibrium cosmological ultrarelativistic pl…
The third quantization formalism of quantum cosmology adds simplicity and conceptual insight into the quantum description of the multiverse. Within such a formalism, the existence of squeezed and entangled states raises the question of whether the complementary principle of quantum mechanics has to be extended to the quantum description of the whole space-time manifold. If so, the 'particle' description entails the consideration of a multiverse scenario and the 'wave' description induces us to consider as well correlations and interactions among the universes of the multiverse.
Algebraic and Positive Geometry of the Universe: from Particles to Galaxies
本文综述了代数几何、D-模理论、组合学与粒子物理及宇宙学交叉的前沿进展，重点阐述费曼积分与正几何的双重表述，并指出正几何旨在为宇宙学和粒子物理现象建立统一数学语言。
In the context of current particle physics theories, it is quite likely that topological defects may be present in our universe. An observation of these fossils from the early universe would lead to invaluable insight into cosmology and particle physics, while their absence provides important constraints on particle-cosmology model building. I describe recent efforts to address cosmological issues in condensed matter systems such as He-3 and a possible solution to the magnetic monopole problem due to defect interactions. (Invited talk at the 1997 RESCEU Symposium, University of Tokyo.)
We consider our universe as a 3d domain wall embedded in a 5d dimensional Minkowski space-time. We address the problem of inflation and late time acceleration driven by bulk particles colliding with the 3d domain wall. The expansion of our universe is mainly related to these bulk particles. Since our universe tends to be permeated by a large number of isolated structures, as temperature diminishes with the expansion, we model our universe with a 3d domain wall with increasing internal structures. These structures could be unstable 2d domain walls evolving to fermi-balls which are candidates to…
The effective gravitational mass as well as the energy and momentum distributions of a radiating charged particle in Einstein's universe are evaluated. The Moller's energy-momentum complex is employed for this computation. The spacetime under study is a generalization of Bonnor and Vaidya spacetime in the sense that the metric is described in the cosmological background of Einstein's universe in lieu of the flat background. Several spacetimes are limiting cases of the one considered here. Particularly for the Reissner-Nordstrom black hole background, our results are exactly the same with those…
We discuss a way of producing anisotropies in the spectrum of superheavy Dark matter, which are due to the distortion of the inflationary space time induced by the recoil of D-particles upon their scattering with ordinary string matter in the Early Universe. We calculate such distortions by world-sheet Liouville string theory (perturbative) methods. The resulting anisotropies are found to be proportional to the average recoil velocity and density of the D-particles. In our analysis we employ a regulated version of de Sitter space, allowing for graceful exit from inflation. This guarantees the …
We study the evolution of a quantum scalar field in a toy universe which has three stages of evolution, viz., (i) an early (inflationary) de Sitter phase (ii) radiation dominated phase and (iii) late-time (cosmological constant dominated) de Sitter phase. Using Schrödinger picture, the scalar field equations are solved separately for the three stages and matched at the transition points. The boundary conditions are chosen so that field modes in the early de Sitter evolves from Bunch-Davies vacuum state. We determine the (time-dependent) particle content of this quantum state for the entire evo…
With the two most profound conceptual revolutions of XXth century physics, quantum mechanics and relativity, which have culminated into relativistic spacetime geometry and quantum gauge field theory as the principles for gravity and the three other known fundamental interactions, the physicist of the XXIst century has inherited an unfinished symphony: the unification of the quantum and the continuum. As an invitation to tomorrow's quantum geometers who must design the new rulers by which to size up the Universe at those scales where the smallest meets the largest, these lectures review the bas…
We study particle decay in de Sitter space-time as given by first order perturbation theory in a Lagrangian interacting quantum field theory. We study in detail the adiabatic limit of the perturbative amplitude and compute the "phase space" coefficient exactly in the case of two equal particles produced in the disintegration. We show that for fields with masses above a critical mass $m_c$ there is no such thing as particle stability, so that decays forbidden in flat space-time do occur here. The lifetime of such a particle also turns out to be independent of its velocity when that lifetime is …
We study particle production and the corresponding entropy increase in the context of cosmology with dynamical vacuum. We focus on the particular form that has been called "running vacuum model" (RVM), which is known to furnish a successful description of the overall current observations at a competitive level with the concordance $Λ$CDM model. It also provides an elegant global explanation of the cosmic history from a non-singular initial state in the very early universe up to our days and further into the final de Sitter era. The model has no horizon problem and provides an alternative expla…
Gravity-induced entanglement between two massive microscopic particles in curved spacetime: II.Friedmann- Lemaître-Robertson-Walker universe
本文将量子引力诱导质量纠缠的研究从 Schwarzschild 背景推广到 FLRW 宇宙，通过相位变化与 QGEM 谱分析大质量微观粒子传播时的引力纠缠形成机制。
We review the basics of the dynamics of closed strings moving along the discretized line \Z. The string excitations are described by a field ϕ_x(τ) where x is the position of the string in the embedding space and τis a semi-infinite ``euclidean time'' parameter related to the longitudinal mode of the string. Interactions due to splitting and joining of closed strings are taken into account by a local potential and occur only along the edge τ=0 of the semi-plane (x, τ).
We investigate a particle physics model for cosmic inflation based on the following assumptions: (i) there are at least two complex scalar fields; (ii) the scalar potential is bounded from below and remains perturbative up to the Planck scale; (iii) we assume slow-roll inflation with maximally correlated adiabatic and entropy fluctuations 50--60 e-folds before the end of inflation. The energy scale of the inflation is set automatically by the model. Assuming also at least one massive right handed neutrino, we explore the allowed parameter space of the scalar potential as a function of the Yuka…
We study kinetic master equations for chemical reactions involving the formation and the natural decay of unstable particles in a thermal bath. We consider the decay channel of one into two particles, and the inverse process, fusion of two thermal particles into one. We present the master equations the evolution of the density of the unstable particles in the early Universe. We obtain the thermal invariant reaction rate using as an input the free space (vacuum) decay time and show the medium quantum effects on $π+π\leftrightarrow ρ$ reaction relaxation time. As another laboratory example we de…
A complete quantum field theoretic study of charged and neutral particle creation in a rapidly/adiabatically expanding Friedman-Robertson-Walker metric for an O(4) scalar field theory with quartic interactions (admitting a phase transition) is given. Quantization is carried out by inclusion of quantum fluctuations. We show that the quantized Hamiltonian admits an su(1,1) invariance. The squeezing transformation diagonalizes the Hamiltonian and shows that the dynamical states are squeezed states. Allowing for different forms of the expansion parameter, we show how the neutral and charged partic…
Scalar fields in Bonnor-Melvin Universe with potential: A study of dynamics of spin-0 particles-antiparticles
本研究在含宇宙学常数的柱对称Bonnor-Melvin磁宇宙框架下，利用Klein-Gordon方程结合Cornell型标量势推导径向波动方程，得到自旋0量子系统解析本征值解，揭示多参数对能谱与波函数的显著影响。
Modern cosmology successfully deals with the origin and the evolution of the Universe at large scales, but it is unable to completely answer the question about the nature of the fundamental objects that it is describing. As a matter of fact, about 95\% of the constituents of the Universe is indeed completely unknown: it cannot be described in terms of known particles. Despite intense efforts to shed light on this literal darkness by dark matter and dark energy direct and indirect searches, not much progress has been made so far. In this work, we take a different perspective by reviewing and el…
The scalar particle production through a scalar field non-minimally coupled with geometry is investigated in the context of a spatially homogeneous and isotropic universe. In this paper, in order to study the evolution of particle production over time in the case of analytical solutions, we focus on a simple Horndeski theory. We first suppose that the universe is dominated by a scalar field and derive the energy conservation condition. Then from the thermodynamic point of view, the macroscopic non-conservation of the scalar field energy-momentum tensor can be explained as an irreversible produ…
We construct exact static inhomogeneous solutions to Einstein's equations with counter flow of particle fluid and a positive cosmological constant by using the Sasaki metrics on three-dimensional spaces. The solutions, which admit an arbitrary function that denotes inhomogeneous number density of particles, are a generalization of Einstein's static universe. On some examples of explicit solutions, we discuss non-linear density contrast and deviation of the metric functions.
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.
Point particles on the string in a three-dimensional AdS universe
本研究在三维AdS时空背景下探究点粒子与弦的相互作用，定义静态时空中的可加局域质量并应用于相关系统，还通过切割粘合方法构建了弦上双粒子振荡的非静态系统。
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…
It is pointed out that the observed extremely high energy cosmic rays (EHECR) above $10^{11}$ GeV and the observed baryon asymmetry of the Universe (BAU), both may have a common origin in baryon number violating decays of supermassive ``X'' particles released from cosmic topological defects (TDs) such as cosmic strings and monopoles. The X particles produced by TDs in the recent epochs produce the EHECR, while the BAU is created by X particles released from TDs mainly in the very early Universe. In this scenario the EHECR is predicted to contain baryons as well as antibaryons with a small asym…
We consider an exactly solvable model for production of fermions in the Friedman flat universe with a scale factor linearly growing with time. Exact solution expressed through the special functions admit an analytical calculation of the number density of created particles. We also discuss in general the role of the phenomenon of the cosmological particle production in the history of universe.
In this paper we suggest a formulation that would bear out the spirit of Prigogine's "Order Out of Chaos" and Wheeler's "Law Without Law". In it a typical elementary particle length, namely the pion Compton wavelength arises from the random motion of the N particles in the universe of dimension R. It is then argued in the light of recent work that this is the origin of the laws of physics and leads to a cosmology consistent with observation.
Strong dynamics constitutes one of the pillars of the standard model of particle interactions, and it accounts for the bulk of the visible matter in the universe. It is therefore a well posed question to ask if the rest of the universe can be described in terms of new highly natural four-dimensional strongly coupled theories. The goal of this brief summary is to provide, for the first time, a coherent overview of how new strong dynamics can be employed to address the relevant challenges in particle physics and cosmology from composite Higgs dynamics to dark matter and inflation.
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