Narrow Results

In this paper, we establish the notion of (r, s)-stability concerning spacelike hypersurfaces with higher-order mean curvatures linearly related in conformally stationary spacetimes of constant sectional curvature. In this setting, we characterize (r, s)-stable closed spacelike hypersurfaces through the analysis of the first eigenvalue of an operator naturally attached to the higher-order mean curvatures. Moreover, we obtain sufficient conditions which assure the (r, s)-stability of complete spacelike hypersurfaces immersed in the de Sitter space.

We study the wave equation for a minimally coupled massive scalar in three-dimensional de Sitter space. We compute the absorption cross-section to investigate its cosmological horizon in the southern diamond. Although the absorption cross-section is not defined exactly, it can be determined from the fact that the low-energy s(j = 0)-wave absorption cross-section for a massless scalar is given by the area of the cosmological horizon. On the other hand, the low-temperature limit of j ≠ 0-mode absorption cross-section is useful for extracting information surrounding the cosmological horizon. Finally we mention a computation of the absorption cross-section on the CFT-side using the dS/CFT correspondence.

The study of BTZ blackhole physics and the cosmological horizon of 3D de Sitter spaces are carried out in unified way using the connections to the Chern Simons theory on three manifolds with boundary. The relations to CFT on the boundary is exploited to construct exact partition functions and obtain logarithmic corrections to Bekenstein formula in the asymptotic regime. Comments are made on the dS/CFT correspondence frising from these studies.

Based on some important properties of dS space, we present a Beltrami model ℬ_Λ that may shed light on the observable puzzle of dS space and the paradox between the special relativity principle and cosmological principle. In ℬ_Λ, there are inertial-type coordinates and inertial-type observers. Thus, the classical observables can be defined for test particles and light signals. In addition, by choosing the definition of simultaneity the Beltrami metric is transformed to the Robertson–Walker-like metric. It is of positive spatial curvature of order Λ. This has already been shown by the CMB power spectrum from WMAP and should be further confirmed by its data in large scale.

In lattice Schrödinger picture, the wave functionals of a free real scalar field in de Sitter space for the Bunch–Davies vacuum and the corresponding excited states are given explicitly in momentum space for the following coupling cases: (i) massless conformal couplng, (ii) massless minimal coupling, and (iii) massive minimal coupling. Implications of these solutions for inflationary scenarios in cosmology are also discussed.

Using properly defined Feynman propagator we obtain nonzero imaginary contribution to the scalar field effective action in even-dimensional de Sitter space. Such a propagator follows from the path integral in de Sitter space and obeys composition principle proposed in arXiv:0709.2899. The obtained expression for the effective action shows particle production with the Gibbons–Hawking rate.

We propose a solution to the longstanding cosmological constant (CC) problem which is based on the fusion of two existing concepts. The first is the suggestion that the proper description of classical gravitational effects is the gauge theory of gravity in which the connection instead of the metric acts as the dynamical variable. The resulting field equation does not then contain the CC term. This removes the connection between the CC and the quantum vacuum energy, and therefore addresses the old CC problem of why quantum vacuum energy does not gravitate. The CC-equivalent in this approach arises from the constant of integration when reducing the field equation to the Einstein equation. The second is the assumption that the universe obeys de Sitter symmetry, with the observed accelerating expansion as its manifestation. We combine these ideas and identify the constant of integration with the inverse-square of the radius of curvature of the de Sitter space. The origin of dark energy (DE) is therefore associated with the inherent spacetime geometry, with the smallness of DE protected by symmetry. This addresses the new CC problem, or the DE puzzle. This approach, however, faces major challenges from quantum considerations. These are the ghost problem associated with higher order gravity theories and the quantum instability of the de Sitter spacetime. We discuss their possible remedies.

We give an interpretation of the temperature in de Sitter universe in terms of a dynamical Unruh effect associated with the Hubble sphere. As with the quantum noise perceived by a uniformly accelerated observer in static spacetimes, observers endowed with a proper motion can in principle detect the effect. In particular, we study a "Kodama observer" as a two-field Unruh detector for which we show the effect is approximately thermal. We also estimate the back-reaction of the emitted radiation and find trajectories associated with the Kodama vector field are stable.

We analyze the propagation of gravitational waves (GWs) in an asymptotically de Sitter space by expanding the perturbation around Minkowski and introducing the effects of the Cosmological Constant (Λ), first as an additional source (de-Donder gauge) and after as a gauge effect (Λ-gauge). In both cases the inclusion of the Cosmological Constant Λ, impedes the detection of a gravitational wave at a distance larger than , where and f and are the frequency and strain of the wave, respectively. We demonstrate that L_c is just a confirmation of the cosmic no hair conjecture (CNC) already explained in the literature.

In this paper, we study the massive spin-½ particle creation in de Sitter (dS) space where the related fields are written in (4+1)-dimensional bulk or the so-called ambient space approach. This approach mimics the flat space quantum field theory (QFT) and the field operators are defined globally on dS space. The main purpose of this study is defining the |in〉 and |out〉 modes for the proposed quantum field which has been written in terms of the dS plane wave in the 4+1 dimensions. We compute, via the Bogoliubov coefficients, the rate of particle creation in dS universe.

We reconsider a recent perturbative calculation [M. A. Băloi, Mod. Phys. Lett. A29, 1450138 (2014)] of particle production in the expanding de Sitter space in an external electromagnetic field and apply it to the case of a constant uniform electric field in two dimensions. We show that perturbative number of created particles significantly differs from the existing nonperturbative result based on the Bogoliubov transformation method. We also point out that for a physically meaningful perturbative amplitude one should restrict to external potentials A_μ which in conformal coordinates vanish at infinite times. Potentials which do not respect this condition lead to gauge-dependent amplitudes, which also show close similarities with amplitudes in flat space in the unphysical case when the external potential suddenly vanishes. These problems are intimately linked with the finite upper limit of the conformal time in the de Sitter space and most probably a similar restriction should be imposed in perturbative calculations in FRW spacetimes with the same property.

In this paper, we study the problem of scalar particle production in external electric field in de Sitter geometry. The total probability is calculated using the previously obtained result in [M. A. Băloi, Mod. Phys. Lett. A29, 1450138 (2014)] for transition amplitude in external electric field on de Sitter space. Then we make a graphical study of the total probability in terms of the ratio mass of the particle/expansion factor. Our results show that the probability depend on the direction in which the particles are emitted and that the probability becomes maximum when particles are emitted on the direction of the electric field. In the Minkowski limit, we obtain that the probability is vanishing.

We study the thermodynamic properties of Schwarzschild–de Sitter (SdS) black hole and Reissner–Nordström–de Sitter (RNdS) black hole in view of global and effective thermodynamic quantities. Making use of the effective first law of thermodynamics, we can derive the effective thermodynamic quantities of de Sitter black holes. It is found that these effective thermodynamic quantities also satisfy Smarr-like formula. Especially, the effective temperatures are nonzero in the Nariai limit. By calculating heat capacity and Gibbs free energy, we find SdS black hole is always thermodynamically stable and RNdS black hole may undergoes phase transition at some points.

The Casimir forces on two parallel plates in conformally flat de Sitter background due to conformally coupled massless scalar field satisfying mixed boundary conditions on the plates is investigated. In the general case of mixed boundary conditions formulae are derived for the vacuum expectation values of the energy–momentum tensor and vacuum forces acting on boundaries. Different cosmological constants are assumed for the space between and outside of the plates to have general results applicable to the case of domain wall formations in the early universe.

The Casimir forces on two parallel plates moving by uniform proper acceleration in static de Sitter background due to conformally coupled massless scalar field satisfying Dirichlet boundary conditions on the plates is investigated. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy–momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.

The Casimir stress on two parallel plates in a de Sitter background corresponding to different metric signatures and cosmological constants is calculated for massless scalar fields satisfying Robin boundary conditions on the plates. Our calculation shows that for the parallel plates with false vacuum between and true vacuum outside, the total Casimir pressure leads to an attraction of the plates at very early universe.

After a brief review of the linearized gravity in de Sitter (dS) four-dimensional space and ambient flat five-dimensional notations, the linearized field equation is written in terms of the Casimir operators of dS group. It is shown that the field equation is gauge invariant under some special gauge transformations. Because of this gauge freedom, a gauge-fixing parameter c is inserted in the field equation. It is shown that the solution to the field equation can be written as the multiplication of a generalized symmetric rank-2 polarization tensor and a massless minimally coupled scalar field in ambient space notations. The graviton two-point function has been thoroughly calculated, which is dS-invariant and free of any divergences. This two-point function has been expressed in terms of the intrinsic dS coordinates, from its ambient space counterpart, which is clearly dS-invariant and free of any divergences again.

Based on conformal invariance and using Dirac's six-cone formalism, a new conformally invariant physical field equation for de Sitter (dS) linear gravity has been obtained, which corresponds to one of the unitary irreducible representations of the dS group and is denoted by in the sense of discrete series. Using ambient space notations, it has been shown that the solution to this new field equation can be written as the multiplication of a generalized symmetric polarization tensor of rank 2 and a massless conformally coupled scalar field in dS space–time. The physical tensor two-point function has been calculated in terms of the conformally coupled scalar two-point function in the ambient space formalism. It has been expressed in terms of dS intrinsic coordinates from its ambient space counterpart, which is dS-invariant and free of any divergences.

We comment on a previous calculation¹ for the scattering amplitude for the Dirac field in an external Coulomb potential in the expanding de Sitter space. The result implies that for initial and final fermion states with identical momenta |p_i|=|p_f| the helicity of the particle is conserved. We make a classical analysis of the scattering problem in the small scattering angle approximation using the Bargmann–Michel–Telegdi equation and show that helicity conservation also manifests in the classical case. We also show that in Minkowski space there is a complete agreement between the classical and quantum polarization angle of the scattered particle.

We discuss some of the issues arising when considering asymptotically de Sitter space–times and attempts to address them. Our development begins at the classical level where several initial value problems are discussed and ends with several proposals for holography in asymptotically de Sitter space–times. Throughout the paper we give a review of some basic notions such as the geometry of Schwarzschild–de Sitter black hole, the Nariai limit and quantum field theory in a fixed de Sitter background. We also briefly discuss some semiclassical aspects such as the nucleation of black holes and the Hartle–Hawking wavefunctional. We end by giving an overview of some open questions. An emphasis is placed on the differences between a static patch observer confined to live in a thermal cavity and the metaobserver who has access to a finite region of the future boundary.