Scalar-tensor theory and the anisotropic perturbations of the inflationary universe

Inflationary higher derivative scalar-tensor theory is analyzed in this paper in a de Sitter background space. A useful model-independent formula of the Friedmann equation is derived and used to study the stability problem associated with the anisotropic perturbations of the inflationary solution. The stability conditions of the de Sitter solution are derived for a general class of models. For a simple demonstration, an induced gravity model is considered in this paper for the effects of the higher derivative interactions including a cubic term.     

Brane-induced-gravity shock waves

We construct exact gravitational field solutions for a relativistic particle localized on a tensional brane in brane-induced gravity. They are a generalization of gravitational shock waves in 4D de Sitter space. We provide the metrics for both the normal branch and the self-inflating branch Dvali-Gabadadze-Porrati brane worlds, and compare them to the 4D Einstein gravity solution and to the case when gravity resides only in the 5D bulk, without any brane-localized curvature terms. At short distances the wave profile looks the same as in four dimensions. The corrections appear only far from the source, where they differ from the long distance corrections in 4D de Sitter space. We also discover a new nonperturbative channel for energy emission into the bulk from the self-inflating [corrected] branch, when gravity is modified at the de Sitter radius.     

Auxiliary Conformally Invariant Higher-Spin Field in de Sitter Space

We employ de Sitter isometry to study a mixed symmetric rank-3 tensor field in de Sitter space by finding the field equation, solution and two-point function which are conformally invariant. It is proved that such a tensor field plays a key role in conformal theory of linear gravity (Binegar et al., Phys. Rev. D 27, 2249, 1983) . In de Sitter space from the group theoretical point of view this kind of tensor could associate with two unitary irreducible representations (UIR) of the de Sitter group (Takook et al., J.Math. Phys. 51, 032503, 2010), which one representation has a flat limit, namely, in zero curvature coincides to the UIR of Poincaré group, however, the second one which is named as auxiliary field, becomes significant in the study of conformal gravity in de Sitter background. We show that the rank-3 tensor solution can be written in terms of a massless minimally coupled scalar field and also the related two-point function is a function of a massless minimally coupled scalar two-point function.     

Spectra in Coherent States with Excited-de Sitter Mode during Inflation

We use an excited-de Sitter mode as the fundamental mode function for the far past time limit during inflation, to study the corrections of spectra of curvature perturbation. Excited-de Sitter mode is actually the approximate solution of the inflaton field equation that asymptotically approaches to the de Sitter mode function in the first approximation. We build coherent state over excited-de Sitter mode. Then, we compute spectrum of the curvature perturbation with this coherent state as the initial state. We show that in this case, the spectrum of curvature perturbation is scale dependent. As a important result of using this coherent state, we find a non-zero non-Gaussian one-point function as a possible tiny source for generation of anisotropy in CMB from the initial mode in the string or Planck scale.     

De Sitter solutions in higher order gravity

We consider de Sitter solutions, relevant for instance in studies of inflation, in cosmologies where the gravitational Lagrangian is a functionf(R),R being the scalar curvature. Previous investigations have mostly concentrated onf(R) = R+R² which always has a solution matching the conventional de Sitter one. We show that this circumstance is rather exceptional, and that one must go to higher terms to see signs of the generic behaviour, In general the de Sitter solutions are different from those of Einstein gravity. We present complete solutions for the general cubic Lagrangian. We also address the question of when the solutions to equations from truncated actions can be expected to well represent solutions of some full (and possibly unknown) theory. Such theories provide the possibility of weakening the bounds on the energy density of the inflaton, allowing an easier reconciliation of the inflationary universe with structure-forming topological defects.     

Three dimensional black hole coupled to the Born-Infeld electrodynamics

A nonlinear charged version of the (2+1)-anti de Sitter black hole solution is derived. The source to the Einstein equations is a Born-Infeld electromagnetic field, which in the weak field limit becomes the (2+1)-Maxwell field. The obtained Einstein-Born-Infeld solution for certain range of the parameters (mass, charge, cosmological and the Born-Infeld constants) represent a static circularly symmetric black hole. Although the covariant metric components and the electric field do not exhibit a singular behavior at r=0 the curvature invariants are singular at that point.     

Stability of hot Reissner-Nordstrom black hole

The stability of de Sitter space in the presence of a black hole is shown. The gravitational and electromagnetic perturbations of a Reissner-Nordstrom black hole which is asymptotically de Sitter instead of asymptotically flat are considered in terms of complex potentials. This result on stability can also be applied to the inflationary scenario.     

Towards a quantization of gauge fields on de Sitter group by functional integral method

A formulation of the de Sitter symmetry as a purely inner symmetry defined on a fixed Minkowski space-time is presented. We define the generators of the de Sitter group and write the structure equations using a constant deformation parameter λ. The conserved gauge currents are calculated, and their physical meaning is given. Local gauge transformations and the corresponding covariant derivative depending on the gauge fields are also obtained. We study the behavior of gauge fields, the torsion and curvature tensors and give a regularization technique in terms of the ζ function.     

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.     

Stability of gravity with a cosmological constant

The stability properties of Einstein theory with a cosmological constant Λ are investigated. For Λ > 0, stability is established for small fluctuations, about the de Sitter background, occurring inside the event horizon and semiclassical stability is analyzed. For Λ < 0, stability is demonstrated for all asymptotically anti-de Sitter metrics. The analysis is based on the general construction of conserved flux-integral expressions associated with the symmetries of a chosen background. The effects of an event horizon, which lead to Hawking radiation, are expressedfor general field hamiltonians. Stability for Λ < 0 is proved, using supergravity techniques, in terms of the graded anti-de Sitter algebra with spinorial charges also expressed as flux integrals.     

The semiclassical limit of causal dynamical triangulations

Previous work has shown that the macroscopic structure of the theory of quantum gravity defined by causal dynamical triangulations (CDT) is compatible with that of a de Sitter universe. After emphasizing the strictly nonperturbative nature of this semiclassical limit we present a detailed study of the three-volume data, which allows us to re-confirm the de Sitter structure, exhibit short-distance discretization effects, and make a first detailed investigation of the presence of higher-order curvature terms in the effective action for the scale factor. Technically, we make use of a novel way of fixing the total four-volume in the simulations.     

Electrostatic and magnetostatic solutions in a Lorentz-violating electrodynamics model

We propose an effective Lorentz-violating electrodynamics model via the static de Sitter metric, which is deviated from the Minkowski metric by a minuscule amount depending on the cosmological constant. We obtain the electromagnetic field equations via the vierbein decomposition of the tensors. In addition, as an application of the electromagnetic field equations obtained, we derive the solutions of the electrostatic field and the magnetostatic field due to a point charge and a circle current, respectively, and discuss the implication of the effect of Lorentz violation in our electromagnetic theory.PACS 04.20.Cv; 04.40.-b; 98.80.Jk; 11.30.Cp     

Quantum vacuum cosmology

It is shown for the case of a conformally flat vacuum that the curvature of space-time may be viewed as the observable consequence of particle interactions involving a scalar field φ, rather than the independent agency of the gravitational field by itself. The quantum nature of gravity comes in as a consequence of the quantum properties of the φ-field (“vacuum fluctuation”), and a direct analogy is drawn between the renormalizations of charge and mass. Cosmological solutions are derived: These being just the conventional Friedmann solutions, or the de Sitter solution. It is pointed out that a totally empty universe must be Minkowskian.     

Gravitational energy in quadratic-curvature gravities

We define energy (E) and compute its values for gravitational systems involving terms quadratic in curvature. There are significant differences, both conceptually and concretely, from Einstein theory. For D=4, all purely quadratic models admit constant curvature vacua with arbitrary Lambda, and E is the "cosmological" Abbott-Deser (AD) expression; instead, E always vanishes in flat, Lambda=0, background. For combined Einstein-quadratic curvature systems without explicit Lambda-term vacuum must be flat space, and E has the usual Arnowitt-Deser-Misner form. A Lambda-term forces unique de Sitter vacuum, with E the sum of contributions from Einstein and quadratic parts to the AD form. We also discuss the effects on energy definition of higher curvature terms and of higher dimension.     

On the Stability of a Class of Modified Gravitational Models

Motivated by the dark energy issue, a minisuperspace approach to the stability for modified gravitational models in a four dimensional cosmological setting is investigated. Specifically, after revisiting the f(R) case, R being the Ricci curvature, we present a stability condition around a de Sitter solution valid for modified gravitational models of generalized type F(R,G,Q), G and Q being the Gauss-Bonnet and quadratic Riemann invariants respectively. A generalization to higher order invariants is presented.     

General relativity with an auxiliary dimension

I consider an extension of General Relativity by an auxiliary nondynamical dimension that enables our space–time to acquire an extrinsic curvature. Obtained gravitational equations, without or with a cosmological constant, have a selfaccelerated solution that is independent of the value of the cosmological constant, and can describe the cosmic speedup of the Universe as a geometric effect. Background evolution of the selfaccelerated solution is identical to that of ordinary de Sitter space. I show that linear perturbations on this solution describe either a massless graviton, or a massive graviton and a scalar, which are free of ghosts and tachyons for certain choices of boundary conditions. The obtained linearized expressions suggest that nonlinear interactions should, for certain boundary conditions, be strongly coupled, although this issue is not studied here. The full nonlinear Hamiltonian of the theory is shown to be positive for the selfaccelerated solution, while in general, it reduces to surface terms in our and auxiliary dimensions.     

Cosmological term in the general theory of relativity and localization of the de Sitter and Einstein groups

The theory of a gauge gravitational field with localization of the de Sitter group is formulated. Starting from the tetradic components of the de Sitter universe, a relationship is established between the Riemannian metric and the de Sitter gauge field. It is shown that the general theory of relativity with the cosmological term is the simplest variant of the de Sitter gauge theory of gravitation, which transforms in the limit of an infinite radius of curvature of the de Sitter universe into the Poincaré-invariant GTR without the cosmological term. A theory of a gauge gravitational field with localization of Einstein's group of motions of the uniform static universe (the Einstein group R × S0 (4)) is formulated in an analogous manner.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 8, pp. 86–90, August, 1984.     

Parametrical embeddings of static spherically symmetric spacetimes

An analysis for a direct calculation of the embeddings in flat spacetimes of static spherically symmetric manifolds with Lorentz metric is worked out. For each manifold with non-constant curvature we arrive at a parametrical embedding which represents an infinite geometrical multiplicity of the embedded surface. The embeddings of manifolds with constant curvature are not parametrical and can be determined univocally. Examples concerning Schwarzschild, Reissner-Weyl, de Sitter and anti-de Sitter spacetimes are considered.