Topic
Scalar curvature
About: Scalar curvature is a research topic. Over the lifetime, 12701 publications have been published within this topic receiving 296040 citations. The topic is also known as: Ricci scalar.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: In this article, the covariant bispectrum is computed for a system of slowly-rolling scalar fields during an inflationary epoch, allowing for an arbitrary field-space metric, and the subsequent evolution using a covariantized version of the separate universe or "delta-N" expansion.
Abstract: We compute the covariant three-point function near horizon-crossing for a system of slowly-rolling scalar fields during an inflationary epoch, allowing for an arbitrary field-space metric. We show explicitly how to compute its subsequent evolution using a covariantized version of the separate universe or "delta-N" expansion, which must be augmented by terms measuring curvature of the field-space manifold, and give the nonlinear gauge transformation to the comoving curvature perturbation. Nonlinearities induced by the field-space curvature terms are a new and potentially significant source of non-Gaussianity. We show how inflationary models with non-minimal coupling to the spacetime Ricci scalar can be accommodated within this framework. This yields a simple toolkit allowing the bispectrum to be computed in models with non-negligible field-space curvature.
86 citations
••
86 citations
••
12 Mar 2002TL;DR: In this paper, sharp local isoperimetric inequalities on Riemannian manifolds involving the scalar curvature are provided. But they do not answer the question asked by Johnson and Morgan.
Abstract: We provide sharp local isoperimetric inequalities on Riemannian manifolds involving the scalar curvature, and thus answer a question asked by Johnson and Morgan.
86 citations
••
TL;DR: In this paper, the authors considered universal lower bounds on the volume of a Riemannian manifold, given in terms of the volumes of lower dimensional objects (primarily the lengths of geodesics).
Abstract: In this survey article we will consider universal lower bounds on the volume of a Riemannian manifold, given in terms of the volume of lower dimensional objects (primarily the lengths of geodesics). By ‘universal’ we mean without curvature assumptions. The restriction to results with no (or only minimal) curvature assumptions, although somewhat arbitrary, allows the survey to be reasonably short. Although, even in this limited case the authors have left out many interesting results.
85 citations