Four-dimensional De Sitter Research Articles

De Sitter space as an arena for doubly special relativity

We show that Doubly Special Relativity (DSR) can be viewed as a theory with energy–momentum space being the four-dimensional de Sitter space. Different formulations (bases) of the DSR theory considered so far can be therefore understood as different coordinate systems on this space. The emerging geometrical picture makes it possible to understand the universality of the non-commutative structure of space–time of doubly special relativity. Moreover, it suggests how to construct the most natural DSR basis, which turns out to be the bicrossproduct basis.

Vortices in de Sitter spacetimes

We investigate vortex solutions to the Abelian Higgs field equations in a four-dimensional de Sitter spacetime background. We obtain both static and dynamic solutions with axial symmetry that are generalizations of the Nielsen–Olesen gauge vortices in flat spacetime. The static solution is located in the static patch of de Sitter space. We numerically solve the field equations in an inflationary (big bang) patch and find a time dependent vortex solution, whose effect to create a deficit angle in the spacetime. We show that this solution can be interpreted in terms of a renormalization group flow in accord with a generalized c-theorem, providing evidence in favour of a dS/CFT correspondence.

Gravitational quasinormal modes for anti-de Sitter black holes

The quasinormal mode spectra for gravitational perturbations of black holes in four-dimensional de Sitter and anti-de Sitter space are investigated. The de Sitter case lends itself to approximation by a Pöshcl–Teller potential. The anti-de Sitter case is relevant to the AdS-CFT correspondence in superstring theory. The ADS-CFT correspondence suggests a preferred set of boundary conditions.

Diracfields and thermal effects in the de Sitter universe

We present a study of Dirac quantum fieldsin a four-dimensional de Sitter spacetime.The theory is based on the requirement ofprecise analyticity properties of thewaves and the correlation functions in thecomplexification of the de Sittermanifold. Holomorphic de Sitterspinorial plane waves are introduced inthis way and used to construct thetwo-point functions, whose properties arefully characterized. The physicalinterpretation of the analyticityproperties of Wightman's functions interms of a KMS-type thermal condition is alsogiven.

Vanishing of the cosmological constant in nonfactorizable geometry

We generalize the results of Randall and Sundrum to a wider class of four-dimensional space-times including the four-dimensional Schwarzschild background and de Sitter universe. We solve the equation for graviton propagation in a general four dimensional background and find an explicit solution for a zero mass bound state of the graviton. We find that this zero mass bound state is normalizable only if the cosmological constant is strictly zero, thereby providing a dynamical reason for the vanishing of cosmological constant within the context of this model. We also show that the results of Randall and Sundrum can be generalized without any modification to the Schwarzschild background.

Bulk versus boundary (gravitational Casimir) effects in the quantum creation of an inflationary brane-worlduniverse

The role of bulk matter quantum effects (via the corresponding effective potential discussed using the example of a conformal scalar) and of boundary matter quantum effects (via the conformal anomalyinduced effective action) is considered in brane-world cosmology.A scenario is used where brane tension is not a free parameter,and the initial classical bulk-brane action is defined by some considerations. The effective bulk-brane equations of motion arealso analysed.The quantum creation of a four-dimensional de Sitter or anti-de Sitter (AdS) braneuniverse living in five-dimensional AdS space is possible when quantum bulkand/or branematter is taken into account. The consideration of only conformal field theory (CFT) living on the brane admits the full analytical treatment. The bulk gravitational Casimir effect leads to deformations of five-dimensional AdS spaceand spherical/hyperbolic brane shapes. The generalization of the above scenario to dominant bulk quantum gravity naturally representsthis scenario as self-consistent warped compactification within an AdS/CFT set-up.

Quantum (in)stability of dilatonic AdS backgrounds and the holographic renormalization group with gravity

Stability of dilatonic AdS spaces due to quantum effects of dilaton coupled conformal matter is considered. When such spaces do not exist on classical level, their dynamical generation occurs. Explicit examples corresponding to quantum creation of d4 dilatonic AdS Universe and of d2 dilatonic AdS Black Hole (BH) are presented. Motivated by holographic RG, in the similar approach the complete d5 effective action is discussed. The intermediate region where it is the sum of two parts: bulk (classical gravity) and boundary quantum action is investigated. The effective equations solution representing d5 AdS Universe with warp scale factor is found. Four-dimensional de Sitter or AdS world is generated on the boundary of such Universe as a result of quantum effects.

Inflation in Kaluza-Klein theory: Relation between the fine-structure constant and the cosmological constant

In this paper we investigate a model of an inflationary universe in Kaluza-Klein theory, which is a four-dimensional de Sitter space plus a one-dimensional compactified internal space. We find that the energy scale for inflation can be predicted from the fine-structure constant in a self-consistent solution of the semi-classical Einstein equations including the Casimir effect. From the observed value of the fine-structure constant, we obtain an energy scale for inflation of $\ensuremath{\epsilon}=1.84\ifmmode\times\else\texttimes\fi{}{10}^{16}{g}_{*}^{1/4}\mathrm{GeV},$ where ${g}_{*}$ is a dimensionless number depending on the spin and number of matter fields existing in the early universe. This value is consistent with the values often discussed for inflation and grand unification. The wave function for this model predicts a high probability for forming such universes, independent of the value of the cosmological constant. The tunneling probability favors the creation of inflationary universes with a compactified dimension, over those with all macroscopic dimensions.

ON BOGOLIUBOV TRANSFORMATION OF SCALAR WAVE FUNCTIONS IN DE SITTER SPACE

We discuss the Bogoliubov transformation of the scalar wave functions caused by the change of coordinates in four-dimensional de Sitter space. It is shown that the exact Bogoliubov coefficients can be obtained from the global coordinates to the static coordinates where there exists manifest horizon. We consider two types of global coordinates. In one global coordinates, it is shown that the Bogoliubov transformation to the static coordinates can be expressed by the discontinuous integral of Weber and Schafheitlin. The positive and negative energy states in the global coordinates degenerate in the static coordinates. In the other global coordinates, we obtain the Bogoliubov coefficients by using the analytic continuation of the hypergeometric functions in two variables. We also discuss the relation between two types of global coordinates and find an integral relation between the mode functions.

Fermions in one-loop quantum cosmology.

In recent papers by D'Eath and Esposito two kinds of boundary conditions, local and nonlocal (spectral), were used to study the contribution of fermions to the one-loop prefactor in the Hartle-Hawking wave function of the Universe. Using the $\ensuremath{\zeta}$-function technique they found that for the case of massless Majorana fermions on a flat background bounded by a three-sphere the values $\ensuremath{\zeta}(0)$ coincide for the two kinds of boundary conditions mentioned above. Implementing our version of $\ensuremath{\zeta}$ regularization elaborated earlier, we calculate $\ensuremath{\zeta}(0)$ for both the massive and massless fermions on the background representing the part of the four-dimensional de Sitter sphere bounded by a three-sphere. For the massless fermions our results coincide with results for a flat background and, consequently, the results for both types of boundary conditions are the same. However, for massive fermions the values $\ensuremath{\zeta}(0)$ for local and spectral boundary conditions differ on the de Sitter background and on the flat one as well.

Two-point functions and stress-energy tensors of p-forms in de Sitter and anti-de Sitter spaces

It is obtained, in four-dimensional de Sitter and anti-de Sitter spaces, the two-point functions of the quantum p-forms corresponding to maximally symmetric and Hadamard vacua. It is then determined the associated renormalized stress-energy tensors.

Bubble formation in anisotropic cosmologies

We discuss the decay of the false vacuum in homogeneous cosmologies, both isotropic and anisotropic. If the false vacuum is isotropic, it is expected that the decay rate is dominated by spherically symmetric bubbles. However, if the universe during its past evolution was trapped in an anisotropic false vacuum one expects this anisotropy to be present in the decay products (bubbles) of that vacuum. In this paper we show the existence of two new, anisotropic types of bubble solution of Kantowski-Sachs type for a general double well potential. The first represents the decay of four-dimensional de Sitter space, and the second the decay of the product of the two-sphere and two-dimensional de Sitter space. We also derive qualitative features of the classical space-times emerging after tunneling.

Notes on the Hawking effect in de Sitter space. II.

The Hawking effect for a quantized massless conformal scalar field in two- and four-dimensional de Sitter space is studied. Two different charts, on which the mode functions are defined, are the spatially flat chart and the static one. The Bogoliubov coefficients are evaluated without any approximation. In both two and four dimensions, the particle number distributions reveal the exact thermal spectrum.

Notes on the Hawking effect in de Sitter space. I.

We consider the Hawking effect for a quantized massless conformal scalar field in two- and four-dimensional de Sitter space. The relation among Bogoliubov coefficients is investigated without explicit integration of Klein-Gordon products. Our method presents a clear view of the property of Bogoliubov coefficients. In the two-dimensional case the thermal distribution is exactly derived. The application to the four-dimensional case is not straightforward, but we can derive the same result with some techniques.

An evaluation of the graviton propagator in de sitter space

The graviton propagator in four-dimensional de Sitter space is found in closed form. The vacuum state is taken to be the de Sitter-invariant “euclidean” or “Gibbons-Hawking” vacuum. The gauge-fixing term used is the standard choice introduced by Christensen and Duff. The propagator is given explicity in this gauge, and is found to be finite for points that are not null-related. The method used is new: mode-sums on the four-sphere are expressed as maximally symmetric bitensors. The result is then given in a completely geometric and coördinate-free form. This same method can easily be used for maximally symmetric spaces of general dimension, including anti-de Sitter space with supersymmetric boundary conditions, and for different choices of gauge.

A positive semi-definite action in a Kaluza-Klein theory with compactification onto time-like extra dimensions

The (4+ N)-dimensional theory is considered whose lagrangian function is L 4+N = √− g ̂ α R ̂ 2 , where R̂ is the Ricci scalar and α is a positive constant. The metric is g ̂ AB = diag(g ab, φ −1 g ̄ mn) . Dimensional reduction leads to an effective four-dimensional lagrangian of induced-gravity type, if L 4 = √−g (κ 1φ −(N−4) 2 + κ 2φ −(N−2) 2 R + φ −N 2 R 2 , where R is the four-dimensional Ricci scalar and κ 1 and κ 2 are constants. The positive semi-definiteness of L avoids the difficulties, pointed out recently by Horowitz and by Rubakov, which can arise in quantum cosmology when the (euclidean) action becomes negative. The compactification is onto a time-like internal space g ̄ mn , as suggested by Aref'eva and Volovich, giving a four-dimensional de Sitter space-time with φ = constant, which, however, is classically unstable on a time scale ∼ H −1. Decrease of the radius φ −1 2 of the internal space is ultimately halted by quantum effects, via some V( φ), and L 4 then includes the usual Hilbert term and a cosmological constant.

Global symmetry breaking in two-dimensional flat spacetime and in de Sitter spacetime.

The breaking of global continuous symmetries in two-dimensional flat spacetime and in four-dimensional de Sitter spacetime is investigated. Infrared divergences require physically allowable quantum states in these spaces to break Lorentz or de Sitter invariance, resulting in two-point functions which are explicitly time dependent. Field expectation values which break the global symmetry must decay in time, but it is possible to have a state which exhibits broken symmetry for a finite time. It is also possible for field correlations and energy density produced by a broken-symmetry state to persist after the symmetry has been restored.

Geometrical interpretation of In�n�-Wigner contractions

The Inonu-Wigner contractions which interrelate the Lie algebras of the isometry groups of metric spaces are discussed with reference to deformations of the absolutes of the spaces. A general formula is derived for the Lie algebra commutation relations of the isometry group for anyN-dimensional metric space. These ideas are illustrated by a discussion of important particular cases, which interrelate the four-dimensional de Sitter, Poincare, and Galilean groups.

Finite-temperature effects in conformally flat space-times

We evaluate the one-loop effective potential for conformally invariant flat space-times. This is achieved by a suitable rescaling of the fields. In the two-dimensional Rindler and Schwarzschild and in the four-dimensional De Sitter metrics the vacuum energy exhibits a thermal feature. The background temperature is quantitatively fixed by the global space-time geometry and its nontrivial topology. For the λϕ4 theory in the De Sitter metric we find a dynamically generated mass for the field φ.