arXiv subjects
Publications and source records attributed to Paul R. Anderson.
Transverse excitations in analogue black holes induce a mass like term in the longitudinal mode equation. With a simple toy model we show that correlation functions display a rather rich structure characterized by groups of parallel peaks. For the most part the structure is completely different from that found in the massless case.
The decay rate of the Bunch-Davies state of a massive scalar field in the expanding flat spatial sections of de Sitter space is determined by an analysis of the particle pair creation process in real time. The Feynman definition of particle and antiparticle Fourier mode solutions of the scalar wave equation, and their adiabatic phase analytically continued to the complexified time domain, show conclusively that the Bunch-Davies state is not the vacuum state at late times. The closely analogous creation of charged particle pairs in a uniform electric field is reviewed and Schwinger's result for the vacuum decay rate is recovered by the real time analysis. The vacuum decay rate in each case is also calculated by switching the background field on adiabatically, allowing it to act for a very long time, and then adiabatically switching it off again. In both the uniform electric field and de Sitter cases the particles created while the field is switched on are verified to be real, in the sense that they persist in the final asymptotic flat zero-field region. In the de Sitter case there is an interesting residual dependence of the rate on how the de Sitter phase is ended, indicating a greater sensitivity to spatial boundary conditions. The electric current of the created particles in the E-field case and their energy density and pressure in the de Sitter case are also computed, and the magnitude of their backreaction effects on the background field estimated. Possible consequences of the Hubble scale instability of the de Sitter vacuum for cosmology, vacuum dark energy, and the cosmological `constant' problem are discussed.
The effects which quantum fields and an $α_0 R^2$ term in the gravitational Lagrangian have on future singularities are investigated. While all values of $α_0$ are considered, an emphasis is placed on those values which are compatible with the universe having undergone Starobinsky inflation in the past. These are also values which lead to stable solutions to the semiclassical backreaction equations in the present universe. The dark energy is modeled as a perfect fluid, and the focus is on type I-IV singularities and little rips which result when the classical Einstein equations are solved with various types of dark energy as a source. First, evidence is provided that the energy densities of massive conformally coupled scalar fields approach that of the conformally invariant scalar field as a type III singularity is approached. Then, solutions to the semiclassical backreaction equations are investigated when conformally invariant fields and the $ α_0 R^2$ term in the gravitational Lagrangian are present. General proofs regarding the behaviors of the solutions are given. The proofs are illustrated by analytic and numerical calculations in specific cases.
An exact correspondence between a black hole and an accelerating mirror is demonstrated. It is shown that for a massless minimally coupled scalar field the same Bogolubov coefficients connecting the "in" and "out" states occur for a (1+1)D flat spacetime with a particular perfectly reflecting accelerating boundary trajectory and a (1+1)D curved spacetime in which a null shell collapses to form a black hole. Generalization of the latter to the (3+1)D case is discussed. The spectral dynamics is computed in both (1+1)-dimensional spacetimes along with the energy flux in the spacetime with a mirror. It is shown that the approach to equilibrium is monotonic, asymmetric in terms of the rate, and there is a specific time which characterizes the system when it is the most out-of-equilibrium.
A complete set of exact analytic solutions to the mode equation is found in the region exterior to the acoustic horizon for a class of 1D Bose-Einstein condensate (BEC) acoustic black holes. From these, analytic expressions for the scattering coefficients and gray-body factor are obtained. The results are used to verify previous predictions regarding the behaviors of the scattering coefficients and gray-body factor in the low frequency limit.
There is an exact correspondence between the simplest solution to Einstein's equations describing the formation of a black hole and a particular moving mirror trajectory. In both cases the Bogolubov coefficients in 1+1 dimensions are identical and can be computed analytically. Particle creation is investigated by using wave packets. The entire particle creation history is computed, incorporating the early-time non-thermal emission due to the formation of the black hole (or the early-time acceleration of the moving mirror) and the evolution to a Planckian spectrum.
An exact correspondence is shown between a new moving mirror trajectory in (1+1)D and a spacetime in (1+1)D in which a black hole forms from the collapse of a null shell. It is shown that the Bogolubov coefficients between the "in" and "out" states are identical and the exact Bogolubov coefficients are displayed. Generalization to the (3+1)D black hole case is discussed.
The validity of the semiclassical approximation is investigated during the preheating phase in models of chaotic inflation using a modification of a criterion previously proposed for semiclassical gravity. If the modified criterion is violated then fluctuations of the two-point function for the quantum fields are large and the semiclassical approximation is not valid. Evidence is provided that the semiclassical approximation breaks down during the early stages of preheating, well before either scattering effects or backreaction effects are important.
It is shown that the gray-body factor for a one-dimensional elongated Bose-Einstein condensate (BEC) acoustic black hole with one horizon does not vanish in the low-frequency ($ω\to 0$) limit. This implies that the analog Hawking radiation is dominated by the emission of an infinite number ($\frac{1}ω$) of soft phonons in contrast with the case of a Schwarzschild black hole where the gray-body factor vanishes as $ω\to 0$ and the spectrum is not dominated by low-energy particles. The infrared behaviors of certain correlation functions are also discussed.
Formal solutions to the mode equations for both spherically symmetric black holes and Bose-Einstein condensate acoustic black holes are obtained by writing the spatial part of the mode equation as a linear Volterra integral equation of the second kind. The solutions work for a massless minimally coupled scalar field in the s-wave or zero angular momentum sector for a spherically symmetric black hole and in the longitudinal sector of a 1D Bose-Einstein condensate acoustic black hole. These solutions are used to obtain in a rigorous way analytic expressions for the scattering coefficients and gray-body factors in the zero frequency limit. They are also used to study the infrared behaviors of the symmetric two-point function and two functions derived from it: the point-split stress-energy tensor for the massless minimally coupled scalar field in Schwarzschild-de Sitter spacetime and the density-density correlation function for a Bose-Einstein condensate acoustic black hole.
The Euclidean or Bunch-Davies O(4,1) invariant 'vacuum' state of quantum fields in global de Sitter space is shown to be unstable to small perturbations, even for a massive free field with no self-interactions. There are perturbations of this state with arbitrarily small energy density at early times that is exponentially blueshifted in the contracting phase of 'eternal' de Sitter space, and becomes large enough to disturb the classical geometry through the semiclassical Einstein eqs. at later times. In the closely analogous case of a constant, uniform electric field, a time symmetric state equivalent to the de Sitter invariant one is constructed, which is also not a stable vacuum state under perturbations. The role of a quantum anomaly in the growth of perturbations and symmetry breaking is emphasized in both cases. In de Sitter space, the same results are obtained either directly from the renormalized stress tensor of a massive scalar field, or for massless conformal fields of any spin, more directly from the effective action and stress tensor associated with the conformal trace anomaly. The anomaly stress tensor shows that states invariant under the O(4) subgroup of the de Sitter group are also unstable to perturbations of lower spatial symmetry, implying that both the O(4,1) isometry group and its O(4) subgroup are broken by quantum fluctuations. Consequences of this result for cosmology and the problem of vacuum energy are discussed.
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 the particle creation process, the mean particle number, and dynamical quantities such as the energy-momentum tensor and current of the created particles in both the de Sitter and electric field backgrounds in real time, establishing the connection to kinetic theory. We compute the energy-momentum tensor for adiabatic vacuum states in de Sitter space initialized at early times in global S^3 sections, and show that particle creation in the contracting phase results in exponentially large energy densities at later times, necessitating an inclusion of their backreaction effects, and leading to large deviation of the spacetime from global de Sitter space before the expanding phase can begin.
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 that are in the out vacuum state. It is shown for most of the trajectories studied that good time resolution of the particle production process can be obtained.
The density density correlation function is computed for the Bogoliubov pseudoparticles created in a Bose-Einstein condensate undergoing a black hole flow. On the basis of the gravitational analogy, the method used relies only on quantum field theory in curved spacetime techniques. A comparison with the results obtained by ab initio full condensed matter calculations is given, confirming the validity of the approximation used provided the profile of the flow varies smoothly on scales compared to the condensate healing length.
We compute exact expressions of the noise kernel, defined as the expectation value of the symmetrized connected stress energy bitensor, for conformally-invariant scalar fields with respect to the conformal vacuum, valid for an arbitrary separation (timelike, spacelike and null) of points in a class of conformally-flat spacetimes. We derive explicit expressions for the noise kernel evaluated in the static de Sitter coordinates with respect to the Gibbons-Hawking vacuum and analyze the behavior of the noise kernel in the region near the cosmological horizon. We develop a quasi-local expansion near the cosmological horizon and compare it with the exact results. This gives insight into the likely range of validity of the quasi-local approximation expressions for the noise kernel for the conformally invariant scalar field in Schwarzschild spacetime which are given in PHYSICAL REVIEW D{\bf 85}, 044037 (2012).
The semiclassical approximation has frequently been used to describe the initial stage of particle production, often called preheating, which occurs after the inflationary epoch in chaotic models of inflation. During this phase backreaction effects from the produced particles on the inflaton field are significant, and one might be concerned about the validity of the semiclassical approximation, even though large backreaction effects are allowed if the inflaton field is coupled to a large number of quantum fields. A criterion is presented for the validity of the semiclassical approximation in this case and the question of whether this criterion is satisfied during preheating is addressed.
A method is given to compute an approximation to the noise kernel, defined as the symmetrized connected 2-point function of the stress tensor, for the conformally invariant scalar field in any spacetime conformal to an ultra-static spacetime for the case in which the field is in a thermal state at an arbitrary temperature. The most useful applications of the method are flat space where the approximation is exact and Schwarzschild spacetime where the approximation is better than it is in most other spacetimes. The two points are assumed to be separated in a timelike or spacelike direction. The method involves the use of a Gaussian approximation which is of the same type as that used by Page to compute an approximate form of the stress tensor for this field in Schwarzschild spacetime. All components of the noise kernel have been computed exactly for hot flat space and one component is explicitly displayed. Several components have also been computed for Schwarzschild spacetime and again one component is explicitly displayed.
Effects of quantized free scalar fields in cosmological spacetimes with Big Rip singularities are investigated. The energy densities for these fields are computed at late times when the expansion is very rapid. For the massless minimally coupled field it is shown that an attractor state exists in the sense that, for a large class of states, the energy density of the field asymptotically approaches the energy density it would have if it was in the attractor state. Results of numerical computations of the energy density for the massless minimally coupled field and for massive fields with minimal and conformal coupling to the scalar curvature are presented. For the massive fields the energy density is seen to always asymptotically approach that of the corresponding massless field. The question of whether the energy densities of quantized fields can be large enough for backreaction effects to remove the Big Rip singularity is addressed.