We calculate the quantum radiation power of black holes which are asymptotic to the Einstein-de Sitter universe at spatial and null infinities. We consider two limiting mass accretion scenarios, no accretion and significant accretion. We find that the radiation power strongly depends on not only the asymptotic condition but also the mass accretion scenario. For the no accretion case, we consider the Einstein-Straus solution, where a black hole of constant mass resides in the dust Friedmann universe. We find negative cosmological correction besides the expected redshift factor. This is given in terms of the cubic root of ratio in size of the black hole to the cosmological horizon, so that it is currently of order $10^{-5} (M/10^{6}M_{\odot})^{1/3} (t/14 {Gyr})^{-1/3}$ but could have been significant at the formation epoch of primordial black holes. Due to the cosmological effects, this black hole has not settled down to an equilibrium state. This cosmological correction may be interpreted in an analogy with the radiation from a moving mirror in a flat spacetime. For the significant accretion case, we consider the Sultana-Dyer solution, where a black hole tends to increase its mass in proportion to the cosmological scale factor. In this model, we find that the radiation power is apparently the same as the Hawking radiation from the Schwarzschild black hole of which mass is that of the growing mass at each moment. Hence, the energy loss rate decreases and tends to vanish as time proceeds. Consequently, the energy loss due to evaporation is insignificant compared to huge mass accretion onto the black hole. Based on this model, we propose a definition of quasi-equilibrium temperature for general conformal stationary black holes.
In supergravity models, the evaporation of light Primordial Black Holes (PBHs) should be a source of gravitinos. By considering this process, new stringent limits are derived on the abundance of small black holes with initial masses less than 10^9 g. In minimal supergravity, the subsequent decay of evaporated gravitinos into cascades of non-equilibrium particles leads to the formation of elements whose abundance is constrained by observations. In gauge mediated supersymmetry breaking models, their density is required not to overclose the Universe. As a result, cosmological models with substant…
In the model of Expansive Nondecelerative Universe, black hole cannot totally evaporate via quantum evaporation process proposed by Hawking. In a limiting case, an equilibrium of gravitation creation and black hole evaporation can be reached keeping the surface of its horizon constant. This conclusion is in accordance with the second law of thermodynamics.
The paper summarizes the background of Expensive Nondecelerative Universe model and its main consequences for gravitation. Applying the Vaidya metrics, the model allows for the localization and determination of the density and quantity of gravitational energy created by a body with the mass m in the distance r. The consequences are manifested both in a macrosystem (Hawking's phenomenon of black holes evaporation) and microworld phenomenon (far-infrared spectral properties)
We study a thermofield double type entangled state on two disjoint universes $A$ and $B$, where one of the universes is asymptotically flat containing a black hole. As we increase the entanglement temperature, this black hole receives back-reaction from the stress energy tensor of the state. This results in lengthening of the wormhole region in the black hole interior, and decreasing of its horizon area, both of which are key features of an evaporating black hole. We then compute the entanglement entropy on the universe $A$ through the island formula, and argue that it naturally follows the Pa…
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 general plane wave solutions of the Proca field in conformal charts of the de Sitter expanding universe are derived for arbitrary polarizations showing how the frequencies can be separated in rest frames, defining thus the rest frame vacuum of this field.
We study cosmological perturbations produced by the most general two-derivative actions involving two scalar fields, coupled to Einstein gravity, with an arbitrary field space metric, that admit scaling solutions. For contracting universes, we show that scale-invariant adiabatic perturbations can be produced continuously as modes leave the horizon for any equation of state parameter $w \ge 0$. The corresponding background solutions are unstable, which we argue is a universal feature of contracting models that yield scale-invariant spectra. For expanding universes, we find that nearly scale-inv…
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 present the Green's functions that are the solutions of the massive Klein-Gordon equation for a scalar field with non-minimal coupling to gravitation for several static and expanding cosmological models. An important feature of such functions is that they can be used to study the appearence of a Casimir energy in models of the universe with compact spatial sections.
We present a semi-classical model for the formation and evaporation of a four dimensional black hole. We solve the equations numerically and obtain solutions describing the entire the space-time geometry from the collapse to the end of the evaporation. The solutions satisfy the evaporation law: $\dot M \propto -M^{-2}$ which confirms dynamically that black holes do evaporate thermally. We find that the evaporation process is in fact the shrinking of a throat that connects a macroscopic interior ``universe" to the asymptotically flat exterior. It ends either by pinching off the throat leaving a…
We construct exact solutions to Einstein equations which represent relativistic disks immersed into an expanding FRW Universe. It is shown that the expansion influences dynamical characteristics of the disks such as rotational curves, surface mass density, etc. The effects of the expansion is exemplified with non-static generalizations of Kuzmin-Curzon and generalized Schwarzschild disks.
Primordial black holes with a narrow mass range are regarded as a nonrelativistic fluid component with an equation of state for dust. The impact of the black hole evaporation on the dynamics of the early universe is studied by resorting to a two-fluid model. We find periods of intense radiation reheating in the initial and final stages of the evaporation.
We show that a relativistic gas may be at ``global'' equilibrium in the expanding universe for any equation of state $0 < p \leq ρ/3$, provided that the gas particles move under the influence of a self-interacting, effective one-particle force in between elastic binary collisions. In the force-free limit we recover the equilibrium conditions for ultrarelativistic matter which imply the existence of a conformal timelike Killing vector.
Astrophysical sources of high frequency gravitational radiation are considered in association with a new interest to very sensitive HFGW receivers required for the laboratory GW Hertz experiment. A special attention is paid to the phenomenon of primordial black holes evaporation. They act like black body to all kinds of radiation, including gravitons, and, therefore, emit an equilibrium spectrum of gravitons during its evaporation. Limit on the density of high frequency gravitons in the Universe is obtained, and possibilities of their detection are briefly discussed.
Mach Principle presents the absolute universe. For example, when Einstein stood on the ground and relaxed, his arms fell down naturally. However, if he rotated his body then his arms were lifted up as the rotation was faster and faster. Mach principle is that the matter of the whole universe can affect local dynamic systems. That is, the matter of the whole universe sets up the local absolute reference frames. However, Einstein's general theory of relativity is against the absolute reference frames of Mach Principle.
We studied the superradiance effect of a charge black hole immersed in an expanding Universe. We considered a test massive charged scalar field scattered off the horizon of the charge McVittie black hole. We carried out a detailed analysis of the electric energy extracted from the horizon of McVittie black hole in two different epochs of the expansion of the Universe, the dust dominated and radiation dominated epochs. We found that we have the superradiance effect in both epochs of the expansion of the Universe. Our study also provides evidence that we have extraction of energy from the horizo…
The quantum stress-energy tensor of a massless scalar field propagating in the two-dimensional Vaidya-de Sitter metric, which describes a classical model spacetime for a dynamical evaporating black hole in an inflationary universe, is analyzed. We present a possible way to obtain the Hawking radiation terms for the model with arbitrary functions of mass. It is used to see how the expansion of universe will affect the dynamical process of black hole evaporation. The results show that the cosmological inflation has an inclination to depress the black hole evaporation. However, if the cosmologica…
We present evidence that recent numerical results from the reduced classical equations of the Lorentzian IIB matrix model can be interpreted as corresponding to the emergence of an expanding universe. In addition, we propose an effective metric to describe the emerging (3+1)-dimensional spacetime. This metric gives, at all times, finite values for the Ricci and Kretschmann curvature scalars. With these results, we are able to give a heuristic discussion of the origin of the Universe in the context of the IIB matrix model.
We study the dynamics of a supersonically expanding ring-shaped Bose-Einstein condensate both experimentally and theoretically. The expansion redshifts long-wavelength excitations, as in an expanding universe. After expansion, energy in the radial mode leads to the production of bulk topological excitations -- solitons and vortices -- driving the production of a large number of azimuthal phonons and, at late times, causing stochastic persistent currents. These complex nonlinear dynamics, fueled by the energy stored coherently in one mode, are reminiscent of a type of "preheating" that may have…
We show that generic anisotropic universes arbitrarily close to the open Friedmann universe allow information processing to continue into the infinite future if there is no cosmological constant or stable gravitationally repulsive stress, and the spatial topology is non-compact. An infinite amount of information can be processed by ``civilisations'' who harness the temperature gradients created by gravitational tidal energy. These gradients are driven by the gravitational waves that sustain the expansion shear and three-curvature anisotropy.
We investigate the possibility that gauge fluctuations are amplified in an expanding universe by parametric resonance, during the oscillatory regime of a scalar field to which they are coupled. We investigate the couplings of gauge fields to a charged scalar field and to an axion. For both couplings, gauge field fluctuations undergo exponential instabilities. We discuss how the presence of other charges or currents may counteract the resonance, but we argue that in some cases the resonance will persist and that hence this mechanism could have some relevance for the problem of large scale primo…
Using a collapsing matter model at the center of an expanding universe as described by Weinberg we assume a special type of generated pressure. This pressure transmits into the surrounding expanding universe. Under certain restriction the ensuing hubble parameter is positive. The deacceleration parameter fluctuates with time, indicating that the universe accelerates for certain time and decelerates for other time intervals.
We present the Heisenberg-picture approach to the quantum evolution of the scalar fields in an expanding FRW universe which incorporates relatively simply the initial quantum conditions such as the vacuum state, the thermal equilibrium state, and the coherent state. We calculate the Wightman function, two-point function, and correlation function of a massive scalar field. We find the quantum evolution of fluctuations of a self-interacting field perturbatively and discuss the renormalization of field equations.
We discuss Einstein-Klein-Gordon system in an environment of an infinite number of scalar fields leading to an external thermal noise. In the lowest order of metric and field perturbations the quadratic fluctuations consist of a sum of quantum and thermal fluctuations. We show that these fluctuations depend on the form of the interaction of the inflaton with the environment.
The spacetime structure of the spatially uniformly expanding universe is described in terms of a kind of global space and global time instead of the space and time we usually recognize. The global space at some instant is a space in which the global time is equal and the global time is equal to the proper time of any point moving together with the expansion of the universe which has elapsed since the big bang. The universe descibed in terms of the global space and time thus defined is open spatially and the Einstein's equations give a solution that the space expands eternally regardless of the…
The complete model of production of baryons in expanding primordial symmetrical hot Universe is constructed in terms of general relativistic kinetic theory
An introduction to the physics and mathematics of the expanding universe, using no more than high-school level / undergraduate mathematics. Covered are the basics of scale factor expansion, the dynamics of the expanding universe, various distance concepts and the generalized redshift-luminosity relation, among other topics.
We have studied the time dependence of w for an expanding universe in the generalised B-D theory and have obtained its explicit dependence on the nature of matter contained in the universe,in different era.Lastly we discuss how the observed accelerated expansion of the present universe can be accomodated in the formalism.
Solutions analogous to the Weber-Wheeler cylindrical pulse waves are found for the case of cylindrical gravitational waves in an expanding universe. These pulse solutions mimic the asymptotic properties of waves from an isolated source in three dimensions and can be used to test the far-field behavior of numerical simulation techniques.
One of the most intriguing problem of modern physics is the question of the endpoint of black hole evaporation. Based on Einstein-dilaton-Gauss-Bonnet four dimensional string gravity model we show that black holes do not disappear and that the end of the evaporation process leaves some relic. The possibility of experimental detection of the remnant black holes is investigated. If they really exist, such objects could be a considerable part of the non baryonic dark matter in our Universe.
Black holes are expected to evaporate through the process of Hawking radiation. This process is expected to cause the uncertainty in a black hole's position to grow to $\sim M^2/M_{Pl}^3$ over the course of it's lifetime, even as its momentum spreads only by $\sim M_{Pl}$. For the black holes that have been observed, which have $M\geq M_\odot$, this greatly exceeds the Hubble volume. However, the decay of black holes and their quantum spreading, are delayed in the Universe while the influx of energy into the black holes exceeds their Hawking luminosity. We show that for these $M\geq M_\odot$ b…
In the model where the Universe is considered as a thin shell expanding in 5-dimensional hyper-space there is a possibility to have just one scale for a particle theory corresponding to the Universe thickness. From a realistic model the relation of this parameter to the Universe size was found.
An exact solution representing black holes in an expanding universe is found. The black holes are maximally charged and the universe is expanding with arbitrary equation of state. It is an exact solution of the Einstein-scalar-Maxwell system, in which we have two Maxwell-type U(1) fields coupled to the scalar field. The potential of the scalar field is an exponential. We find a regular horizon, which depends on one parameter (the ratio of the energy density of U(1) fields to that of the scalar field). The horizon is static because of the balance on the horizon between gravitational attractive …
We show that the use of suitable theorems for black hole formation in Friedmann expanding universes leads to a modification of the Bekenstein-Hawking entropy. By adopting an argument similar to the original Bekenstein one, we write down the expression for the Bekenstein-Hawking entropy suitable for non-static isotropic expanding universes together with the equation of state of a black hole. This equation can be put in a form similar to the one of an ideal gas but with a factor depending on the Hubble radius. Moreover, we give some argument on a possible relation between our entropy expression …
Using squeezed vacuum state formalism of quantum optics, an approximate solution to the semiclassical Einstein equation is obtained in Bianchi type-I universe. The phenomena of nonclassical particle creation is also examined in the anisotropic background cosmology.
In terms of proposed by authors general-relativistic kinetic model of baryon production in expanding primordially symmetrical hot Universe calculates distribution function of extra-massive bosons and concerned with it variables.
Wormhole spacetimes in an expanding universe: Energy conditions and future singularities
Central China Normal University（华中师范大学）；High Energy Accelerator Research Organization (KEK)（高能加速器研究机构）；Kobayashi-Maskawa Institute for the Origin of Particles and the Universe（小林益川粒子宇宙起源研究所）；ICREA（加泰罗尼亚高级研究院）；Institute of Space Sciences (ICE, CSIC)（空间科学研究所）
The mathematical concept of the Newtonian limit of Einstein's field equations in the expanding Friedmann universe is formulated. The geodesic equations of motion of planets and light are derived and compared.
It is pointed out that very recent results based on supernovae observations that the universe will accelerate and expand for ever with ever decreasing density have been predicted in a recent cosmological model which also deduces hitherto purely empirical features like the mysterious relation between the pion mass and the Hubble Constant.
We investigate photon emission from a moving particle in an expanding universe. This process is analogous to the radiation from an accelerated charge in the classical electromagnetic theory. Using the framework of quantum field theory in curved spacetime, we demonstrate that the Wentzel-Kramers-Brillouin (WKB) approximation leads to the Larmor formula for the rate of the radiation energy from a moving charge in an expanding universe. Using exactly solvable models in a radiation-dominated universe and in a Milne universe, we examine the validity of the WKB formula. It is shown that the quantum …
We consider a model of an expanding Universe in string theory that yields `environmental' CPT violation for fermions, in the sense of different dispersion relations for fermions and antifermions. These are induced by a cosmological background with constant torsion provided by the Kalb-Ramond antisymmetric tensor field (axion) of the string gravitational multiplet. This effect induces different densities of neutrinos and antineutrinos while in chemical equilibrium, offering new scenarios for leptogenesis and baryogenesis even in the absence of CP violation.
We extend the Kelvin-Helmholtz instability to an expanding background. We study the evolution of a non-viscous irrotational fluid and find that for wavelengths much smaller than the Hubble scale small perturbations of the fluid are unstable for wavenumbers larger than a critical value. We then apply this result in the early universe, treating cold dark matter as a classical fluid with vanishing background pressure.
An analytic means of studying the resonant decay of the inflaton field is developed for the case of background expansion, $H \neq 0$. It is shown that the parametric resonance in the inflaton's decay need not disappear when the expansion of the universe is taken into account, although the total number of particles produced is fewer than in the $H \simeq 0$ case.
The Thompson cross section for scattering of electromagnetic waves by a free electron in an expanding universe is derived here. The equations of motion of the electron are obtained using the Einstein-Infeld-Hoffmann (EIH) surface integral method. These integrals are evaluated approximately by perturbing off an Einstein-deSitter cosmological field. It is found that the Thompson cross section varies with time as the inverse square of the cosmic scale factor R(t).
We study the scalar curvature of spacelike hypersurfaces in the family of cosmological models known as generalized Robertson-Walker spacetimes, and give several rigidity results under appropriate mathematical and physical assumptions. On the other hand, we show that this family of spacetimes provides suitable models obeying the null convergence condition to explain accelerated expanding universes.
The geometric transitions from the evolution in the complex plane of time provide channels for particle production for a quantum field in expanding universes. The production rate for one pair is obtained by squaring and summing the scattering matrix between the in-vacuum and the transported one over all possible independent closed paths of winding number 1.
We describe a C++ program that we have written and made available for calculating the evolution of interacting scalar fields in an expanding universe. The program is particularly useful for the study of reheating and thermalization after inflation. The program and its full documentation are available on the Web at http://physics.stanford.edu/gfelder/latticeeasy/ . In this paper we provide a brief overview of what the program does and what it is useful for.
New boundary conditions are imposed on the familiar cylindrical gravitational wave vacuum spacetimes. The new spacetime family represents cylindrical waves in a flat expanding (Kasner) universe. Space sections are flat and nonconical where the waves have not reached and wave amplitudes fall off more rapidly than they do in Einstein-Rosen solutions, permitting a more regular null inifinity.
We use higher derivative classical gravity to study the nonlinear coupling between the cosmological expansion of the universe and metric oscillations of Planck frequency and very small amplitude. We derive field equations at high orders in the derivative expansion and find that the nature of the new dynamics is extremely restricted. For the equation of state parameter $w>0$ the relative importance of the oscillations grows logarithmically. Their effect on the cosmological expansion resembles that of dark energy.
In this review we focus our attention on scalar-tensor gravity models and their empirical verification in terms of black hole and wormhole physics. We focus on a black hole, embedded in an expanding universe, describing both cosmological and astrophysical scales. We show that in scalar-tensor gravity it is quite common that the local geometry is isolated from the cosmological expansion, so that it does not backreact on the black hole metric. We try to extract common features of scalar-tensor black holes in an expanding universe and point out the gaps that must be filled.
The effect of the expanding universe on planetary motion is considered to first order in the Hubble constant H. Orbital elements are shown to be unaffected, but there is a small change in the connection between planetary proper time and coordinate time. This can produce an apparent anomalous acceleration in velocities inferred from echo-ranging, but the effect is too small by many orders of magnitude to account for the Pioneer 10/11 anomaly.
Parametric resonance has been discussed as a mechanism for copious particle production following inflation. Here we present a simple and intuitive calculational method for estimating the efficiency of parametric amplification as a function of parameters. This is important for determining whether resonant amplification plays an important role in the reheating process. We find that significant amplification occurs only for a limited range of couplings and interactions.
We discuss the diffusion equation resulting from a strong dissipation limit of the random wave equation arising in the models of warm inflation. We show that the long wave power spectrum of scalar perturbations in the model of an exponential expansion coincides with the spectrum of quantum fluctuations on this space time.
In this thesis, we have reviewed how the expansion of the Universe amplifies the quantum vacuum fluctuations, and how the relic GWs spectrum is related with the scale factor. We have evaluated the spectrum in different scenarios: a model of expanding universe with an era dominated by mini black holes and radiation right after the inflation and a model with an era of accelerated expansion right after the radiation era. Next, we have applied the generalized second law of thermodynamics to the latter model. Finally, we have extended the GSL study to a single stage universe model dominated by dark…
The primordial Universe might be highly inhomogeneous. We perform the 3+1D Numerical Relativity simulation for the evolution of scalar field in an initial inhomogeneous expanding Universe, and investigate how it populates the landscape with both de Sitter (dS) and AdS vacua. The simulation results show that eventually either the field in different region separates into different vacua, so that the expanding dS or AdS bubbles (the bubble wall is expanding but the spacetime inside AdS bubbles is contracting) come into being with clear bounderies, or overall region is dS expanding with a few smal…
