Non-gaussianity from the second-order cosmological perturbation

Several conserved and/or gauge invariant quantities described as the second-order curvature perturbation have been given in the literature. We revisit various scenarios for the generation of second-order non-gaussianity in the primordial curvature perturbation \zeta, employing for the first time a unified notation and focusing on the normalisation f_{NL} of the bispectrum. When the classical curvature perturbation first appears a few Hubble times after horizon exit, |f_{NL}| is much less than 1 and is, therefore, negligible. Thereafter \zeta (and hence f_{NL}) is conserved as long as the pressure is a unique function of energy density (adiabatic pressure). Non-adiabatic pressure comes presumably only from the effect of fields, other than the one pointing along the inflationary trajectory, which are light during inflation (`light non-inflaton fields'). During single-component inflation f_{NL} is constant, but multi-component inflation might generate |f_{NL}| \sim 1 or bigger. Preheating can affect f_{NL} only in atypical scenarios where it involves light non-inflaton fields. The curvaton scenario typically gives f_{NL} \ll -1 or f_{NL} = +5/4. The inhomogeneous reheating scenario can give a wide range of values for f_{NL}. Unless there is a detection, observation can eventually provide a limit |f_{NL}| \lsim 1, at which level it will be crucial to calculate the precise observational limit using second order theory.Comment: Latex file in Revtex style. 13 pages, 1 figure. v2: minor changes. Discussion in Subsection VI-A enlarged. References added. Conclusions unchanged. v3: minor typographic changes. Correlated and uncorrelated \chi^2 non-gaussianity concepts and consequences introduced. Section VI-A enlarged. Small change in Table I. References updated and added. Conclusions unchanged. Version to appear in Physical Review

Teaching controversial issues: Talking about religious freedom and the imagined ‘other’

Symposium: Teaching Controversial Issues Lee Jerome, Judy Pace, Helen Young, Sally Elton-Chalcraft and Anna Liddle The call to tackle controversial issues in citizenship, history, and other social studies disciplines increases as the world faces greater social, political, and economic crises (Kerr & Huddleston, 2015). Teachers’ ability to frame issues and their relevant content knowledge, utilize effective pedagogies, and create a supportive atmosphere is essential (Hahn, 1998). Controversial issues are "those problems and disputes that divide society and for which significant groups within society offer conflicting explanations and solutions based on alternative values" (Stradling et al., 1984, p. 2). They include public issues, related, for example, to terrorism, reproductive rights, and immigration (Hess, 2009), and sensitive questions related to contested histories (Foster, 2014) such as the partition of Ireland and culpability for genocide. Research shows that the discussion of controversial issues in an open classroom climate develops political knowledge and engagement (Hess & McAvoy, 2015) as well as tolerance (Avery, 2002). But teaching them successfully requires a particular set of knowledge, skills, and dispositions (Hess, 2009). Identifying an issue as controversial may be controversial itself (Camicia, 2008) and issues considered intensely controversial in some countries (e.g. gay marriage, collective health care) may be less so in others, and issues become more or less controversial over time (Hess, 2009). Therefore, teaching controversial issues often involves risk-taking (Kitson & McCully, 2005). Curricular resources and pedagogical structures can assist greatly, but school curriculum, culture, and policy can impede teachers’ efforts. In this symposium we share recent research that explores curricular, pedagogic, and policy implications of pursuing open explorations of controversial issues. Paper 1: Learning to teach controversial issues: Developmental and Contextual Factors How do preservice teachers learn to teach controversial issues in citizenship, social studies, and history? What factors support and constrain their risk-taking? This paper takes up Kitson & McCully’s (2005) continuum of risk-taking and reports findings from a study on preparing preservice teachers to teach controversial issues, conducted in Northern Ireland, England, and the United States. Out of 15 interviewed, 12 creatively used tools from their methods courses to teach lessons that made students explore different perspectives on an important issue. The novices practiced "contained risk-taking" (Author): They espoused social aims but only some taught to these aims. They used provocative resources but critical examination of them was minimal. They used dialogic pedagogies but sustained discussion was limited. Linkages between history and current concerns close to home were made in Northern Ireland but not in England. Factors that supported or constrained risk-taking included curriculum, timetables, students, mentor teachers, and school culture. The paper discusses implications for teacher education and school policy. Paper 2: Enabling young people to build their understanding of terrorism and extremism? A review of resources. This paper reviews the teaching resources on the Educate Against Hate website (DfE, on-line), which has been developed by the UK government ‘to provide practical advice, support and resources to protect children from extremism and radicalisation.’ The paper considers the resources in relation to research which has previously indicated what young people say they want and need (e.g. Jerome & Elwick, 2019), exploring their provenance; their adoption of counter-narratives; their levels of bias; their avoidance of issues; and their overall coherence. The paper concludes that the resources fall significantly short of young people’s expectations and often represent simplistic and uncritical counter-narratives. It argues that a genuinely educational approach will take more heed of young people’s opinions, and engage in a more critical exploration of the issues in order to support young people to build their understanding and make sense of their world post-9/11. Paper 3: Talking about religious freedom and the imagined ‘other’ This paper reports on student discussions in small groups and whole class plenaries related to religious freedom and toleration. We reflect on the ways in which students engaged with the stimulus material offered to them and illustrate how they often used their imagination to move significantly beyond the facts they were given. We argue this reflects a playful commitment to develop cognitive empathy and de-centre their discussions through forms of thought experiment, and that this therefore reflects the need to recognise the legitimate other in such debates. Our findings have implications for whether / how the fundamental British values should be taught more critically as controversial issues

Non-Gaussianity in Axion N-flation Models

We study perturbations in the multifield axion N-flation model, taking account of the full cosine potential. We find significant differences from previous analyses which made a quadratic approximation to the potential. The tensor-to-scalar ratio and the scalar spectral index move to lower values, which nevertheless provide an acceptable fit to observation. Most significantly, we find that the bispectrum non-Gaussianity parameter fNL may be large, typically of order 10 for moderate values of the axion decay constant, increasing to of order 100 for decay constants slightly smaller than the Planck scale. Such a non-Gaussian fraction is detectable. We argue that this property is generic in multifield models of hilltop inflation

False Vacuum Inflation with a Quartic Potential

We consider a variant of Hybrid Inflation, where inflation is driven by two interacting scalar fields, one of which has a `Mexican hat' potential and the other a quartic potential. Given the appropriate initial conditions one of the fields can be trapped in a false vacuum state, supported by couplings to the other field. The energy of this vacuum can be used to drive inflation, which ends when the vacuum decays to one of its true minima. Depending on parameters, it is possible for inflation to proceed via two separate epochs, with the potential temporarily steepening sufficiently to suspend inflation. We use numerical simulations to analyse the possibilities, and emphasise the shortcomings of the slow-roll approximation for analysing this scenario. We also calculate the density perturbations produced, which can have a spectral index greater than one.Comment: 10 pages, RevTeX 3.0, no figure

Stochastic approaches to inflation model building

While inflation gives an appealing explanation of observed cosmological data, there are a wide range of different inflation models, providing differing predictions for the initial perturbations. Typically models are motivated either by fundamental physics considerations or by simplicity. An alternative is to generate large numbers of models via a random generation process, such as the flow equations approach. The flow equations approach is known to predict a definite structure to the observational predictions. In this paper, we first demonstrate a more efficient implementation of the flow equations exploiting an analytic solution found by Liddle (2003). We then consider alternative stochastic methods of generating large numbers of inflation models, with the aim of testing whether the structures generated by the flow equations are robust. We find that while typically there remains some concentration of points in the observable plane under the different methods, there is significant variation in the predictions amongst the methods considered.Comment: 7 pages RevTeX4 with 7 figures. Updated to match version accepted by PRD. Calculations extended to sixth-order and extra clarifications adde

Can We See Lorentz-Violating Vector Fields in the CMB?

We investigate the perturbation theory of a fixed-norm, timelike Lorentz-violating vector field. After consistently quantizing the vector field to put constraints on its parameters, we compute the primordial spectra of perturbations generated by inflation in the presence of this vector field. We find that its perturbations are sourced by the perturbations of the inflaton; without the inflaton perturbation the vector field perturbations decay away leaving no primordial spectra of perturbations. Since the inflaton perturbation does not have a spin-1 component, the vector field generically does not generate any spin-1 ``vector-type'' perturbations. Nevertheless, it will modify the amplitude of both the spin-0 ``scalar-type'' and spin-2 ``tensor-type'' perturbation spectra, leading to violations of the inflationary consistency relationship.Comment: 36 pages, 1 fig, RevTex4, Submitted to PR

Expansion-Free Evolving Spheres Must Have Inhomogeneous Energy Density Distributions

In a recent paper a systematic study on shearing expansion-free spherically symmetric distributions was presented. As a particular case of such systems, the Skripkin model was mentioned, which corresponds to a nondissipative perfect fluid with a constant energy density. Here we show that such a model is inconsistent with junction conditions. It is shown that in general for any nondissipative fluid distribution, the expansion-free condition requires the energy density to be inhomogeneous. As an example we consider the case of dust, which allows for a complete integration.Comment: 8 pages, Latex. To appear in Phys. Rev.D. Typos correcte

The Small Scale Velocity Dispersion of Galaxies: A Comparison of Cosmological Simulations

The velocity dispersion of galaxies on small scales ($r\sim1h^{-1}$ Mpc), $\sigma_{12}(r)$, can be estimated from the anisotropy of the galaxy-galaxy correlation function in redshift space. We apply this technique to ``mock-catalogs'' extracted from N-body simulations of several different variants of Cold Dark Matter dominated cosmological models to obtain results which may be consistently compared to similar results from observations. We find a large variation in the value of $\sigma_{12}(1 h^{-1} Mpc)$ in different regions of the same simulation. We conclude that this statistic should not be considered to conclusively rule out any of the cosmological models we have studied. We attempt to make the statistic more robust by removing clusters from the simulations using an automated cluster-removing routine, but this appears to reduce the discriminatory power of the statistic. However, studying $\sigma_{12}$ as clusters with different internal velocity dispersions are removed leads to interesting information about the amount of power on cluster and subcluster scales. We also compute the pairwise velocity dispersion directly and compare this to the values obtained using the Davis-Peebles method, and find that the agreement is fairly good. We evaluate the models used for the mean streaming velocity and the pairwise peculiar velocity distribution in the original Davis-Peebles method by comparing the models with the results from the simulations.Comment: 20 pages, uuencoded (Latex file + 8 Postscript figures), uses AAS macro