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

On a modular property of N=2 superconformal theories in four dimensions

In this note we discuss several properties of the Schur index of N=2 superconformal theories in four dimensions. In particular, we study modular properties of this index under SL(2,Z) transformations of its parameters.Comment: 23 page, 2 figure

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

Unstable superheavy relic particles as a source of neutrinos responsible for the ultrahigh-energy cosmic rays

Decays of superheavy relic particles may produce extremely energetic neutrinos. Their annihilations on the relic neutrinos can be the origin of the cosmic rays with energies beyond the Greisen-Zatsepin-Kuzmin cutoff. The red shift acts as a cosmological filter selecting the sources at some particular value z_e, for which the present neutrino energy is close to the Z pole of the annihilation cross section. We predict no directional correlation of the ultrahigh-energy cosmic rays with the galactic halo. At the same time, there can be some directional correlations in the data, reflecting the distribution of matter at red shift z=z_e. Both of these features are manifest in the existing data. Our scenario is consistent with the neutrino mass reported by Super-Kamiokande and requires no lepton asymmetry or clustering of the background neutrinos.Comment: 3 pages, revtex; references adde

Non-canonical generalizations of slow-roll inflation models

We consider non-canonical generalizations of two classes of simple single-field inflation models. First, we study the non-canonical version of "ultra-slow roll" inflation, which is a class of inflation models for which quantum modes do not freeze at horizon crossing, but instead evolve rapidly on superhorizon scales. Second, we consider the non-canonical generalization of the simplest "chaotic" inflation scenario, with a potential dominated by a quartic (mass) term for the inflaton. We find a class of related non-canonical solutions with polynomial potentials, but with varying speed of sound. These solutions are characterized by a constant field velocity, and we dub such models {\it isokinetic} inflation. As in the canonical limit, isokinetic inflation has a slightly red-tilted power spectrum, consistent with current data. Unlike the canonical case, however, these models can have an arbitrarily small tensor/scalar ratio. Of particular interest is that isokinetic inflation is marked by a correlation between the tensor/scalar ratio and the amplitude of non-Gaussianity such that parameter regimes with small tensor/scalar ratio have {\it large} associated non-Gaussianity, which is a distinct observational signature.Comment: 12 pages, 3 figures, LaTeX; V2: version submitted to JCAP. References adde

Priority concerns for people with intellectual and developmental disabilities during the COVID-19 pandemic

BACKGROUND: The approach taken to support individuals during the coronavirus disease 2019 (COVID-19) pandemic needs to take into account the requirements of people with intellectual disabilities and/or autism, who represent a major vulnerable group, with higher rates of co-occurring health conditions and a greater risk of dying prematurely. To date, little evidence on COVID-related concerns have been produced and no report has provided structured feedback from the point of view of people with intellectual disabilities and/or autism or of their family/carers. AIMS: To provide systemised evidence-based information of the priority concerns for people with intellectual disabilities and/or autism regarding the COVID-19 pandemic. METHOD: Senior representatives of major UK-based professional and service-user representative organisations with a stake in the care of people with intellectual disabilities and/or autism were contacted to provide a list of concerns across three domains: 'mental health and challenging behaviour', 'physical health and epilepsy' and 'social circumstances and support'. The feedback was developed into statements on frequently reported priorities. These statements were then rated independently by expert clinicians. A video-conference meeting to reconcile outliers and to generate a consensus statement list was held. RESULTS: Thirty-two organisations were contacted, of which 26 (81%) replied. From the respondent's data, 30 draft consensus statements were generated. Following expert clinician review, there was initially strong consensus for seven statements (23%), increasing to 27 statements (90%) following video conferencing. CONCLUSIONS: These recommendations highlight the expectations of people with intellectual disabilities and/or autism in the current pandemic. This could support policymakers and professionals' deliver and evidence person-centred care

On the Slow Roll Expansion for Brane Inflation

One possibility for identifying the inflaton in the framework of string theory is that it is a $D$-brane modulus. This option involves a specific, non-canonical form of the kinetic energy -- the Dirac-Born-Infeld action. This note investigates the applicability of the slow roll approximation in inflationary models of this type. To this end the slow roll expansion of Liddle, Parsons and Barrow is derived for the case of the DBI action. The resulting slow roll conditions augment the standard ones valid in the case of canonical kinetic terms. It is also shown that in DBI models inflation does not require that the potential dominate the energy density.Comment: References adde

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

A Fermi Surface Model for Large Supersymmetric AdS_5 Black Holes

We identify a large family of 1/16 BPS operators in N=4 SYM that qualitatively reproduce the relations between charge, angular momentum and entropy in regular supersymmetric AdS_5 black holes when the main contribution to their masses is given by their angular momentum.Comment: 32 pages, 6 figures, LaTeX uses JHEP3 class; ver 2- added acknowledgment, minor change

Jet interactions with a giant molecular cloud in the Galactic centre and ejection of hypervelocity stars

The hypervelocity OB stars in the Milky Way Galaxy were ejected from the central regions some 10-100 million years ago. We argue that these stars, {as well as many more abundant bound OB stars in the innermost few parsecs,} were generated by the interactions of an AGN jet from the central black hole with a dense molecular cloud. Considerations of the associated energy and momentum injection have broader implications for the possible origin of the Fermi bubbles and for the enrichment of the intergalactic medium.Comment: 4 pages, 1 figure. Astronomy and Astrophysics Letters, in pres