A tracker solution to the cold dark matter cosmic coincidence problem

Recently, we introduced the notion of "tracker fields," a form of quintessence which has an attractor-like solution. Using this concept, we showed how to construct models in which the ratio of quintessence to matter densities today is independent of initial conditions. Here we apply the same idea to the standard cold dark matter component in cases where it is composed of oscillating fields. Combining these ideas, we can construct a model in which quintessence, cold dark matter, and ordinary matter all contribute comparable amounts to the total energy density today irrespective of initial conditions.Comment: 8 pages, 2 eps figures, use epsfig.sty, accepted for publication in Physics Letters

Cosmological Tracking Solutions

A substantial fraction of the energy density of the universe may consist of quintessence in the form of a slowly-rolling scalar field. Since the energy density of the scalar field generally decreases more slowly than the matter energy density, it appears that the ratio of the two densities must be set to a special, infinitesimal value in the early universe in order to have the two densities nearly coincide today. Recently, we introduced the notion of tracker fields to avoid this initial conditions problem. In the paper, we address the following questions: What is the general condition to have tracker fields? What is the relation between the matter energy density and the equation-of-state of the universe imposed by tracker solutions? And, can tracker solutions explain why quintessence is becoming important today rather than during the early universe

Is Schr\"{o}dinger's Conjecture for the Hydrogen Atom Coherent States Attainable

We construct the most general SO(4,2) hydrogen atom coherent states which are the counterpart of Schr\"{o}dinger's harmonic oscillator coherent states. We show that these states cannot be localized and cannot follow the classical orbits. Thus, Schr\"{o}dinger's conjecture for the hydrogen atom coherent states is unattainable.Comment: 10 pages, report

Parametric Resonance in an Expanding Universe

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.Comment: 18 pages, Latex, 4 figure

A new cosmological tracker solution for Quintessence

In this paper we propose a quintessence model with the potential $V(\Phi )=V_{o}[ \sinh {(\alpha \sqrt{\kappa_{o}}\Delta \Phi})] ^{\beta}$, which asymptotic behavior corresponds to an inverse power-law potential at early times and to an exponential one at late times. We demonstrate that this is a tracker solution and that it could have driven the Universe into its current inflationary stage. The exact solutions and the description for a complete evolution of the Universe are also given. We compare such model with the current cosmological observations.Comment: 13 pages REVTeX, 5 eps color figure

From Heisenberg matrix mechanics to EBK quantization: theory and first applications

Despite the seminal connection between classical multiply-periodic motion and Heisenberg matrix mechanics and the massive amount of work done on the associated problem of semiclassical (EBK) quantization of bound states, we show that there are, nevertheless, a number of previously unexploited aspects of this relationship that bear on the quantum-classical correspondence. In particular, we emphasize a quantum variational principle that implies the classical variational principle for invariant tori. We also expose the more indirect connection between commutation relations and quantization of action variables. With the help of several standard models with one or two degrees of freedom, we then illustrate how the methods of Heisenberg matrix mechanics described in this paper may be used to obtain quantum solutions with a modest increase in effort compared to semiclassical calculations. We also describe and apply a method for obtaining leading quantum corrections to EBK results. Finally, we suggest several new or modified applications of EBK quantization.Comment: 37 pages including 3 poscript figures, submitted to Phys. Rev.

Classical inflaton field induced creation of superheavy dark matter

We calculate analytically and numerically the production of superheavy dark matter (X) when it is coupled to the inflaton field \phi within the context of a slow-roll m_\phi^2 \phi^2/2 inflationary model with coupling g^2 X^2 \phi^2/2. We find that X particles with a mass as large as 1000 H_i, where H_i is the value of the Hubble expansion rate at the end of inflation, can be produced in sufficient abundance to be cosmologically significant today. This means that superheavy dark matter may have a mass of up to 10^{-3} Planck mass. We also derive a simple formula that can be used to estimate particle production as a result of a quantum field's interaction with a general class of homogeneous classical fields. Finally, we note that the combined effect of the inflaton field and the gravitational field on the X field causes the production to be a nonmonotonic function of g^2.Comment: 42 page LaTeX file with 8 PostScript figures included with eps

Resolving the cosmological coincidence problem

Recent observations suggest that a large fraction of the energy density of the universe has negative pressure. One explanation is vacuum energy density; another is quintessence in the form of a scalar field slowly evolving down a potential. In either case, a key problem is to explain why the energy density nearly coincides with the matter density today. The densities decrease at different rates as the universe expands, so coincidence today appears to require that their ratio be set to a specific, infinitesimal value in the early universe. In this thesis, we introduce the notion of a “tracker field,” a form of quintessence, and show how it may explain the coincidence. We also address the following questions: What is the general condition to have tracker fields? What is the relation between the matter energy density and the equation-of-state of the universe imposed by tracker solutions? And, can tracker solutions help to explain why quintessence is becoming important today rather than during the early universe? We also apply the tracker idea to the standard cold dark matter component in cases where it is composed of oscillating fields. Combining these ideas, we construct a model in which quintessence, cold dark matter, and ordinary matter all contribute comparable amounts to the total energy density today irrespective of initial conditions

Resolving the cosmological coincidence problem

Recent observations suggest that a large fraction of the energy density of the universe has negative pressure. One explanation is vacuum energy density; another is quintessence in the form of a scalar field slowly evolving down a potential. In either case, a key problem is to explain why the energy density nearly coincides with the matter density today. The densities decrease at different rates as the universe expands, so coincidence today appears to require that their ratio be set to a specific, infinitesimal value in the early universe. In this thesis, we introduce the notion of a “tracker field,” a form of quintessence, and show how it may explain the coincidence. We also address the following questions: What is the general condition to have tracker fields? What is the relation between the matter energy density and the equation-of-state of the universe imposed by tracker solutions? And, can tracker solutions help to explain why quintessence is becoming important today rather than during the early universe? We also apply the tracker idea to the standard cold dark matter component in cases where it is composed of oscillating fields. Combining these ideas, we construct a model in which quintessence, cold dark matter, and ordinary matter all contribute comparable amounts to the total energy density today irrespective of initial conditions