Nongaussianity from Particle Production During Inflation

In a variety of models the motion of the inflaton may trigger the production of some non-inflaton particles during inflation, for example via parametric resonance or a phase transition. Such models have attracted interest recently for a variety of reasons, including the possibility of slowing the motion of the inflaton on a steep potential. In this review we show that interactions between the produced particles and the inflaton condensate can lead to a qualitatively new mechanism for generating cosmological fluctuations from inflation. We illustrate this effect using a simple prototype model g^2 (\phi-\phi_0)^2\chi^2 for the interaction between the inflaton, \phi, and iso-inflaton, \chi. Such interactions are quite natural in a variety of inflation models from supersymmetry and string theory. Using both lattice field theory simulations and analytical calculations, we study the quantum production of \chi particles and their subsequent rescatterings off the condensate \phi(t), which generates bremsstrahlung radiation of light inflaton fluctuations \delta\phi. This mechanism leads to observable features in the primordial power spectrum. We derive observational constraints on such features and discuss their implications for popular models of inflation, including brane/axion monodromy. Inflationary particle production also leads to a very novel kind of nongaussian signature which may be observable in future missions. We argue that this mechanism provides a simple and well-motivated option to generate large nongaussianity, without fine-tuning the inflationary trajectory or appealing to re-summation of an infinite series of high dimension operators.Comment: 53 pages, 15 figures. Invited review article, published in Advances in Astronom

Improving PSF modelling for weak gravitational lensing using new methods in model selection

A simple theoretical framework for the description and interpretation of spatially correlated modelling residuals is presented, and the resulting tools are found to provide a useful aid to model selection in the context of weak gravitational lensing. The description is focused upon the specific problem of modelling the spatial variation of a telescope point spread function (PSF) across the instrument field of view, a crucial stage in lensing data analysis, but the technique may be used to rank competing models wherever data are described empirically. As such it may, with further development, provide useful extra information when used in combination with existing model selection techniques such as the Akaike and Bayesian Information Criteria, or the Bayesian evidence. Two independent diagnostic correlation functions are described and the interpretation of these functions demonstrated using a simulated PSF anisotropy field. The efficacy of these diagnostic functions as an aid to the correct choice of empirical model is then demonstrated by analyzing results for a suite of Monte Carlo simulations of random PSF fields with varying degrees of spatial structure, and it is shown how the diagnostic functions can be related to requirements for precision cosmic shear measurement. The limitations of the technique, and opportunities for improvements and applications to fields other than weak gravitational lensing, are discussed.Comment: 18 pages, 12 figures. Modified to match version accepted for publication in MNRA

QCSP on partially reflexive forests

We study the (non-uniform) quantified constraint satisfaction problem QCSP(H) as H ranges over partially reflexive forests. We obtain a complexity-theoretic dichotomy: QCSP(H) is either in NL or is NP-hard. The separating condition is related firstly to connectivity, and thereafter to accessibility from all vertices of H to connected reflexive subgraphs. In the case of partially reflexive paths, we give a refinement of our dichotomy: QCSP(H) is either in NL or is Pspace-complete

A New Formulation of the Initial Value Problem for Nonlocal Theories

There are a number of reasons to entertain the possibility that locality is violated on microscopic scales, for example through the presence of an infinite series of higher derivatives in the fundamental equations of motion. This type of nonlocality leads to improved UV behaviour, novel cosmological dynamics and is a generic prediction of string theory. On the other hand, fundamentally nonlocal models are fraught with complications, including instabilities and complications in setting up the initial value problem. We study the structure of the initial value problem in an interesting class of nonlocal models. We advocate a novel new formulation wherein the Cauchy surface is "smeared out" over the underlying scale of nonlocality, so that the the usual notion of initial data at t=0 is replaced with an "initial function" defined over -M^{-1} \leq t \leq 0 where M is the underlying scale of nonlocality. Focusing on some specific examples from string theory and cosmology, we show that this mathematical re-formulation has surprising implications for the well-known stability problem. For D-brane decay in a linear dilaton background, we are able to show that the unstable directions in phase space cannot be accessed starting from a physically sensible initial function. Previous examples of unstable solutions in this model therefore correspond to unphysical initial conditions, an observation which is obfuscated in the old formulation of the initial value problem. We also discuss implication of this approach for nonlocal cosmological models.Comment: 36 pages, 9 figures. Accepted for publication in Nuclear Physics