Testing Two-Field Inflation

We derive semi-analytic formulae for the power spectra of two-field inflation assuming an arbitrary potential and non-canonical kinetic terms, and we use them both to build phenomenological intuition and to constrain classes of two-field models using WMAP data. Using covariant formalism, we first develop a framework for understanding the background field kinematics and introduce a "slow-turn" approximation. Next, we find covariant expressions for the evolution of the adiabatic/curvature and entropy/isocurvature modes, and we discuss how the mode evolution can be inferred directly from the background kinematics and the geometry of the field manifold. From these expressions, we derive semi-analytic formulae for the curvature, isocurvature, and cross spectra, and the spectral observables, all to second-order in the slow-roll and slow-turn approximations. In tandem, we show how our covariant formalism provides useful intuition into how the characteristics of the inflationary Lagrangian translate into distinct features in the power spectra. In particular, we find that key features of the power spectra can be directly read off of the nature of the roll path, the curve the field vector rolls along with respect to the field manifold. For example, models whose roll path makes a sharp turn 60 e-folds before inflation ends tend to be ruled out because they produce strong departures from scale invariance. Finally, we apply our formalism to confront four classes of two-field models with WMAP data, including doubly quadratic and quartic potentials and non-standard kinetic terms, showing how whether a model is ruled out depends not only on certain features of the inflationary Lagrangian, but also on the initial conditions. Ultimately, models must possess the right balance of kinematical and dynamical behaviors, which we capture in a set of functions that can be reconstructed from spectral observables.Comment: Revised to match accepted PRD version: Improved discussion of background kinematics and multi-field effects, added tables summarizing key quantities and their links to observables, more detailed figures, fixed typos in former equations (103) and (117). 49 PRD pages, 11 figure

Field Testing of Software Applications

When interacting with their software systems, users may have to deal with problems like crashes, failures, and program instability. Faulty software running in the field is not only the consequence of ineffective in-house verification and validation techniques, but it is also due to the complexity and diversity of the interactions between an application and its environment. Many of these interactions can be hardly predicted at testing time, and even when they could be predicted, often there are so many cases to be tested that they cannot be all feasibly addressed before the software is released. This Ph.D. thesis investigates the idea of addressing the faults that cannot be effectively addressed in house directly in the field, exploiting the field itself as testbed for running the test cases. An enormous number of diverse environments would then be available for testing, giving the possibility to run many test cases in many different situations, timely revealing the many failures that would be hard to detect otherwise

Testing Multi-Field Inflation: A Geometric Approach

We develop an approach for linking the power spectra, bispectrum, and trispectrum to the geometric and kinematical features of multifield inflationary Lagrangians. Our geometric approach can also be useful in determining when a complicated multifield model can be well approximated by a model with one, two, or a handful of fields. To arrive at these results, we focus on the mode interactions in the kinematical basis, starting with the case of no sourcing and showing that there is a series of mode conservation laws analogous to the conservation law for the adiabatic mode in single-field inflation. We then treat the special case of a quadratic potential with canonical kinetic terms, showing that it produces a series of mode sourcing relations identical in form to that for the adiabatic mode. We build on this result to show that the mode sourcing relations for general multifield inflation are extension of this special case but contain higher-order covariant derivatives of the potential and corrections from the field metric. In parallel, we show how these interactions depend on the geometry of the inflationary Lagrangian and on the kinematics of the associated field trajectory. Finally, we consider how the mode interactions and effective number of fields active during inflation are reflected in the spectra and introduce a multifield consistency relation, as well as a multifield observable that can potentially distinguish two-field scenarios from scenarios involving three or more effective fields.Comment: 21 pages, 4 figures + tables. Revised to clarify several points and reorganized Section III for pedagogical reasons. Error in one equation and typos were corrected, as well as additional references adde

Multiple Testing for Neuroimaging via Hidden Markov Random Field

Traditional voxel-level multiple testing procedures in neuroimaging, mostly $p$-value based, often ignore the spatial correlations among neighboring voxels and thus suffer from substantial loss of power. We extend the local-significance-index based procedure originally developed for the hidden Markov chain models, which aims to minimize the false nondiscovery rate subject to a constraint on the false discovery rate, to three-dimensional neuroimaging data using a hidden Markov random field model. A generalized expectation-maximization algorithm for maximizing the penalized likelihood is proposed for estimating the model parameters. Extensive simulations show that the proposed approach is more powerful than conventional false discovery rate procedures. We apply the method to the comparison between mild cognitive impairment, a disease status with increased risk of developing Alzheimer's or another dementia, and normal controls in the FDG-PET imaging study of the Alzheimer's Disease Neuroimaging Initiative.Comment: A MATLAB package implementing the proposed FDR procedure is available with this paper at the Biometrics website on Wiley Online Librar

Testing Galactic Magnetic Field Models using Near-Infrared Polarimetry

This work combines new observations of NIR starlight linear polarimetry with previously simulated observations in order to constrain dynamo models of the Galactic magnetic field. Polarimetric observations were obtained with the Mimir instrument on the Perkins Telescope in Flagstaff, AZ, along a line of constant Galactic longitude (\ell = 150\circ) with 17 pointings of the 10' \times 10' field of view between -75\circ < b < 10\circ, with more frequent pointings towards the Galactic midplane. A total of 10,962 stars were photometrically measured and 1,116 had usable polarizations. The observed distribution of polarization position angles with Galactic latitude and the cumulative distribution function of the measured polarizations are compared to predicted values. While the predictions lack the effects of turbulence and are therefore idealized, this comparison allows significant rejection of A0-type magnetic field models. S0 and disk-even halo-odd magnetic field geometries are also rejected by the observations, but at lower significance. New predictions of spiral-type, axisymmetric magnetic fields, when combined with these new NIR observations, constrain the Galactic magnetic field spiral pitch angle to -6\circ \pm 2\circ.Comment: 11 pages, 10 figures, Accepted for publication in Ap

Testing Nonperturbative Ansaetze for the QCD Field Strength Correlator

A test for the Gaussian and exponential Ansaetze for the nonperturbative parts of the coefficient functions, D^{nonpert.} and D_1^{nonpert.}, which parametrize the gauge-invariant bilocal correlator of the field strength tensors in the stochastic vacuum model of QCD, is proposed. It is based on the evaluation of the heavy-quark condensate within this model by making use of the world-line formalism and equating the obtained result to the one following directly from the QCD Lagrangian. This yields a certain relation between D^{nonpert.}(0) and D_1^{nonpert.}(0), which is further compared with an analogous relation between these quantities known from the existing lattice data. Such a comparison leads to the conclusion that at the distances smaller than the correlation length of the vacuum, Gaussian Ansatz is more suitable than the exponential one.Comment: 10 pages, LaTeX2e, 1 table, no figure

Testing and comparing tachyon inflation to single standard field inflation

We compare the standard single scalar field inflationary predictions with those of an inflationary phase driven by a tachyon field. A slow-roll formalism is defined for tachyon inflation and we derive the spectra of scalar and tensor perturbations as well as the consistency relations. At lowest order the predictions of standard and tachyon inflation are the same. Higher order deviations are present and their observational relevance is discussed. We discuss the observational consequences of some typical inflationary tachyon potentials and compare them with recent data. All the models predict a negative and very small running of the scalar spectral index, and they consistently lie within the 1$\sigma$ contour of the data set. However, the regime of blue scalar spectral index and large gravity waves is not explored by these models.Comment: Proceedings of the 10th Marcel Grossmann Meeting, Rio de Janeiro, July 2003, 6 pages, 1 figur

Dynamic Mutant Subsumption Analysis using LittleDarwin

Many academic studies in the field of software testing rely on mutation testing to use as their comparison criteria. However, recent studies have shown that redundant mutants have a significant effect on the accuracy of their results. One solution to this problem is to use mutant subsumption to detect redundant mutants. Therefore, in order to facilitate research in this field, a mutation testing tool that is capable of detecting redundant mutants is needed. In this paper, we describe how we improved our tool, LittleDarwin, to fulfill this requirement