Conformal hydrodynamics in Minkowski and de Sitter spacetimes

We show how to generate non-trivial solutions to the conformally invariant, relativistic fluid dynamic equations by appealing to the Weyl covariance of the stress tensor. We use this technique to show that a recently studied solution of the relativistic conformally invariant Navier–Stokes equations in four-dimensional Minkowski space can be recast as a static flow in three-dimensional de Sitter space times a line. The simplicity of the de Sitter form of the flow enables us to consider several generalizations of it, including flows in other spacetime dimensions, second order viscous corrections, and linearized perturbations. We also construct the anti-de Sitter dual of the original four-dimensional flow. Finally, we discuss possible applications to nuclear physics.     

Boltzmann equation in de Sitter space

In a time dependent background like de Sitter space, Feynman–Dyson perturbation theory breaks down due to infra-red divergences. We investigate an interacting scalar field theory in Schwinger–Keldysh formalism. We derive a Boltzmann equation from a Schwinger–Dyson equation inside the cosmological horizon. Our solution shows that the particle production is compensated by the reduction of the on-shell states due to unitarity. Although the degrees of freedom inside the horizon leads to a small and diminishing screening effect of the cosmological constant, there is a growing screening effect from those outside the horizon.     

Phase transitions in de Sitter space

An effective potential in de Sitter space is calculated for a model of two interacting scalar fields in one-loop approximation and in a self-consistent approximation which takes into account an infinite set of diagrams. Various approaches to renormalization in de Sitter space are discussed. The results are applied to analyze the phase transition in the Hawking-Moss version of the inflationary universe scenario. Requiring that inflation is sufficiently large, we derive constraints on the parameters of the model.     

Anisotropic perturbation of de Sitter space

A model-independent expression for the Friedmann equation in Bianchi type spaces is derived. In addition, a model-independent stability analysis of the higher curvature de Sitter solution is discussed. Stability conditions of the de Sitter solution are derived explicitly for a cubic model with interesting effects. It is known that quadratic terms do not contribute to this de Sitter background solution. Higher curvature terms are all critical to the stability of the de Sitter space. PACS 98.80.Cq; 04.20.-q; 04.20.Cv     

Scalar massless field in de Sitter space

A method for quantizing a scalar massless field in the de Sitter space is demonstrated; the method is based on the conformai invariance of the field equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 19–24, July, 1972.The author would like to thank Professor N. A. Chernikov for his aid and É. A. Tagirov for helpful criticism.     

Semiclassical perdurance of de Sitter space

We investigate the classical and semiclassical instabilities of de Sitter space. Due to the presence of a cosmological event horizon and its associated Hawking temperature, de Sitter space might be expected to behave in some respects like flat space at finite temperature. We use the euclidean formulation of quantum gravity to show that de Sitter space does exhibit a semiclassical instability to the nucleation of black holes. We find, however, no analog to the classical instability due to gravitational clumping of thermally excited gravitons.     

The gravitational anomalies in de Sitter space

All solutions to the consistency equations are determined which have to be satisfied by anomalies in gravitational theories with a de Sitter-invariant groundstate. They turn out to be identical with the solutions for a Poincaré-invariant groundstate.     

Entropic uncertainty relation in de Sitter space

The uncertainty principle restricts our ability to simultaneously predict the measurement outcomes of two incompatible observables of a quantum particle. However, this uncertainty could be reduced and quantified by a new Entropic Uncertainty Relation (EUR). By the open quantum system approach, we explore how the nature of de Sitter space affects the EUR. When the quantum memory A$A$ freely falls in the de Sitter space, we demonstrate that the entropic uncertainty acquires an increase resulting from a thermal bath with the Gibbons–Hawking temperature. And for the static case, we find that the temperature coming from both the intrinsic thermal nature of the de Sitter space and the Unruh effect associated with the proper acceleration of A$A$ also brings effect on entropic uncertainty, and the higher the temperature, the greater the uncertainty and the quicker the uncertainty reaches the maximal value. And finally the possible mechanism behind this phenomenon is also explored.     

Analogies between Kruskal space and de Sitter space

The relation between Kruskal and Schwarzschild coordinates is analogous to that between hyperboloid and de Sitter coordinates; the Kruskal diagram is analogous to the hyperboloid diagram; and the crossing over of horizons in Kruskal space is analogous to the well-known crossing over of the particle horizon and the event horizon in cosmology.     

Gravitational radiation in asymptotic de Sitter space

A solution of the gravitational field equations is found by using an axially symmetric metric which is asymptotically a de Sitter space metric. We use the general approach of Bondi, van der Burg, and Metzner as applied to the asymptotic flat-space case and search for the necessary conditions for gravitational radiation in asymptotic de Sitter space. We find that the character of the gravitational radiation, if it exists at all, is considerably different from that obtained in the case of asymptotic flat space.     

第五讲暗能量和德西特时空

最近的天文观测表明，宇宙是在加速膨胀，而不是原来认为的减速膨胀．为解释加速膨胀，必须在宇宙的物质能量中引入暗能量这一成分，文章讨论了暗能量的可能侯选者，特别强调了宇宙常数问题、德西特时空问题以及和德西特时空相关的一些基本问题．     

Warped compactification to de Sitter space

We explore in detail the prospects of obtaining a four-dimensional de Sitter universe in classical supergravity models with warped and time-independent extra dimensions, presenting explicit cosmological solutions of the (4+n)$(4+n)$-dimensional Einstein equations with and without a bulk cosmological constant term. For the first time in the literature we show that there may exist a large class of warped supergravity models with a noncompact extra dimension which lead to a finite 4D Newton constant as well as a massless 4D graviton localized on an inflating four-dimensional FLRW universe. This result helps establish that the ‘no-go’ theorem forbidding acceleration in ‘standard’ compactification of string/M-theory on physically compact spaces should not apply to a general class of warped supergravity models that allows at least one noncompact direction. We present solutions for which the size of the radial dimension takes a constant value in the large volume limit, providing an explicit example of spontaneous compactification.