Showing papers on "Scalar field published in 1997"

Towards the theory of reheating after inflation

Abstract: Reheating after inflation occurs due to particle production by the oscillating inflaton field. In this paper we briefly describe the perturbative approach to reheating, and then concentrate on effects beyond the perturbation theory. They are related to the stage of parametric resonance, which we call preheating. It may occur in an expanding universe if the initial amplitude of oscillations of the inflaton field is large enough. We investigate a simple model of a massive inflaton field $\ensuremath{\varphi}$ coupled to another scalar field $\ensuremath{\chi}$ with the interaction term ${g}^{2}{\ensuremath{\varphi}}^{2}{\ensuremath{\chi}}^{2}$. Parametric resonance in this model is very broad. It occurs in a very unusual stochastic manner, which is quite different from parametric resonance in the case when the expansion of the universe is neglected. Quantum fields interacting with the oscillating inflaton field experience a series of kicks which, because of the rapid expansion of the universe, occur with phases uncorrelated to each other. Despite the stochastic nature of the process, it leads to exponential growth of fluctuations of the field $\ensuremath{\chi}$. We call this process stochastic resonance. We develop the theory of preheating taking into account the expansion of the universe and back reaction of produced particles, including the effects of rescattering. This investigation extends our previous study of reheating after inflation. We show that the contribution of the produced particles to the effective potential $V(\ensuremath{\varphi})$ is proportional not to ${\ensuremath{\varphi}}^{2}$, as is usually the case, but to $|\ensuremath{\varphi}|$. The process of preheating can be divided into several distinct stages. In the first stage the back reaction of created particles is not important. In the second stage back reaction increases the frequency of oscillations of the inflaton field, which makes the process even more efficient than before. Then the effects related to scattering of $\ensuremath{\chi}$ particles on the oscillating inflaton field terminate the resonance. We calculate the number density of particles ${n}_{\ensuremath{\chi}}$ produced during preheating and their quantum fluctuations $〈{\ensuremath{\chi}}^{2}〉$ with all back reaction effects taken into account. This allows us to find the range of masses and coupling constants for which one can have efficient preheating. In particular, under certain conditions this process may produce particles with a mass much greater than the mass of the inflaton field.

Inhomogeneous Cosmological Models

Abstract: List of illustrations Preface Acknowledgements 1 Preliminaries 2 The Szekeres-Szafron family of solutions 3 Physics and cosmology in an inhomogeneous universe 4 The Stephani-Barnes family of solutions 5 Solutions with null radiation 6 Solutions with a 'stiff fluid'/scalar field source 7 Other solutions 8 Averaging out inhomogeneities of geometry and matter in cosmological models 9 Comments Appendices Bibliography Index

Structure Formation with a Self-Tuning Scalar Field

Abstract: A scalar field with an exponential potential has the particular property that it is attracted into a solution in which its energy scales as the dominant component (radiation or matter) of the Universe, contributing a fixed fraction of the total energy density. We study the growth of perturbations in a cold dark matter dominated $\ensuremath{\Omega}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ universe with this extra field, with an initial flat spectrum of adiabatic fluctuations. The observational constraints from structure formation are satisfied as well, or better, than in other models, with a contribution to the energy density from the scalar field ${\ensuremath{\Omega}}_{\ensuremath{\varphi}}\ensuremath{\sim}0.1$ which is small enough to be consistent with entry into the attractor prior to nucleosynthesis.

Lorentz-invariant actions for chiral p-forms

Abstract: We demonstrate how a Lorentz-covariant formulation of the chiral p-form model in D=2(p+1) containing infinitely many auxiliary fields is related to a Lorentz-covariant formulation with only one auxiliary scalar field entering a chiral p-form action in a nonpolynomial way. The latter can be regarded as a consistent Lorentz-covariant truncation of the former. We make the Hamiltonian analysis of the model based on the nonpolynomial action and show that the Dirac constraints have a simple form and are all first class. In contrast with the Siegel model the constraints are not the square of second-class constraints. The canonical Hamiltonian is quadratic and determines the energy of a single chiral p-form. In the case of D=2 chiral scalars the constraint can be improved by use of a {open_quotes}twisting{close_quotes} procedure (without the loss of the property to be first class) in such a way that the central charge of the quantum constraint algebra is zero. This points to the possible absence of an anomaly in an appropriate quantum version of the model. {copyright} {ital 1997} {ital The American Physical Society}

General rotating black holes in string theory: Greybody factors and event horizons

Abstract: We derive the wave equation for a minimally coupled scalar field in the background of a general rotating five-dimensional black hole. It is written in a form that involves two types of thermodynamic variables, defined at the inner and outer event horizon, respectively. We model the microscopic structure as an effective string theory, with the thermodynamic properties of the left- and right-moving excitations related to those of the horizons. Previously known solutions to the wave equation are generalized to the rotating case, and their regime of validity is sharpened. We calculate the greybody factors and interpret the resulting Hawking emission spectrum microscopically in several limits. We find a $U$-duality-invariant expression for the effective string length that does not assume a hierarchy between the charges. It accounts for the universal low-energy absorption cross section in the general nonextremal case.

Foliation fields and 3D cartography in geology: Principles of a method based on potential interpolation

Abstract: A modeling method that takes into account known points on a geological interface and plane orientation data such as stratification or foliation planes is described and tested. The orientations data do not necessarily belong to one of the interfaces but are assumed to sample the main anisotropy of a geological formation as in current geological situations. The problem is to determine the surfaces which pass through the known points on interfaces and which are compatible with the orientation data. The method is based on the interpolation of a scalar field defined in the space the gradient in which is orthogonal to the orientations, given that some points have the same but unknown scalar value (points of the same interface), and that scalar gradient is known on the other points (foliations). The modeled interfaces are represented as isovalues of the interpolated field. Preliminary two-dimensional tests carried-out with different covariance models demonstrate the validity of the method, which is easily transposable in three dimensions.

Motion by Mean Curvature from the Ginzburg-Landau Interface Model

Abstract: We consider the scalar field φ t with a reversible stochastic dynamics which is defined by the standard Dirichlet form relative to the Gibbs measure with formal energy . The potential V is even and strictly convex. We prove that under a suitable large scale limit the φ t -field becomes deterministic such that locally its normal velocity is proportional to its mean curvature, except for some anisotropy effects. As an essential input we prove that for every tilt there is a unique shift invariant, ergodic Gibbs measure for the -field.

Scalar wave falloff in asymptotically anti–de Sitter backgrounds

Abstract: Conformally invariant scalar waves in black hole spacetimes which are asymptotically anti--de Sitter spacetimes are investigated. We consider both the $(2+1)$-dimensional black hole and $(3+1)$-dimensional Schwarzschild--anti-de Sitter spacetime as backgrounds. Analytical and numerical methods show that the waves decay exponentially in the $(2+1)$-dimensional black hole background. However, the falloff pattern of the conformal scalar waves in the Schwarzschild--anti-de Sitter background is generally neither exponential nor an inverse power rate, although the approximate falloff of the maximal peak is weakly exponential. We discuss the implications of these results for mass inflation.

Electroweak Baryogenesis and the Expansion Rate of the Universe

Abstract: The standard requirement for the production of baryons at the electroweak phase transition, that the phase transition be first order and the sphaleron bound be satisfied, is predicated on the assumption of a radiation-dominated universe at that epoch. One simple alternative, domination by the energy in a kinetic mode of a scalar field which scales as ${1/a}^{6}$, gives a significantly weakened sphaleron bound for the preservation of a baryon asymmetry produced at a first-order phase transition, and allows the possibility that the observed baryon asymmetry be produced when the phase transition is second order or crossover. Such a phase of ``kination'' at the electroweak scale can occur in various ways as a scalar field evolves after inflation in an exponential potential.

Detectability of inflation-produced gravitational waves

Abstract: Introduction Inflation addresses most of the fundamental problems in cosmology – the origin of the flatness, large-scale smoothness, and small density inhomogeneities needed to seed all the structure seen in the Universe today. If correct, it would extend our understanding of the Universe to as early as 10 −32 sec and open a window on physics at energies of order 10 15 GeV. However, at the moment there is little evidence to confirm or to contradict inflation and no standard model of inflation. The key to testing inflation is to focus on its three basic predictions [1]: spatially flat Universe (total energy density equal to the critical energy density); almost scaleinvariant spectrum of gaussian density perturbations [2]; and almost scale-invariant spectrum of stochastic gravitational waves [3]. The first two predictions have important implications: the existence of nonbaryonic dark matter, as big-bang nucleosynthesis precludes baryons from contribution more than about 10% of the critical density [4], and the cold dark matter scenario for structure formation, based upon the idea that the nonbaryonic dark matter is slowly moving elementary particles left over from the earliest moments [5,6]. A host of cosmological observations are now beginning to sharply test the first two predictions [6]. Gravity waves are a telling test and probe of inflation: They provide a consistency check (see below); they are essential to learning about the scalar potential that drives inflation [7]; and they are a compelling signature of inflation – both a flat Universe and scale-invariant density perturbations were advocated before inflation. Detecting inflation-produced gravity waves presents a great experimental challenge [8]. In this Letter we discuss the potential of CBR anisotropy or polarization and of direct detection by the laser-interferometers to test this key prediction of inflation. Quantum Fluctuations The (Fourier) spectra of metric fluctuations excited during inflation are characterized by power laws in wavenumber k, k n for density perturbations (scalar metric fluctuations) and k nT −3 for gravity waves (tensor metric fluctuations). Scale invariance for density perturbations (n = 1) corresponds to fluctuations in the Newtonian potential that are independent of wavenumber; scale invariance for gravity waves (nT = 0) corresponds to dimensionless horizon-crossing strain amplitudes that are independent of wavenumber. The power-law indices are related to the scalar field potential, V (�), that drives inflation: n − 1 = − m 2

Casimir energies for massive scalar fields in a spherical geometry

Abstract: The Casimir energy corresponding to a massive scalar field with Dirichlet boundary conditions on a spherical surface is obtained. The field is considered, separately, inside and outside the surface. The renormalization procedure that is necessary to apply in each situation is studied in detail, in particular, the differences occurring with respect to the case when the field occupies the whole space. The final result contains several constants that experience renormalization and can be determined only experimentally. The nontrivial finite parts that appear in the massive case are found exactly, providing a precise determination of the complete, renormalized zero-point energy for the first time.

Rotating boson stars in general relativity

Abstract: We have succeeded in obtaining highly relativistic structures of stationary axisymmetric configurations consisting of massive complex scalar fields, i.e., rotating boson stars. Scalar fields are assumed to have harmonic azimuthal angular dependence, i.e., $\ensuremath{\varphi}={\ensuremath{\varphi}}_{0}(t,r,\ensuremath{\theta}){e}^{\mathrm{im}\ensuremath{\varphi}}$, where $m$ is an integer. Equilibrium configurations are characterized by values of $m$ so that the total angular momentum of the boson star becomes discrete. We have solved sequences of equilibrium states with $m=1$ and $m=2$ by changing one parameter which characterizes the model. The maximum mass for $m=1$ models is ${1.314M}_{\mathrm{Pl}}^{2}/\ensuremath{\mu}$, where ${M}_{\mathrm{Pl}}$ and $\ensuremath{\mu}$ are the Planck mass and the mass of the scalar field, respectively. It is interesting that properly defined specific angular momentum for rotating boson stars is constant in space.

Lattice study of classical inflaton decay

Abstract: We study numerically the decay of the inflaton by solving the full nonlinear equations of motion on the lattice. We confirm that parametric resonance is effective in transferring energy from the inflaton to a scalar field as long as the self-interactions of the second field are very small. However, in the very broad resonance case $(q\ensuremath{\gg}1)$ the decay rate is limited by scatterings, which significantly slows down the decay. We also find that the inflaton cannot decay via parametric resonance into a scalar field with moderate self-interactions. This means that the preheating stage may be completely absent in many natural inflationary models.

Restrictions on negative energy density in flat spacetime

Abstract: In a previous paper, a bound on the negative energy density seen by an arbitrary inertial observer was derived for the free massless, quantized scalar field in four-dimensional Minkowski spacetime. This constraint has the form of an uncertainty-principle-type limitation on the magnitude and duration of the negative energy density. That result was obtained after a somewhat complicated analysis. The goal of the current paper is to present a much simpler method for obtaining such constraints. Similar ``quantum inequality'' bounds on negative energy density are derived for the electromagnetic field, and for the massive scalar field in both two- and four-dimensional Minkowski spacetime.

Higher spin fields and the problem of the cosmological constant

Abstract: The cosmological evolution of free massless vector or tensor (but not gauge) fields minimally coupled to gravity is analyzed. It is shown that there are some unstable solutions for these fields in the de Sitter background. The back reaction of the energy-momentum tensor of such solutions to the original cosmological constant exactly cancels the latter and the expansion regime changes from the exponential to the power-law one. In contrast with the adjustment mechanism realized by a scalar field the gravitational coupling constant in this model is time independent and the resulting cosmology may resemble the realistic one.

Hamilton-Jacobi approach to non-slow-roll inflation

Abstract: I describe a general approach to characterizing cosmological inflation outside the standard slow-roll approximation, based on the Hamilton-Jacobi formulation of scalar field dynamics. The basic idea is to view the equation of state of the scalar field matter as the fundamental dynamical variable, as opposed to the field value or the expansion rate. I discuss how to formulate the equations of motion for scalar and tensor fluctuations in situations where the assumption of slow roll is not valid. I apply the general results to the simple case of inflation from an ``inverted'' polynomial potential, and to the more complicated case of hybrid inflation.

Telling tails in the presence of a cosmological constant

Abstract: We study the evolution of massless scalar waves propagating on spherically symmetric spacetimes with a nonzero cosmological constant. Considering test fields on both Schwarzschild\char21{}de Sitter and Reissner\char21{}Nordstr\"om\char21{}de Sitter backgrounds, we demonstrate the existence of exponentially decaying tails at late times. Interestingly, the $\mathcal{l}=0$ mode asymptotes to a nonzero value, contrasting the asymptotically flat situation. We also compare these results, for $\mathcal{l}=0$, with a numerical integration of the Einstein-scalar field equations, finding good agreement between the two. Finally, the significance of these results to the study of the Cauchy horizon stability in black-hole\char21{}de Sitter spacetimes is discussed.

Inflaton decay and heavy particle production with negative coupling

Abstract: We study the decay of the inflaton in a general Z{sub 2}{times}Z{sub 2} symmetric two scalar theory. Since the dynamics of the system is dominated by states with large occupation numbers which admit a semiclassical description, the decay can be studied by solving the classical equations of motion on the lattice. Of particular interest is the case when the cross coupling between the inflaton and the second scalar field is negative, which is naturally allowed in many realistic models. While the inflaton decays {ital via} parametric resonance in the positive coupling case we find that for negative coupling there is a new mechanism of particle production which we call {ital negative coupling instability}. Because of this new mechanism the variances of the fields grow significantly larger before the production is shut off by the back reaction of the created particles, which could have important consequences for symmetry restoration by nonthermal phase transitions. We also find that heavy particles are produced much more efficiently with negative coupling, which is of prime importance for GUT baryogenesis. Using a simple toy model for baryogenesis and the results of our lattice simulations we show that for natural values of the cross coupling enough 10{supmore » 14}GeV bosons are created to produce a baryon to entropy ratio consistent with observation. This is to be contrasted with the situation for positive coupling, where the value of the cross coupling required to produce such massive particles is technically unnatural. In addition to our numerical results we obtain analytical estimates for the maximum variances of the fields in an expanding universe for all cases of interest: massive and massless inflaton, positive and negative cross coupling, with and without significant self-interactions for the second field. {copyright} {ital 1997} {ital The American Physical Society}« less

Long-time asymptotics for a classical particle interacting with a scalar wave field

Abstract: We consider the Harniltonian system consisting of scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subject to a confining external potential. The stationary solutions of the system are a Coulomb type wave field centered at those particle positions for which the external force vanishes. We prove that solutions of finite energy converge, in suitable local energy seminorms, to the set of stationary solutions in the long time limit t f oo. The rate of relaxation to a stable stationary solution is determined by spatial decay of initial data. 'Supported partly by French-Russian A.M.Liapunov Center of Moscow State University, by research grants of RFBR (9601-00527) and of Volkswagen-Stiftung.

Quantum scalar field on three-dimensional (BTZ) black hole instanton: Heat kernel, effective action and thermodynamics

Abstract: We consider the behavior of a quantum scalar field on three-dimensional Euclidean backgrounds: anti\char21{}de Sitter space, the regular BTZ black hole instanton, and the BTZ instanton with a conical singularity at the horizon. The corresponding heat kernel and effective action are calculated explicitly for both rotating and nonrotating holes. The quantum entropy of the BTZ black hole is calculated by differentiating the effective action with respect to the angular deficit at the conical singularity. The renormalization of the UV-divergent terms in the action and entropy is considered. The structure of the UV-finite term in the quantum entropy is of particular interest. Being negligible for large outer horizon area ${A}_{+},$ it behaves logarithmically for small ${A}_{+}.$ Such behavior might be important at late stages of black hole evaporation.

Quantum inequalities in two-dimensional Minkowski spacetime

Abstract: We generalize some results of Ford and Roman constraining the possible behaviors of the renormalized expected stress-energy tensor of a free massless scalar field in two-dimensional Minkowski spacetime. Ford and Roman showed that the energy density measured by an inertial observer, when averaged with respect to the observers proper time by integrating against some weighting function, is bounded below by a negative lower bound proportional to the reciprocal of the square of the averaging time scale. However, the proof required a particular choice for the weighting function. We extend the Ford-Roman result in two ways. (i) We calculate the optimum (maximum possible) lower bound and characterize the state which achieves this lower bound; the optimum lower bound differs by a factor of six from the bound derived by Ford and Roman for their choice of smearing function. (ii) We calculate the lower bound for arbitrary, smooth positive weighting functions. We also derive similar lower bounds on the spatial average of energy density at a fixed moment of time.

Janis-Newman-Winicour and Wyman solutions are the same

Abstract: We show that the well-known most general static and spherically symmetric exact solution to the Einstein-massless scalar equations given by Wyman is the same as one found by Janis, Newman and Winicour several years ago. We obtain the energy associated with this space–time and find that the total energy for the case of the purely scalar field is zero.

Quantum field theory on spacetimes with a compactly generated Cauchy horizon

Abstract: We prove two theorems which concern difficulties in the formulation of the quantum theory of a linear scalar field on a spacetime, \(\), with a compactly generated Cauchy horizon. These theorems demonstrate the breakdown of the theory at certain base points of the Cauchy horizon, which are defined as ‘past terminal accumulation points’ of the horizon generators. Thus, the theorems may be interpreted as giving support to Hawking's ‘Chronology Protection Conjecture’, according to which the laws of physics prevent one from manufacturing a ’time machine‘. Specifically, we prove:

Self-Consistent Wormhole Solutions of Semiclassical Gravity

Abstract: We present the first results of a self-consistent solution of the semiclassical Einstein field equations corresponding to a Lorentzian wormhole coupled to a quantum scalar field. The specific solution presented here represents a wormhole connecting two asymptotically spatially flat regions. In general, the diameter of the wormhole throat, in units of the Planck length, can be arbitrarily large, depending on the values of the scalar coupling $\ensuremath{\xi}$ and the boundary values for the shape and redshift functions. In all cases we have considered, there is a fine structure in the form of Planck-scale oscillations or ripples superimposed on the solutions.

Understanding critical collapse of a scalar field

Abstract: I construct a spherically symmetric solution for a massless real scalar field minimally coupled to general relativity which is discretely self-similar (DSS) and regular. This solution coincides with the intermediate attractor found by Choptuik in critical gravitational collapse. The echoing period is ?=3.4453±0.0005. The solution is continued to the future self-similarity horizon, which is also the future light cone of a naked singularity. The scalar field and metric are C1 but not C2 at this Cauchy horizon. The curvature is finite nevertheless, and the horizon carries regular null data. These are very nearly flat. The solution has exactly one growing perturbation mode, thus confirming the standard explanation for universality. The growth of this mode corresponds to a critical exponent of ?=0.374±0.001, in agreement with the best experimental value. I predict that in critical collapse dominated by a DSS critical solution, the scaling of the black hole mass shows a periodic wiggle, which like ? is universal. My results carry over to the free complex scalar field. Connections with previous investigations of self-similar scalar field solutions are discussed, as well as an interpretation of ? and ? as anomalous dimensions.

Resonant decay of cosmological bose condensates

Abstract: We present results of fully nonlinear calculations of decay of the inflaton interacting with another scalar field X . Combining numerical results for a cosmologically interesting range of the resonance parameter, q{le}10{sup 6} , with analytical estimates, we extrapolate them to larger q . We find that scattering of X fluctuations off the Bose condensate is a very efficient mechanism limiting growth of X fluctuations. For a single-component X , the resulting variance, at large q , is much smaller than that obtained in the Hartree approximation. {copyright} {ital 1997} {ital The American Physical Society}

Topological Black Holes -- Outside Looking In

Abstract: I describe the general mathematical construction and physical picture of topological black holes, which are black holes whose event horizons are surfaces of non-trivial topology. The construction is carried out in an arbitrary number of dimensions, and includes all known special cases which have appeared before in the literature. I describe the basic features of massive charged topological black holes in $(3+1)$ dimensions, from both an exterior and interior point of view. To investigate their interiors, it is necessary to understand the radiative falloff behaviour of a given massless field at late times in the background of a topological black hole. I describe the results of a numerical investigation of such behaviour for a conformally coupled scalar field. Significant differences emerge between spherical and higher genus topologies.

Homogeneous scalar field cosmologies with an exponential potential

Abstract: We shall study spatially homogeneous cosmological models containing a self-interacting scalar field with an exponential potential of the form V(φ)=Λekφ. The asymptotic properties of these models are discussed. In particular, their possible isotropization and inflation are investigated for all values of the parameter k. A particular class of models is analyzed qualitatively using the theory of dynamical systems, illustrating the general asymptotic behavior.