Robert J. Scherrer

A Classification of scalar field potentials with cosmological scaling solutions

An attractive method of obtaining an effective cosmological constant at the present epoch is through the potential energy of a scalar field. Considering models with a perfect fluid and a scalar field, we classify all potentials for which the scalar field energy density scales as a power law of the scale factor when the perfect fluid density dominates. There are three possibilities. The first two are well known; the much-investigated exponential potentials have the scalar field mimicking the evolution of the perfect fluid, while for negative power laws, introduced by Ratra and Peebles, the scalar field density grows relative to that of the fluid. The third possibility is a new one, where the potential is a positive power law and the scalar field energy density decays relative to the perfect fluid. We provide a complete analysis of exact solutions and their stability properties, and investigate a range of possible cosmological applications.

Purely kinetic k-essence as unified dark matter

We examine k-essence models in which the Lagrangian p is a function only of the derivatives of a scalar field phi and does not depend explicity on phi. The evolution of phi for an arbitrary functional form for p can be given in terms of an exact analytic solution. For quite general conditions on the functional form of p, such models can evolve to a state characterized by a density scaling with the scale factor as rho = rho_0 + rho_1(a/a_0)^{-3}, but with a sound speed c_s^2 << 1 at all times. Such models can serve as a unified model for dark matter and dark energy, while avoiding the problems of the generalized Chaplygin gas models, which are due to a non-negligible sound speed in these models. A dark energy component with c_s << 1 serves to suppress cosmic microwave background fluctuations on large angular scales.

Statistics of primordial density perturbations from discrete seed masses

The statistics of density perturbations for general distributions of seed masses with arbitrary matter accretion is examined. Formal expressions for the power spectrum, the N-point correlation functions, and the density distribution function are derived. These results are applied to the case of uncorrelated seed masses, and power spectra are derived for accretion of both hot and cold dark matter plus baryons. The reduced moments (cumulants) of the density distribution are computed and used to obtain a series expansion for the density distribution function. Analytic results are obtained for the density distribution function in the case of a distribution of seed masses with a spherical top-hat accretion pattern. More generally, the formalism makes it possible to give a complete characterization of the statistical properties of any random field generated from a discrete linear superposition of kernels. In particular, the results can be applied to density fields derived by smoothing a discrete set of points with a window function.

Big Bang nucleosynthesis in crisis

A new evaluation of the constraint on the number of light neutrino species ({ital N}{sub {nu}}) from big bang nucleosynthesis suggests a discrepancy between the predicted light element abundances and those inferred from observations, unless the inferred primordial {sup 4}He abundance has been underestimated by 0.014{plus_minus}0.004 (1{sigma}) or less than 10% (95% C.L.) of {sup 3}He survives stellar processing. With the quoted systematic errors in the observed abundances and a conservative chemical evolution parametrization, the best fit to the combined data is {ital N}{sub {nu}}=2.1{plus_minus}0.3 (1{sigma}) and the upper limit is {ital N}{sub {nu}}{lt}2.6 (95% C.L.). The data are inconsistent with the standard model ({ital N}{sub {nu}}=3) at the 98.6% C.L. {copyright} {ital 1995} {ital The} {ital American} {ital Physical} {ital Society}.

Thawing quintessence with a nearly flat potential

The thawing quintessence model with a nearly flat potential provides a natural mechanism to produce an equation of state parameter, w, close to -1 today. We examine the behavior of such models for the case in which the potential satisfies the slow-roll conditions: [(1/V)(dV/d{phi})]{sup 2}<<1 and (1/V)(d{sup 2}V/d{phi}{sup 2})<<1, and we derive the analog of the slow-roll approximation for the case in which both matter and a scalar field contribute to the density. We show that in this limit, all such models converge to a unique relation between 1+w, {omega}{sub {phi}}, and the initial value of (1/V)(dV/d{phi}). We derive this relation and use it to determine the corresponding expression for w(a), which depends only on the presentday values for w and {omega}{sub {phi}}. For a variety of potentials, our limiting expression for w(a) is typically accurate to within {delta}w < or approx. 0.005 for w<-0.9. For redshift z < or approx. 1, w(a) is well fit by the Chevallier-Polarski-Linder parametrization, in which w(a) is a linear function of a.

Prospects for Determining the Equation of State of the Dark Energy: What Can Be Learned from Multiple Observables?

The dark energy that appears to produce the accelerating expansion of the universe can be characterized by an equation of state p ¼ wwith w < � 1 . A number of observational tests have been proposed to study the value or redshift dependence of w, including Type Ia supernova distances, the Sunyaev-Zeldovich effect, cluster abundances, strong and weak gravitational lensing, galaxy and quasar clustering, galaxy ages, the Lyforest, and cosmic microwave background anisotropies. The proposed observational tests based on these phenomena measure either the distance-redshift relation d(z), the Hubble parameter H(z), the age of the universe t(z), the linear growth factor D1(z), or some combination of these quantities. We compute the evolution of these four observables and of the combination H(z)d(z) that enters the Alcock-Paczyznski aniso- tropy test in models with constant w, in quintessence models with some simple forms of the potential V(� ), and in toy models that allow more radical time variations of w. Measurement of any of these quantities to a precision of a few percent is generally sufficient to discriminate between w ¼� 1 and � 2 . However, the time dependence predicted in quintessence models is extremely difficult to discern because the quintessence com- ponent is dynamically unimportant at the redshifts where w departs substantially from its low-z value. Even for the toy models that allow substantial changes in w at low redshift, there is always a constant-w model that produces very similar evolution of all of the observables simultaneously. We conclude that measurement of the effective equation of state of the dark energy may be achieved by several independent routes in the next few years but that detecting time variation in this equation of state will prove very difficult except in special- ized cases. Subject headings: cosmological parameters — cosmology: theory

Models for Little Rip Dark Energy

Abstract We examine in more detail specific models which yield a little rip cosmology, i.e., a universe in which the dark energy density increases without bound but the universe never reaches a finite time singularity. We derive the conditions for the little rip in terms of the inertial force in the expanding universe and present two representative models to illustrate in more detail the difference between little rip models and those which are asymptotically de Sitter. We derive conditions on the equation of state parameter of the dark energy to distinguish between the two types of models. We show that coupling between dark matter and dark energy with a little rip equation of state can alter the evolution, changing the little rip into an asymptotic de Sitter expansion. We give conditions on minimally coupled phantom scalar field models and on scalar-tensor models that indicate whether or not they correspond to a little rip expansion. We show that, counterintuitively, despite local instability, a little rip cosmology has an infinite lifetime.

Dark energy from a quintessence (phantom) field rolling near a potential minimum (maximum)

We examine dark-energy models in which a quintessence or a phantom field, {phi}, rolls near the vicinity of a local minimum or maximum, respectively, of its potential V({phi}). Under the approximation that (1/V)(dV/d{phi}) 3/4, w(a) has oscillatory behavior. For phantom fields, the dividing line between these two types of behavior is at (1/V)(d{sup 2}V/d{phi}{sup 2})=-3/4. Our analytical expressions agree within 1% with the exact (numerically derived) behavior, for all of the particular cases examined, for both quintessence and phantom fields. We present observational constraints on these models.

Cosmological quantum chromodynamics, neutron diffusion, and the production of primordial heavy elements

A simple one-dimensional model is used to describe the evolution of neutron density before and during nucleosynthesis in a high-entropy bubble left over from the cosmic quark-hadron phase transition. It is shown why cosmic nucleosynthesis in such a neutron-rich environment produces a surfeit of elements heavier than lithium. Analytical and numerical techniques are used to estimate the abundances of carbon, nitrogen, and heavier elements up to Ne-22. A high-density neutron-rich region produces enough primordial N-14 to be observed in stellar atmospheres. It shown that very heavy elements may be created in a cosmological r-process; the neutron exposure in the neutron-rich regions is large enough for the Ne-22 to trigger a catastrophic r-process runaway in which the quantity of heavy elements doubles in much less than an expansion time due to fission cycling. A primordial abundance of r-process elements is predicted to appear as an excess of rare earth elements in extremely metal-poor stars. 42 references.

Pseudo-rip: Cosmological models intermediate between the cosmological constant and the little rip

If we assume that the cosmic energy density will remain constant or strictly increase in the future, then the possible fates for the universe can be divided into four categories based on the time asymptotics of the Hubble parameter H(t): the cosmological constant, for which H(t) = constant, the big rip, for which H(t) goes to infinity at finite time, the little rip, for which H(t) goes to infinity as time goes to infinity, and the pseudo-rip, for which H(t) goes to a constant as time goes to infinity. Here we examine the last of these possibilities in more detail. We provide models that exemplify the pseudo-rip, which is an intermediate case between the cosmological constant and the little rip. Structure disintegration in the pseudo-rip depends on the model parameters. We show that pseudo-rip models for which the density and Hubble parameter increase monotonically can produce an inertial force which does not increase monotonically, but instead peaks at a particular future time and then decreases.