arXiv subjects

Lev Kofman

Publications and source records attributed to Lev Kofman.

70 records · Page 4Linked to original sources

arXiv1998

Aspects of Preheating after Inflation

In inflationary cosmology, the particles constituting the Universe are created after inflation in the process of reheating due to the interaction with the oscillating inflaton field. We briefly review the basics of the slow reheating, and the stage of fast preheating, when the particles are created explosively in the regime of parametric resonance. The non-perturbative, out-of-equilibrium character of the parametric resonance changes many features of reheating. For these proceedings, we will highlight a few aspects of preheating: the structural dependence of the parametric resonance on the inflationary model, including $V(ϕ)={m^2 \over 2}ϕ^2$, ${λ\over 4}ϕ^4$, $1-\cos {ϕ\over f}$; ``rescattering'' of created particles; and phase transitions after inflation.

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arXiv1998

Reheating and Preheating after Inflation

It is assumed that during inflation, all energy was contained in a slow-rolling inflaton field $ϕ$. The particles constituting the Universe are created due to interactions with the field $ϕ$ coherently oscillating after inflation. The leading channel of the particle production would be the non-perturbative regime of parametric resonance, preheating. Some of the recent developments in the theory of preheating are briefly reviewed. As a prototype we use the model ${λ\over 4}ϕ^4 + {m^2 \over 2}ϕ^2+ {g^2\over 2}ϕ^2χ^2$ in an expanding universe. In different domains of parameters the character of preheating $(ϕ\to χ)$ or $(ϕ\to δϕ)$ is different, ranging from regular Lamé to stochastic parametric resonances. Fortunately, in many important cases simple analytic resonant solutions are found. Eventually, a picture which unifies the different regimes emerges.

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arXiv1997

Towards the Theory of Reheating After Inflation

Reheating after inflation occurs due to particle production by the oscillating inflaton field. In this paper we describe the perturbative approach to reheating, and then concentrate on effects beyond the perturbation theory. They are related to the stage of parametric resonance called 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 coupled to another scalar field X. Parametric resonance in this model is very broad. It occurs in a very unusual stochastic manner, which is different from the 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 occur with phases uncorrelated to each other. We call this process stochastic resonance. We develop the theory of preheating taking into account the expansion of the universe and backreaction of produced particles, including the effects of rescattering. The process of preheating can be divided into several distinct stages. At the first stage the backreaction of created particles is not important. At the second stage backreaction 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 X-particles terminate the resonance. We calculate the density of X-particles and their quantum fluctuations with all backreaction effects taken into account. This allows us to find the range of masses and coupling constants for which one has efficient preheating. In particular, under certain conditions this process may produce particles with a mass much greater than the mass of the inflaton field.

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arXiv1997

Structure of Resonance in Preheating after Inflation

We consider preheating in the theory $1/4 λϕ^4 + 1/2 g^2ϕ^2χ^2 $, where the classical oscillating inflaton field $ϕ$ decays into $χ$-particles and $ϕ$-particles. The parametric resonance which leads to particle production in this conformally invariant theory is described by the Lame equation. It significantly differs from the resonance in the theory with a quadratic potential. The structure of the resonance depends in a rather nontrivial way on the parameter $g^2/λ$. We construct the stability/instability chart in this theory for arbitrary $g^2/λ$. We give simple analytic solutions describing the resonance in the limiting cases $g^2/λ\ll 1$ and $g^2/λ\gg 1$, and in the theory with $g^2=3λ$, and with $g^2 =λ$. From the point of view of parametric resonance for $χ$, the theories with $g^2=3λ$ and with $g^2 =λ$ have the same structure, respectively, as the theory $1/4 λϕ^4$, and the theory $λ/(4 N) (ϕ^2_i)^2$ of an N-component scalar field $ϕ_i$ in the limit $N \to \infty$. We show that in some of the conformally invariant theories such as the simplest model $1/4 λϕ^4$, the resonance can be terminated by the backreaction of produced particles long before $<χ^2>$ or $<ϕ^2 >$ become of the order $ϕ^2$. We analyze the changes in the theory of reheating in this model which appear if the inflaton field has a small mass.

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arXiv1996

Statistics of Gravitational Microlensing Magnification. II. Three-Dimensional Lens Distribution

In Paper I we studied the theory of gravitational microlensing for a planar distribution of point masses. In this second paper, we extend the analysis to a three-dimensional lens distribution. First we study the lensing properties of three-dimensional lens distributions by considering in detail the critical curves, the caustics, the illumination patterns, and the magnification cross-sections sigma(A) of multiplane configurations with two, three, and four point masses. For N_\ast point masses that are widely separated in Lagrangian space, we find that there are ~ 2^{N_\ast} - 1 critical curves in total, but that only ~ N_\ast of these produce prominent caustic-induced features at the high magnification end of sigma(A). In the case of a low optical depth random distribution of point masses, we show that the multiplane lens equation near a point mass can be reduced to the single plane equation of a point mass perturbed by weak shear. This allows us to calculate the caustic-induced feature in the macroimage magnification distribution P(A) as a weighted sum of the semi-analytic feature derived in Paper I for a planar lens distribution. The resulting semi-analytic caustic-induced feature is similar to the feature in the planar case, but it does not have any simple scaling properties, and it is shifted to higher magnification. The semi-analytic distribution is compared to the results of previous numerical simulations for optical depth tau ~ 0.1, and they are in better agreement than a similar comparison in the planar case. We explain this by estimating the fraction of caustics of individual lenses that merge with those of their neighbors. For tau=0.1, the fraction is approx 20%, much less than the approx 55% for the planar case.

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arXiv1996

Statistics of Gravitational Microlensing Magnification. I. Two-Dimensional Lens Distribution

(Abridged) In this paper we refine the theory of microlensing for a planar distribution of point masses. We derive the macroimage magnification distribution P(A) at high magnification (A-1 >> tau^2) for a low optical depth (tau << 1) lens distribution by modeling the illumination pattern as a superposition of the patterns due to individual ``point mass plus weak shear'' lenses. We show that a point mass plus weak shear lens produces an astroid- shaped caustic and that the magnification cross-section obeys a simple scaling property. By convolving this cross-section with the shear distribution, we obtain a caustic-induced feature in P(A) which also exhibits a simple scaling property. This feature results in a 20% enhancement in P(A) at A approx 2/tau. In the low magnification (A-1 << 1) limit, the macroimage consists of a bright primary image and a large number of faint secondary images formed close to each of the point masses. Taking into account the correlations between the primary and secondary images, we derive P(A) for low A. The low-A distribution has a peak of amplitude ~ 1/tau^2 at A-1 ~ tau^2 and matches smoothly to the high-A distribution. We combine the high- and low-A results and obtain a practical semi-analytic expression for P(A). This semi-analytic distribution is in qualitative agreement with previous numerical results, but the latter show stronger caustic-induced features at moderate A for tau as small as 0.1. We resolve this discrepancy by re-examining the criterion for low optical depth. A simple argument shows that the fraction of caustics of individual lenses that merge with those of their neighbors is approx 1-exp(-8 tau). For tau=0.1, the fraction is surprisingly high: approx 55%. For the purpose of computing P(A) in the manner we did, low optical depth corresponds to tau << 1/8.

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arXiv1996

Comments on "Analytic and Numerical Study of Preheating Dynamics"

In a recent paper Boyanovsky et al (hep-ph/9608205) studied preheating for a particular theory of the inflaton field. Although they results essentially confirm those of the original papers on reheating after inflation, they claimed that most of the earlier works on preheating did not take into account backreaction of created particles, misused the Mathieu equation, and were inconclusive about the symmetry restoration after preheating. We explain why we cannot agree with these statements.

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arXiv1996

The Origin of Matter in the Universe: Reheating after Inflation

In the inflationary scenario all the matter constituting the universe was created from the process of reheating after inflation. Recent development of the theory of reheating is briefly reviewed. The list of topics includes elementary (perturbative) theory of reheating; quantum field theory in a time-varying background; parametric resonance and explosive particle creation; non-thermal phase transitions from reheating; baryogenesis from reheating; residual oscillations of the scalar field, and other cosmological applications.

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arXiv1996

Non-Thermal Phase Transitions after Inflation

At the first stage of reheating after inflation, parametric resonance may rapidly transfer most of the energy of an inflaton field $ϕ$ to the energy of other bosons. We show that quantum fluctuations of scalar and vector fields produced at this stage are much greater than they would be in a state of thermal equilibrium. This leads to cosmological phase transitions of a new type, which may result in a copious production of topological defects and in a secondary stage of inflation after reheating.

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arXiv1995

How Filaments are Woven into the Cosmic Web

Observations indicate galaxies are distributed in a filament-dominated web-like structure. Numerical experiments at high and low redshift of viable structure formation theories also show filament-dominance. We present a simple quantitative explanation of why this is so, showing that the final-state web is actually present in embryonic form in the overdensity pattern of the initial fluctuations, with nonlinear dynamics just sharpening the image. The web is largely defined by the position and primordial tidal fields of rare events in the medium, with the strongest filaments between nearby clusters whose tidal tensors are nearly aligned. Applications of the cosmic web theory to observations include probing cluster-cluster bridges by weak gravitational lensing, X-rays, and the Sunyaev-Zeldovich effect and probing high redshift galaxy-galaxy bridges by low column density Lyman alpha absorption lines.

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arXiv1995

Mixed Dark Matter Model in Halos of Clusters

We discuss the structure of clusters in a class of flat cosmological models with the fraction of mass Ω_{CDM} ~0.8 in cold dark matter, and the rest in hot dark matter in the form of massive neutrinos. We consider such Cold+Hot Dark Matter (CHDM) models with one, two or three massive neutrinos, with total mass ~4.6eV. Neutrinos of such low mass cannot constitute halos of galaxies and groups, but only of clusters of galaxies. The limit on the density of neutrinos in the central parts of galaxy clusters is estimated from the phase space den- sity constraints. The ratio of the neutrino density to that of CDM through the cluster is found analytically. It appears that the density of neutrinos is suppressed within the Abell radius. However, neutrinos contribute ~20% of the mass density to the cluster halo. Our numerical simulations match analytical results. The simulations indicate that the cluster halo dark matter density profile has the power-law slope ~-2.5 which is close to that in the model with cosmological constant. We also found that in the CHDM models the velocity dispersion is almost constant across the cluster. This is quite different from the model with cosmological constant or the open model where the velocity dispersion falls in the cluster outskirts. We discuss X-ray emission and weak gravitational lensing by clusters in the model. We input the found spherically symmetrical fit to the CHDM mass density profile and the X-ray surface brightness for the cluster A2256 into simple equation of hydrostatic equilibrium of the hot gas. X-ray temperature derived this way departures from both the data and actual prediction of the model, which give almost constant temperature. We found also that the problem of high baryonic fraction in clusters is not resolved in the CHDM models.

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arXiv1994

Statistics of Cosmological Inhomogeneities

This contribution to the Proceedings is based on the talk given at the Conference on Birth of the Universe and Fundamental Physics, Rome, May 18-21, 1994. Some selected topics of the subject are reviewed: Models of Primordial Fluctuations; Reconstruction of the Cosmological Density Probability Distribution Function (PDF) from Cumulants; PDFs from the Zel'dovich Approximation and from Summarizing Perturbation Series; Fitting by the Log-normal Distribution.

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arXiv1994

Reheating after Inflation

The theory of reheating of the Universe after inflation is developed. The transition from inflation to the hot Universe turns out to be strongly model-dependent and typically consists of several stages. Immediately after inflation the field $ϕ$ begins rapidly rolling towards the minimum of its effective potential. Contrary to some earlier expectations, particle production during this stage does not lead to the appearance of an extra friction term $Γ\dotϕ$ in the equation of motion of the field $ϕ$. Reheating becomes efficient only at the next stage, when the field $ϕ$ rapidly oscillates near the minimum of its effective potential. We have found that typically in the beginning of this stage the classical inflaton field $ϕ$ very rapidly (explosively) decays into $ϕ$-particles or into other bosons due to broad parametric resonance. This stage cannot be described by the standard elementary approach to reheating based on perturbation theory. The bosons produced at this stage, as well as some part of the classical field $ϕ$ which survives the stage of explosive reheating, should further decay into other particles, which eventually become thermalized. The last stages of decay can be described in terms of perturbation theory. Complete reheating is possible only in those theories where a single massive $ϕ$-particle can decay into other particles. This imposes strong constraints on the structure of inflationary models. On the other hand, this means that a scalar field can be a cold dark matter candidate even if it is strongly coupled to other fields.

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arXiv1994

Equations of Gravitational Instability are Non-Local

Few recent generations of cosmologists have solved non-local newtonian equations of the gravitational instability in an expanding universe. In this approach pancaking is the predominant form of first collapsing objects. Relativistic counterparts of these equations contain the electric and magnetic parts of the Weyl tensor. In the linear theory the magnetic part is associated with gravitational waves. If the magnetic part is ignored, then the newtonian limit of the relativistic equations is reduced to the closed set of the local Lagrangian equations. Recently this fact drew much attention since the gravitational instability in that form would greatly simplify the study of cosmic structure formation. In particular, the filamentary structure of collapsing is predicted. In this paper we resolve the contradiction between the newtonian theory and relativistic version adopted in some recent papers. We show that dropping the magnetic part from the basic relativistic equations is {\it incorrect}. The correct newtonian limit is derived by the $1/c$-expansion of the GR equations and the Bianchi identities for the Weyl tensor. The last ones begin with $\sim 1/c^3$ order, therefore one {\it must} take into account the magnetic part in the post newtonian order $\sim 1/c^3$, which contains non-local terms, related to the non-local gravitational interaction. For the first time we rigorously show that the GR equations with the magnetic part are reduced precisely to the canonic newtonian non-local equations. Thus, the correct treatment of the relativistic version of the gravitational instability resurrects the canonic picture of the structure formation.

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arXiv1993

Cosmological Distribution Functions

The evolution of probability distribution functions (PDFs) of continuous density, velocity and velocity derivatives ( deformation tensor) fields in the theory of cosmological gravitational instability are considered. We show that in the Newtonian theory the dynamical equations cannot be reduced to the closed set of Lagrangian equations. Since continuous fields from galaxy surveys need sufficiently large smoothing which exceeds the scale of nonlinearity, one can use the Zel'dovich approximation to describe the mildly non-linear matter evolution, which allows the closed set of Lagrangian equations. The closed kinetic equation for the joint PDF of cosmological continuous fields is derived in this approximation. The analytical theory of the cosmological PDFs with arbitrary (including Gaussian) initial statistics is developed, based on the solution on the kinetic equaiton. For Gaussian initial fluctuations, the PDFs are parametrized by only linear {\it rms} fluctuations $σ$ on given filtering scale. Density PDF $P(ρ, t)$ and PDF $M(λ_1, λ_2, λ_3; t)$ of eigenvalues of the deformation tensor field in the Eulerian space evolve very rapidly in non-linear regime. On the contrary, velocity PDF $Q(\vec v, t)$ remains invariant under non-linear evolution. For small $σ$ the Edgworth series is suggested to reconstruct

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arXiv1993

Evolution of One-Point Distributions from Gaussian Initial Fluctuations

We study the quasilinear evolution of the one-point probability density functions (PDFs) of the smoothed density and velocity fields in a cosmological gravitating system beginning with Gaussian initial fluctuations. Our analytic results are based on the Zel'dovich approximation and laminar flow. A numerical analysis extends the results into the multistreaming regime using the smoothed fields of a CDM N-body simulation. We find that the PDF of velocity, both Lagrangian and Eulerian, remains Gaussian under the laminar Zel'dovich approximation, and it is almost indistinguishable from Gaussian in the simulations. The PDF of mass density deviates from a normal distribution early in the quasilinear regime and it develops a shape remarkably similar to a lognormal distribution with one parameter, the \rms density fluctuation $σ$. Applying these results to currently available data we find that the PDFs of the velocity and density fields, as recovered by the \pot\ procedure from observed velocities assuming $Ω=1$, or as deduced from a redshift survey of \iras\ galaxies assuming that galaxies trace mass, are consistent with Gaussian initial fluctuations.

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