Testing Inflation: A Bootstrap Approach

We note that the essential idea of inflation, that the universe underwent a brief period of accelerated expansion followed by a long period of decelerated expansion, can be encapsulated in a "closure condition" which relates the amount of accelerated expansion during inflation to the amount of decelerated expansion afterward. We present a protocol for systematically testing the validity of this condition observationally.Comment: 4 pages, 2 figures, matches Phys. Rev. Lett. versio

Mathematical Description and Mechanistic Reasoning: A Pathway Toward STEM Integration

Because reasoning about mechanism is critical to disciplined inquiry in science, technology, engineering, and mathematics (STEM) domains, this study focuses on ways to support the development of this form of reasoning. This study attends to how mechanistic reasoning is constituted through mathematical description. This study draws upon Smith’s (2007) characterization of mathematical description of scientific phenomena as ‘‘bootstrapping,’’ where negotiating the relationship between target phenomena and represented relations is fundamental to learning. In addition, the development of mathematical representation presents a viable pathway towards STEM integration. In this study, participants responded to an assessment of mechanistic reasoning while cognitive interviews were conducted to characterize their reasoning about mechanism and mathematical description of the systems of levers represented in the items. Participant item responses were modeled using item response theory and participant talk and gesture were coded according to developed analytic frameworks. Participants were elementary, middle, and high school students as well as college undergraduates, and adults without college education. The results suggest a relationship between participants’ tendencies to describe these systems mathematically and their mechanistic reasoning ability. Moreover, there are specific elements of mechanistic reasoning that are more highly associated with mathematical description. In addition, there is a relationship between a participant’s propensity to both mathematically describe and mechanistically trace mechanical systems

Assessing Mechanistic Reasoning: Supporting Systems Tracing

Reasoning about mechanism is central to disciplined inquiry in science and engineering and should thus be one of the foundations of a science, technology, engineering, and mathematics education. In addition, mechanistic reasoning is one of the core competencies listed in the Next Generation Science Standards (NGSS) Engineering Concepts and Practices (NGSS Lead States, 2013). Mechanistic explanations focus on the processes that underlie cause–effect relationships and consider how the activities of system components affect one another. While some assessment work has been accomplished in engineering education, to date mechanistic reasoning is an area where limited assessment development has been accomplished for pre-college populations. The data in this study come from the calibration of the Assessment of Mechanistic Reasoning Project (AMRP) (Weinberg, 2012), designed to diagnose individuals’ mechanistic reasoning about systems of levers. This assessment presents a domain-specific characterization of mechanistic reasoning and illuminates what is easy and difficult about this form of reasoning. The study participants included elementary, middle, and high school students as well as college undergraduates and adults without higher education. Within this calibration study, item analyses, reliability, and validity measures were conducted using item response theory modeling; the AMRP assessment was found to have high reliability and validity. In addition, this study shows that machine characteristics such as number of levers, lever type, and arrangement of levers can affect the difficulty of mechanistic reasoning

Supporting Mechanistic Reasoning in Domain-Specific Contexts

Mechanistic reasoning is an epistemic practice central within science, technology, engineering, and mathematics disciplines. Although there has been some work on mechanistic reasoning in the research literature and standards documents, much of this work targets domain-general characterizations of mechanistic reasoning; this study provides domain-specific illustrations of mechanistic reasoning. The data in this study comes from the Assessment of Mechanistic Reasoning Project (AMRP) (Weinberg, 2012), designed using item response theory modeling to diagnose individuals’ mechanistic reasoning about systems of levers. Such a characterization of mechanistic reasoning illuminates what is easy and difficult about this form of reasoning, within the subdomain of simple machines. Moreover, this work indicates how domain-general principles may be limited. The study participants included elementary, middle, and high school students as well as college undergraduates and adults without higher education. Although the majority of participants responded to the AMRP by diagnosing at least one mechanistic element (elements inherent to the working of systems of levers) as they predicted its motion, such reasoning was not trivial. In fact, the diverse reasoning by participants shows how systems of levers support elements of mechanistic reasoning. Moreover, this study provides evidence that the development of mechanistic reasoning is dependent on domain-specific experience

The Standard Model of Particle Physics

Particle physics has evolved a coherent model that characterizes forces and particles at the most elementary level. This Standard Model, built from many theoretical and experimental studies, is in excellent accord with almost all current data. However, there are many hints that it is but an approximation to a yet more fundamental theory. We trace the development of the Standard Model and indicate the reasons for believing that it is incomplete.Comment: 25 pages, 17 figures; accepted for publication in Rev. Mod. Physics (APS centenary issue

Complete Set of Homogeneous Isotropic Analytic Solutions in Scalar-Tensor Cosmology with Radiation and Curvature

We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters. Our goal is to obtain analytically the complete set of configurations of a homogeneous and isotropic universe as a function of time. This leads to a geodesically complete description of the universe, including the passage through the cosmological singularities, at the classical level. We give all the solutions analytically without any restrictions on the parameter space of the model or initial values of the fields. We find that for generic solutions the universe goes through a singular (zero-size) bounce by entering a period of antigravity at each big crunch and exiting from it at the following big bang. This happens cyclically again and again without violating the null energy condition. There is a special subset of geodesically complete non-generic solutions which perform zero-size bounces without ever entering the antigravity regime in all cycles. For these, initial values of the fields are synchronized and quantized but the parameters of the model are not restricted. There is also a subset of spatial curvature-induced solutions that have finite-size bounces in the gravity regime and never enter the antigravity phase. These exist only within a small continuous domain of parameter space without fine tuning initial conditions. To obtain these results, we identified 25 regions of a 6-parameter space in which the complete set of analytic solutions are explicitly obtained.Comment: 38 pages, 29 figure

Challenges for Superstring Cosmology

We consider whether current notions about superstring theory below the Planck scale are compatible with cosmology. We find that the anticipated form for the dilaton interaction creates a serious roadblock for inflation and makes it unlikely that the universe ever reaches a state with zero cosmological constant and time-independent gravitational constant.Comment: 14 pages, 2 figures available as eps files on reques

Redundance of Δ\Delta-isobar Parameters in Effective Field Theories

It is shown that the off-shell parameters in the interaction Lagrangian of pions, nucleons, and $\Delta$-isobars are redundant in the framework of effective field theories. Our results also suggest the necessity of including the $\Delta$ as an explicit dynamical degree of freedom.Comment: 11 pages, RevTex, no figures, a minor error corrected, to appear in PL

Non-relativistic Maxwell-Chern-Simons Vortices

The non-relativistic Maxwell-Chern-Simons model recently introduced by Manton is shown to admit self-dual vortex solutions with non-zero electric field. The interrelated ``geometric'' and ``hidden'' symmetries are explained. The theory is also extended to (non-relativistic) spinors. A relativistic, self-dual model, whose non-relativistic limit is the Manton model is also presented. The relation to previous work is discussed.Comment: 20 pages plain TeX. Revised: minor errors corrected and symmetries explained in a clearer way. Version as will appear in Ann. Phys. (N.Y.

Gauge-Dependent Cosmological "Constant"

When the cosmological constant of spacetime is derived from the 5D induced-matter theory of gravity, we show that a simple gauge transformation changes it to a variable measure of the vacuum which is infinite at the big bang and decays to an astrophysically-acceptable value at late epochs. We outline implications of this for cosmology and galaxy formation.Comment: 14 pages, no figures, expanded version to be published in Class. Quantum Gra