scholarly journals TRIANGLES IN THE de-SITTER PLANE

2019 ◽  
Vol 40 (2) ◽  
pp. 499-511
Author(s):  
Tuğba MERT
Keyword(s):  
De Sitter ◽  
De Sitter Plane

scholarly journals K teorii ploscadej giperboliceskoj ploskosti polozitel'noj krivizny

2016 ◽  
Vol 99 (113) ◽  
pp. 139-154 ◽  
Author(s):  
L.N. Romakina
Keyword(s):  
Hyperbolic Plane ◽  
Positive Curvature ◽  
De Sitter ◽  
Coordinate Systems ◽  
Projective Model ◽  
Orthogonal Coordinate Systems ◽  
De Sitter Plane

A hyperbolic plane ? of positive curvature is the projective model of the de Sitter plane. In article the ways of measurement of the figures areas of the plane ? are offered. The cyclic orthogonal coordinate systems are described. One family of coordinate curves in such systems form by concentric cycles (by hyperbolic cycles, elliptic cycles or oricycles). Other family of coordinate curves form by the axes of these cycles. The formulas for the calculation of the figures areas of the plane ? are received.

scholarly journals Classification of curves on de Sitter plane

2020 ◽  
Vol 13 (1) ◽  
pp. 1-8
Author(s):  
Irina Streltsova
Keyword(s):  
Differential Invariant ◽  
Differential Invariants ◽  
Minkowski Geometry ◽  
De Sitter ◽  
Gravitational Fields ◽  
Singular Orbits ◽  
Sitter Model ◽  
The Universe ◽  
De Sitter Plane

In 1917, de Sitter used the modified Einstein equation and proposed a model of the Universe without physical matter, but with a cosmological constant. De Sitter geometry, as well as Minkowski geometry, is maximally symmetrical. However, de Sitter geometry is better suited to describe gravitational fields. It is believed that the real Universe was described by the de Sitter model in the very early stages of expansion (inflationary model of the Universe). This article is devoted to the problem of classification of regular curves on the de Sitter space. As a model of the de Sitter plane, the upper half-plane on which the metric is given is chosen. For this purpose, an algebra of differential invariants of curves with respect to the motions of the de Sitter plane is constructed. As it turned out, this algebra is generated by one second-order differential invariant (we call it by de Sitter curvature) and two invariant differentiations. Thus, when passing to the next jets, the dimension of the algebra of differential invariants increases by one. The concept of regular curves is introduced. Namely, a curve is called regular if the restriction of de Sitter curvature to it can be considered as parameterization of the curve. A theorem on the equivalence of regular curves with respect to the motions of the de Sitter plane is proved. The singular orbits of the group of proper motions are described.

Cosmological spacetimes

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Cosmological Model ◽  
Large Scale ◽  
Cosmic Time ◽  
De Sitter ◽  
Matter Distribution ◽  
Observable Universe ◽  
Cosmological Principle ◽  
Riemannian Spacetime ◽  
The Universe ◽  
Copernican Principle

This chapter provides a few examples of representations of the universe on a large scale—a first step in constructing a cosmological model. It first discusses the Copernican principle, which is an approximation/hypothesis about the matter distribution in the observable universe. The chapter then turns to the cosmological principle—a hypothesis about the geometry of the Riemannian spacetime representing the universe, which is assumed to be foliated by 3-spaces labeled by a cosmic time t which are homogeneous and isotropic, that is, ‘maximally symmetric’. After a discussion on maximally symmetric space, this chapter considers spacetimes with homogenous and isotropic sections. Finally, this chapter discusses Milne and de Sitter spacetimes.

scholarly journals Systematics of type IIA moduli stabilisation

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Fernando Marchesano ◽  
David Prieto ◽  
Joan Quirant ◽  
Pramod Shukla
Keyword(s):  
Scalar Potential ◽  
Systematic Search ◽  
Stability Criteria ◽  
De Sitter ◽  
Large Subset

Abstract We analyse the flux-induced scalar potential for type IIA orientifolds in the presence of p-form, geometric and non-geometric fluxes. Just like in the Calabi-Yau case, the potential presents a bilinear structure, with a factorised dependence on axions and saxions. This feature allows one to perform a systematic search for vacua, which we implement for the case of geometric backgrounds. Guided by stability criteria, we consider configurations with a particular on-shell F-term pattern, and show that no de Sitter extrema are allowed for them. We classify branches of supersymmetric and non-supersymmetric vacua, and argue that the latter are perturbatively stable for a large subset of them. Our solutions reproduce and generalise previous results in the literature, obtained either from the 4d or 10d viewpoint.

scholarly journals Massive Dirac quasinormal modes in Schwarzschild–de Sitter black holes: Anomalous decay rate and fine structure

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Almendra Aragón ◽  
Ramón Bécar ◽  
P. A. González ◽  
Yerko Vásquez
Keyword(s):  
Black Holes ◽  
Fine Structure ◽  
Decay Rate ◽  
Quasinormal Modes ◽  
De Sitter

scholarly journals Winding uplifts and the challenges of weak and strong SUSY breaking in AdS

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Arthur Hebecker ◽  
Sascha Leonhardt
Keyword(s):  
Complex Structure ◽  
Susy Breaking ◽  
Technical Level ◽  
De Sitter ◽  
Large Complex ◽  
Breaking Scale ◽  
Large Complex Structure

Abstract We discuss the problem of metastable SUSY breaking in the landscape. While this is clearly crucial for the various de Sitter proposals, it is also interesting to consider the SUSY breaking challenge in the AdS context. For example, it could be that a stronger form of the non-SUSY AdS conjecture holds: it would forbid even metastable non-SUSY AdS in cases where the SUSY-breaking scale is parametrically above/below the AdS scale. At the technical level, the present paper proposes to break SUSY using the multi-cosine-shaped axion potentials which arise if a long winding trajectory of a ‘complex-structure axion’ appears in the large-complex-structure limit of a Calabi-Yau orientifold. This has been studied in the context of ‘Winding Inflation’, but the potential for SUSY breaking has not been fully explored. We discuss the application to uplifting LVS vacua, point out the challenges which one faces in the KKLT context, and consider the possibility of violating the non-SUSY AdS conjecture in the type-IIA setting of DGKT.

scholarly journals Unimodular vs nilpotent superfield approach to pure dS supergravity

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sukruti Bansal ◽  
Silvia Nagy ◽  
Antonio Padilla ◽  
Ivonne Zavala
Keyword(s):  
String Theory ◽  
General Framework ◽  
Recent Progress ◽  
High Energy ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
New Approach ◽  
Sitter Spacetime ◽  
Novel Approach ◽  
De Sitter Vacua

Abstract Recent progress in understanding de Sitter spacetime in supergravity and string theory has led to the development of a four dimensional supergravity with spontaneously broken supersymmetry allowing for de Sitter vacua, also called de Sitter supergravity. One approach makes use of constrained (nilpotent) superfields, while an alternative one couples supergravity to a locally supersymmetric generalization of the Volkov-Akulov goldstino action. These two approaches have been shown to give rise to the same 4D action. A novel approach to de Sitter vacua in supergravity involves the generalisation of unimodular gravity to supergravity using a super-Stückelberg mechanism. In this paper, we make a connection between this new approach and the previous two which are in the context of nilpotent superfields and the goldstino brane. We show that upon appropriate field redefinitions, the 4D actions match up to the cubic order in the fields. This points at the possible existence of a more general framework to obtain de Sitter spacetimes from high-energy theories.

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