Numerical calculation of second order perturbations

We numerically solve the Klein-Gordon equation at second order in cosmological perturbation theory in closed form for a single scalar field, describing the method employed in detail. We use the slow-roll version of the second order source term and argue that our method is extendable to the full equation. We consider two standard single field models and find that the results agree with previous calculations using analytic methods, where comparison is possible. Our procedure allows the evolution of second order perturbations in general and the calculation of the non-linearity parameter f_NL to be examined in cases where there is no analytical solution available.Comment: 18 pages, 12 figures; v2 version published by JCA

Second Order Perturbations During Inflation Beyond Slow-roll

We numerically calculate the evolution of second order cosmological perturbations for an inflationary scalar field without resorting to the slow-roll approximation or assuming large scales. In contrast to previous approaches we therefore use the full non-slow-roll source term for the second order Klein-Gordon equation which is valid on all scales. The numerical results are consistent with the ones obtained previously where slow-roll is a good approximation. We investigate the effect of localised features in the scalar field potential which break slow-roll for some portion of the evolution. The numerical package solving the second order Klein-Gordon equation has been released under an open source license and is available for download.Comment: v2: version published in JCAP, references added; v1: 21 pages, 11 figures, numerical package available at http://pyflation.ianhuston.ne

Markerless Motion Capture in the Crowd

This work uses crowdsourcing to obtain motion capture data from video recordings. The data is obtained by information workers who click repeatedly to indicate body configurations in the frames of a video, resulting in a model of 2D structure over time. We discuss techniques to optimize the tracking task and strategies for maximizing accuracy and efficiency. We show visualizations of a variety of motions captured with our pipeline then apply reconstruction techniques to derive 3D structure.Comment: Presented at Collective Intelligence conference, 2012 (arXiv:1204.2991

Constraining Inflationary Scenarios with Braneworld Models and Second Order Cosmological Perturbations

Inflationary cosmology is the leading explanation of the very early universe. Many different models of inflation have been constructed which fit current observational data. In this work theoretical and numerical methods for constraining the parameter space of a wide class of such models are described. First, string-theoretic models with large non-Gaussian signatures are investigated. An upper bound is placed on the amplitude of primordial gravitational waves produced by ultra-violet Dirac-Born-Infeld inflation. In all but the most finely tuned cases, this bound is incompatible with a lower bound derived for inflationary models which exhibit a red spectrum and detectable non-Gaussianity. By analysing general non-canonical actions, a class of models is found which can evade the upper bound when the phase speed of perturbations is small. The multi-coincident brane scenario with a finite number of branes is one such model. For models with a potentially observable gravitational wave spectrum the number of coincident branes is shown to take only small values. The second method of constraining inflationary models is the numerical calculation of second order perturbations for a general class of single field models. The Klein-Gordon equation at second order, written in terms of scalar field variations only, is numerically solved. The slow roll version of the second order source term is used and the method is shown to be extendable to the full equation. This procedure allows the evolution of second order perturbations in general and the calculation of the non-Gaussianity parameter in cases where there is no analytical solution available.Comment: PhD Thesis, Queen Mary, Univ of London, Supervisor: James E. Lidsey. (211 pages, 35 figures

Calculating Non-adiabatic Pressure Perturbations during Multi-field Inflation

Isocurvature perturbations naturally occur in models of inflation consisting of more than one scalar field. In this paper we calculate the spectrum of isocurvature perturbations generated at the end of inflation for three different inflationary models consisting of two canonical scalar fields. The amount of non-adiabatic pressure present at the end of inflation can have observational consequences through the generation of vorticity and subsequently the sourcing of B-mode polarisation. We compare two different definitions of isocurvature perturbations and show how these quantities evolve in different ways during inflation. Our results are calculated using the open source Pyflation numerical package which is available to download.Comment: v2: Typos fixed, references and comments added; v1: 8 pages, 10 figures, software available to download at http://pyflation.ianhuston.ne