Self-interacting scalar fields with geometrical interpretations

The idea is advanced that particles arise as distortions of a reimannian background and that such distortions represent particular conformally flat solutions of the “cosmological” Einstein equations with extremely large “cosmological” constants. Particle interactions then appear as gravitational in origin. The idea is illustrated with the help of two scalar models. In the first one the “De Sitter” space can be interpreted as a relativistic field whose ground state undergoes a transition from degenerate to nondegenerate for the critical value of some parameter. In the second one a deeper understanding is reached of the role of the “De Sitter” space in confinement problems and of the nature of the ensemble of vacuum states recently introduced in conformally invariant field theories by Fubini.     

On the cosmological viability of the Hu-Sawicki type modified induced gravity

It has been shown recently that the normal branch of a DGP braneworld scenario self-accelerates if the induced gravity on the brane is modified in the spirit of f(R) modified gravity. Within this viewpoint, we investigate cosmological viability of the Hu-Sawicki type modified induced gravity. Firstly, we present a dynamical system analysis of a general f(R)-DGP model. We show that in the phase space of the model, there exist three standard critical points; one of which is a de Sitter point corresponding to accelerating phase of the universe expansion. The stability of this point depends on the effective equation of state parameter of the curvature fluid. If we consider the curvature fluid to be a canonical scalar field in the equivalent scalar-tensor theory, the mentioned de Sitter phase is unstable, otherwise it is an attractor, stable phase. We show that the effective equation of state parameter of the model realizes an effective phantom-like behavior. A cosmographic analysis shows that this model, which admits a stable de Sitter phase in its expansion history, is a cosmologically viable scenario.     

Quantized De Sitter space,the connection to the Pauli principle and an application to Feynman's relativistic quark theory II

A continuation of a previous paper, in which a model of a quantized space-time theory has been investigated, considers further problems of a quantized De Sitter space. There will be shown that a De Sitter space is a very useful starting point to a non-local relativistic quantum field theory, containing the Pauli principle, for the theory of elementary particles, as a connection to Feynman's relativistic quark theory, where the groupSU(3) has a particular importance, will be discussed. This method offers the possibility of treating weak local differences from a space with De Sitter metric as a perturbation. Therefore the problem of a fundamental elementary lengthl _o must be considered in connection with the general theory of relativity.     

Holographic dual of de Sitter universe with AdS bubbles

We study the proposal that a de Sitter (dS) universe with an Anti-de Sitter (AdS) bubble can be replaced by a dS universe with a boundary CFT. To explore this duality, we consider incident gravitons coming from the dS universe through the bubble wall into the AdS bubble in the original picture. In the dual picture, this process has to be identified with the absorption of gravitons by CFT matter. We have obtained a general formula for the absorption probability in general d+1 spacetime dimensions. The result shows the different behavior depending on whether spacetime dimensions are even or odd. We find that the absorption process of gravitons from the dS universe by CFT matter is controlled by localized gravitons (massive bound state modes in the Kaluza-Klein decomposition) in the dS universe. The absorption probability is determined by the effective degrees of freedom of the CFT matter and the effective gravitational coupling constant which encodes information of localized gravitons. We speculate that the dual of (d+1)-dimensional dS universe with an AdS bubble is also dual to a d-dimensional dS universe with CFT matter.     

One Electron Atom in Special Relativity with de Sitter Space-Time Symmetry (II)：—Higher Order Contributions

This is a follow of previous work entitled "One Electron Atom in Special Relativity with de Sitter Space-Time Symmetry" [Commun. Theor. Phys. 57 (2012) 930]. In this paper, we consider the higher order calculations and contributions in the previous framework to solve one electron atoms in de Sitter invariant relativistic quantum mechanics. The next-to-leading-order calculations in 1/R²-expansions show that the fine-structure constant α is variant with cosmologic time going by in the de Sitter invariant special relativistic quantum mechanics with standard FRW cosmologic model.     

An Integral Transform in de Sitter Space

An integral transform on (4 + 1) de Sitter space, which is a generalization of the Fourier transform for a Dirac particle in Minkowski space, is considered, and proofs of its relevant properties are provided. With this integral transform we demonstrate explicitly that the momentum space eigenvalue equation for the second order Casimir operator of the de Sitter group is equivalent to a wave equation in Minkowski momentum space, which describes the mass-spin relation of a mechanical system in Minkowski space, consisting of two equal mass, point-like constituents rotating uniformly at a distance R from their geometric center, where R is the radius of the de Sitter space. Applications to the relativistic rotator are considered. Contrary to our previous results, we find that the relativistic rotator does not go into a structureless relativistic mass point in the elementary limit obtained by contracting the de Sitter group into the Poincaré group. Our analysis can be carried over, with relatively minor modifications, to anti-de Sitter space, and similar results hold there. Additional physical consequences are also discussed.     

Nonlocal gravitational models and exact solutions

A nonlocal gravity model with a function f (□^?1 R), where □ is the d’Alembert operator, is considered. The algorithm, allowing to reconstruct f(□^?1 R), corresponding to the given Hubble parameter and the state parameter of the matter, is proposed. Using this algorithm, we find the functions f(□^?1 R), corresponding to de Sitter solutions.     

A background-dependent approach to the theory of gravitation II. Relativistic gravitational equations

On the basis of the results of Paper I and guided by a Machian view of nature, we find new gravitational equations which are background dependent. Such equations describe a purely geometrical theory of gravitation, and their dependence on the background structure is through the total energy-momentum tensor on the past sheet of the light cone of each space-time pointx [θ^μν x, say], i.e., through the integral on the past sheet of the light cone ofx of the parallel transport of the energy-momentum tensor from the space-time point in which it is defined tox along the geodesic connecting the two space-time points. Following Gürsey, we assume that the source of the De Sitter metric is not the cosmological term, but, rather, the energy-momentum tensor of a “uniform distribution of mass scintillations” [T ^μν x, say].T ^μν x, indeed, turns out to be equal to the metric tensor times a constant factor. As a consequence, in any local inhomogeneity A of a space-time whose background structure is determined by the Perfect Cosmological Principle,θ ^μν turns out to be approximately equal to the metric tensor times a constant factor, providedT=g _αβ T ^αβ is sufficiently small and the structure of the past sheet of the light cones of the space-time points belonging to Λ is not too much perturbed by the local gravitational field. As a consequence, in Λ the new equations approximately reduce to Einstein's equations. If one considers a “superuniverse model” in which our universe is considered as a local inhomogeneity in a De Sitter background, then from the above result there follows a fortiori the agreement of the new gravitational equations with the classical tests of gravitation. Furthermore, the dependence on the background structure is such that the new equations (i) incorporate the idea that the frame has to be fixeddirectly in connection with cosmological observations, and (ii) are singular in the absence of matter in the whole space-time. Moreover, (iii) the coupling constant turns out to be dimensionless in natural units (c=1=?), and (iv) a local inertial frame in a De Sitter background is determined by the condition that with respect to it the background structure is homogeneous in space and in time and is Lorentz invariant.     

Einstein,de Sitter and the beginning of relativistic cosmology in 1917

In 1917, both Einstein and de Sitter proposed a new interpretation of the universe as a whole: the structure of the universe could be described in terms of relativistic field equations. Their contributions marked the beginning of the modern scientific comprehension of the origin and evolution of the universe. Our aim is to propose a critical review paper, based on references in primary sources, on the formulation in 1917 of Einstein’s and de Sitter’s models of the universe, which represents a fundamental chapter in the history of relativistic Cosmology.     

Screening of cosmological constant for de Sitter Universe in non-local gravity,phantom-divide crossing and finite-time future singularities

We investigate de Sitter solutions in non-local gravity as well as in non-local gravity with Lagrange constraint multiplier. We examine a condition to avoid a ghost and discuss a screening scenario for a cosmological constant in de Sitter solutions. Furthermore, we explicitly demonstrate that three types of the finite-time future singularities can occur in non-local gravity and explore their properties. In addition, we evaluate the effective equation of state for the universe and show that the late-time accelerating universe may be effectively the quintessence, cosmological constant or phantom-like phases. In particular, it is found that there is a case in which a crossing of the phantom divide from the non-phantom (quintessence) phase to the phantom one can be realized when a finite-time future singularity occurs. Moreover, it is demonstrated that the addition of an R ² term can cure the finite-time future singularities in non-local gravity. It is also suggested that in the framework of non-local gravity, adding an R ² term leads to possible unification of the early-time inflation with the late-time cosmic acceleration.     

A new vacuum state in de Sitter space

We present a new vacuum state which can be defined in a region of de Sitter space. This region corresponds to a K=?1 Robertson-Walker coordinatization of de Sitter space. The renormalized expectation value of the stress tensor for the conformally invariant massless scalar field in this vacuum is evaluated, and is found to differ from the corresponding result in the usual de Sitter-invariant vacuum by the absence of a pure radiation term. We also indicate that this can be accounted for by regarding the de Sitter-invariant vacuum as a thermal state relative to the new vacuum.     

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.     

Dirac wave equation in the de Sitter universe

We present and discuss the Dirac wave equation in the de Sitter universe. This equation is obtained by factoring the second-order Casimir invariant operator associated to the Fantappié-de Sitter group.     

Large-Scale Corrections to the CMB Anisotropy from Asymptotic de Sitter Mode

In this study, large-scale effects from asymptotic de Sitter mode on the CMB anisotropy are investigated. Besides the slow variation of the Hubble parameter onset of the last stage of inflation, the recent observational constraints from Planck and WMAP on spectral index confirm that the geometry of the universe can not be pure de Sitter in this era. Motivated by these evidences, we use this mode to calculate the power spectrum of the CMB anisotropy on the large scale. It is found that the CMB spectrum is dependent on the index of Hankel function ν which in the de Sitter limit \(\nu \rightarrow \frac {3}{2}\), the power spectrum reduces to the scale invariant result. Also, the result shows that the spectrum of anisotropy is dependent on angular scale and slow-roll parameter and these additional corrections are swept away by a cutoff scale parameter H ? M_? < M _P .     

Finite renormalizations of 0Sp(N, 4) supersymmetry

The calculation of the one-loop effective potential of the Wess-Zumino model is carried out using Green functions which propagate fields inn-dimensional anti-de Sitter space. The divergent parts of the amplitudes are independent of the choice of boundary conditions. The finite counterterms can be adjusted in such a way that the renormalized action be supersymmetric invariant. Addressing the question of the survival of the supersymmetry invariance of the vacuum state, we derive the result of the persistence of supersymmetry in the semiclassical approximation.     

Asymptotic freedom and entropy in a perpetually oscillating universe

A model of a perpetually oscillating universe is considered. In this model the universe, when contracting to Planck dimensions, transforms from the Friedmann to the De Sitter phase with one and the same $\text{Λ ～}\text{1}\text{l}{}^2{}_{\mathrm{<mtext>P</mtext><mtext>1</mtext>}}$, irrespective of the value of the total bare mass of the Friedmann universe.     

Beltrami-de Sitter时空中标量和旋量粒子的量子理论

参照在Minkowski时空中,从粒子的相对论性经典理论过渡到量子理论,建立标量粒子和旋量粒子的相对论性波动方程的方案,在Beltrami-de Sitter时空中建立了de Sitter不变的标量粒子和旋量粒子的相对论性量子力学的基本方程,它们恰恰分别是Beltrami-de Sitter时空中的Klein-Gordon方程和Dirac方程。在Beltrami-anti de Sitter时空的同时类空超曲面簇上求解了这些方程,得到了分立的本征值和相应的本征函数。 关键词：     

Study of relativistic bound state wave functions in quasielastic (e,e′ p) reactions

The unpolarized response functions of the quasielastic ¹⁶O(e,e′ p)¹⁵N reaction are calculated for three different types of relativistic bound-state wave functions. The wave functions are obtained from relativistic Hartree, relativistic Hartree-Fock and density-dependent relativistic Hartree calculations that reproduce the experimental rms charge radius of ¹⁶O. The sensitivity of the unpolarized response functions to the single-particle structure of the different models is investigated in the relativistic plane-wave impulse approximation. Redistributions of the momentum dependence in the longitudinal and transverse response function can be related to the binding energy of the single-particle states. The interference responses R_LT and R_TT reveal a strong sensitivity to the small component of the relativistic bound-state wave function.