New Solutions of the Inflationary Flow Equations

The inflationary flow equations are a frequently used method of surveying the space of inflationary models. In these applications the infinite hierarchy of differential equations is truncated in a way which has been shown to be equivalent to restricting the set of models considered to those characterized by polynomial inflaton potentials. This paper explores a different method of solving the flow equations, which does not truncate the hierarchy and in consequence covers a much wider class of models while retaining the practical usability of the standard approach.Comment: References added, and a couple of comment

Ribbons on the CBR Sky: A Powerful Test of a Baryon Symmetric Universe

If the Universe consists of domains of matter and antimatter, annihilations at domain interfaces leave a distinctive imprint on the Cosmic Background Radiation (CBR) sky. The signature is anisotropies in the form of long, thin ribbons of width $\theta_W\sim 0.1^\circ$, separated by angle $\theta_L\simeq 1^\circ(L/100h^{-1}{Mpc})$ where L is the characteristic domain size, and y-distortion parameter $y \approx 10^{-6}$. Such a pattern could potentially be detected by the high-resolution CBR anisotropy experiments planned for the next decade, and such experiments may finally settle the question of whether or not our Hubble volume is baryon symmetric.Comment: LaTeX, 10 pages, 4 figures in epsf. Revised version corrects a couple of relevant mistake

Boundary Effective Field Theory and Trans-Planckian Perturbations: Astrophysical Implications

We contrast two approaches to calculating trans-Planckian corrections to the inflationary perturbation spectrum: the New Physics Hypersurface [NPH] model, in which modes are normalized when their physical wavelength first exceeds a critical value, and the Boundary Effective Field Theory [BEFT] approach, where the initial conditions for all modes are set at the same time, and modified by higher dimensional operators enumerated via an effective field theory calculation. We show that these two approaches -- as currently implemented -- lead to radically different expectations for the trans-Planckian corrections to the CMB and emphasize that in the BEFT formalism we expect the perturbation spectrum to be dominated by quantum gravity corrections for all scales shorter than some critical value. Conversely, in the NPH case the quantum effects only dominate the longest modes that are typically much larger than the present horizon size. Furthermore, the onset of the breakdown in the standard inflationary perturbation calculation predicted by the BEFT formalism is likely to be associated with a feature in the perturbation spectrum, and we discuss the observational signatures of this feature in both CMB and large scale structure observations. Finally, we discuss possible modifications to both calculational frameworks that would resolve the contradictions identified here.Comment: Reworded commentary, reference added (v2) References added (v3

A Hamilton-Jacobi approach to non-slow-roll inflation

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.Comment: 21 pages, RevTeX (minor revisions to match published version

Completing Natural Inflation

If the inflaton is a pseudo-scalar axion, the axion shift symmetry can protect the flatness of its potential from too large radiative corrections. This possibility, known as natural inflation, requires an axion scale which is greater than the (reduced) Planck scale. It is unclear whether such a high value is compatible with an effective field theoretical description, and if the global axionic symmetry survives quantum gravity effects. We propose a mechanism which provides an effective large axion scale, although the original one is sub-Planckian. The mechanism is based on the presence of two axions, with a potential provided by two anomalous gauge groups. The effective large axion scale is due to an almost exact symmetry between the couplings of the axions to the anomalous groups. We also comment on a possible implementation in heterotic string theory.Comment: 9 pages, 1 figur

Dark energy in hybrid inflation

The situation that a scalar field provides the source of the accelerated expansion of the universe while rolling down its potential is common in both the simple models of the primordial inflation and the quintessence-based dark energy models. Motivated by this point, we address the possibility of causing the current acceleration via the primordial inflation using a simple model based on hybrid inflation. We trigger the onset of the motion of the quintessence field via the transition field, and find that the fate of the universe depends on the true vacuum energy determined by choosing the parameters. We also briefly discuss the variation of the equation of state and the possible implementation of our scenario in supersymmetric theories.Comment: (v1) 10 pages, 1 figure; (v2) 12 pages, considerably revised, to appear in Physical Review

Summary: Working Group on QCD and Strong Interactions

In this summary of the considerations of the QCD working group at Snowmass 2001, the roles of quantum chromodynamics in the Standard Model and in the search for new physics are reviewed, with empahsis on frontier areas in the field. We discuss the importance of, and prospects for, precision QCD in perturbative and lattice calculations. We describe new ideas in the analysis of parton distribution functions and jet structure, and review progress in small-$x$ and in polarization.Comment: Snowmass 2001. Revtex4, 34 pages, 4 figures, revised to include additional references on jets and lattice QC

Sharing Social Network Data: Differentially Private Estimation of Exponential-Family Random Graph Models

Motivated by a real-life problem of sharing social network data that contain sensitive personal information, we propose a novel approach to release and analyze synthetic graphs in order to protect privacy of individual relationships captured by the social network while maintaining the validity of statistical results. A case study using a version of the Enron e-mail corpus dataset demonstrates the application and usefulness of the proposed techniques in solving the challenging problem of maintaining privacy \emph{and} supporting open access to network data to ensure reproducibility of existing studies and discovering new scientific insights that can be obtained by analyzing such data. We use a simple yet effective randomized response mechanism to generate synthetic networks under $\epsilon$-edge differential privacy, and then use likelihood based inference for missing data and Markov chain Monte Carlo techniques to fit exponential-family random graph models to the generated synthetic networks.Comment: Updated, 39 page

Air Pollution Exposure Assessment for Epidemiologic Studies of Pregnant Women and Children: Lessons Learned from the Centers for Children’s Environmental Health and Disease Prevention Research

The National Children’s Study is considering a wide spectrum of airborne pollutants that are hypothesized to potentially influence pregnancy outcomes, neurodevelopment, asthma, atopy, immune development, obesity, and pubertal development. In this article we summarize six applicable exposure assessment lessons learned from the Centers for Children’s Environmental Health and Disease Prevention Research that may enhance the National Children’s Study: a) Selecting individual study subjects with a wide range of pollution exposure profiles maximizes spatial-scale exposure contrasts for key pollutants of study interest. b) In studies with large sample sizes, long duration, and diverse outcomes and exposures, exposure assessment efforts should rely on modeling to provide estimates for the entire cohort, supported by subject-derived questionnaire data. c) Assessment of some exposures of interest requires individual measurements of exposures using snapshots of personal and microenvironmental exposures over short periods and/or in selected microenvironments. d) Understanding issues of spatial–temporal correlations of air pollutants, the surrogacy of specific pollutants for components of the complex mixture, and the exposure misclassification inherent in exposure estimates is critical in analysis and interpretation. e) “Usual” temporal, spatial, and physical patterns of activity can be used as modifiers of the exposure/outcome relationships. f) Biomarkers of exposure are useful for evaluation of specific exposures that have multiple routes of exposure. If these lessons are applied, the National Children’s Study offers a unique opportunity to assess the adverse effects of air pollution on interrelated health outcomes during the critical early life period