Ricci Scalar Research Articles

On Born's deformed reciprocal complex gravitational theory and noncommutative gravity

Born's reciprocal relativity in flat spacetimes is based on the principle of a maximal speed limit (speed of light) and a maximal proper force (which is also compatible with a maximal and minimal length duality) and where coordinates and momenta are unified on a single footing. We extend Born's theory to the case of curved spacetimes and construct a deformed Born reciprocal general relativity theory in curved spacetimes (without the need to introduce star products) as a local gauge theory of the deformed Quaplectic group that is given by the semi-direct product of U ( 1 , 3 ) with the deformed (noncommutative) Weyl–Heisenberg group corresponding to noncommutative generators [ Z a , Z b ] ≠ 0 . The Hermitian metric is complex-valued with symmetric and nonsymmetric components and there are two different complex-valued Hermitian Ricci tensors R μ ν , S μ ν . The deformed Born's reciprocal gravitational action linear in the Ricci scalars R , S with Torsion-squared terms and BF terms is presented. The plausible interpretation of Z μ = E μ a Z a as noncommuting p-brane background complex spacetime coordinates is discussed in the conclusion, where E μ a is the complex vielbein associated with the Hermitian metric G μ ν = g ( μ ν ) + i g [ μ ν ] = E μ a E ¯ ν b η a b . This could be one of the underlying reasons why string-theory involves gravity.

Stability of asymptotically AdS wormholes in vacuum against scalar field perturbations

The stability of certain class of asymptotically AdS wormholes in vacuum against scalar field perturbations is analyzed. For a free massive scalar field, the stability of the perturbation is guaranteed provided the squared mass is bounded from below by a negative quantity. Depending on the base manifold of the AdS asymptotics, this lower bound could be more stringent than the Breitenlohner-Freedman bound. An exact expression for the spectrum is found analytically. For a scalar field perturbation with a nonminimal coupling, slow fall-off asymptotic behavior is also allowed, provided the squared mass fulfills certain negative upper bound. Although the Ricci scalar is not constant, an exact expression for the spectrum of the scalar field can also be found, and three different quantizations for the scalar field can be carried out. They are characterized by the fall-off of the scalar field, which can be fast or slow with respect to each asymptotic region. For these perturbations, stability can be achieved in a range of negative squared masses which depends on the base manifold of the AdS asymptotics. This analysis also extends to a class of gravitational solitons with a single conformal boundary.

NONMINIMAL ISOTROPIC COSMOLOGICAL MODEL WITH YANG–MILLS AND HIGGS FIELDS

We establish a nonminimal Einstein–Yang–Mills–Higgs model, which contains six coupling parameters. The first three parameters relate to the nonminimal coupling of a non-Abelian gauge field and a gravity field, the next two parameters describe the so-called derivative nonminimal coupling of a scalar multiplet with a gravity field, and the sixth parameter introduces the standard coupling of a scalar field with a Ricci scalar. The formulated six-parameter nonminimal Einstein–Yang–Mills–Higgs model is applied to cosmology. We show that there exists a unique exact cosmological solution of the de Sitter type for a special choice of the coupling parameters. The nonminimally extended Yang–Mills and Higgs equations are satisfied for arbitrary gauge and scalar fields, when the coupling parameters are specifically related to the curvature constant of the isotropic space–time. Based on this special exact solution, we discuss the problem of a hidden anisotropy of the Yang–Mills field, and give an explicit example, when the nonminimal coupling effectively screens the anisotropy induced by the Yang–Mills field and thus restores the isotropy of the model.

Matter Loops Corrected Modified Gravity in Palatini Formulation

Recently, corrections to the standard Einstein–Hilbert action were proposed to explain the current cosmic acceleration in stead of introducing dark energy. In the Palatini formulation of those modified gravity models, there is an important observation due to Arkani–Hamed: matter loops will give rise to a correction to the modified gravity action proportional to the Ricci scalar of the metric. In the presence of such a term, we show that the current forms of modified gravity models in Palatini formulation, specifically, the 1/R gravity and ln R gravity, will have phantoms. Then we study the possible instabilities due to the presence of phantom fields. We show that the strong instability in the metric formulation of 1/R gravity indicated by Dolgov and Kawasaki will not appear and the decay timescales for the phantom fields may be long enough for the theories to make sense as effective field theory. On the other hand, if we change the sign of the modification terms to eliminate the phantoms, some other inconsistencies will arise for the various versions of the modified gravity models. Finally, we comment on the universal property of the Palatini formulation of the matter loops corrected modified gravity models and its implications.

Dynamics of nonlocal cosmology

Nonlocal quantum corrections to gravity have been recently proposed as a possible solution to the cosmological fine-tuning problems. We study the dynamics of a class of nonlocal actions defined by the function of the inverse d'Alembertian of the Ricci scalar. Power-law and exponential functions are considered in detail, but we also show a method to reconstruct a nonlocal correction that generates a given background expansion. We find that even the simplest terms can, while involving only Planck scale constants, drive the late time acceleration without changing early cosmology. This leads to a sudden future singularity which, however, may be avoided by regularizing the d'Alembertian. We also consider the Einstein frame versions of these models.

The viability of theories with matter coupled to the Ricci scalar

Recently there has been a proposal for modified gravitational f(R) actions which include a direct coupling between the matter action and the Ricci scalar, R. Of particular interest is the specific case where both the action and the coupling are linear in R. It is shown that such an action leads to a theory of gravity which includes higher order derivatives of the matter fields without introducing more dynamics in the gravity sector and, therefore, cannot be a viable theory for gravitation.

Aspects of cosmological expansion inF(R) gravity models

We study cosmological expansion inF(R) gravity using the trace of the field equations. High frequency oscillations in the Ricci scalar,whose amplitude increases as one evolves backward in time, have been predicted inrecent works. We show that the approximations used to derive this result veryquickly break down in any realistic model due to the non-linear nature of theunderlying problem. Using a combination of numerical and semi-analytic techniques,we study a range of models which are otherwise devoid of known pathologies.We find that high frequency asymmetric oscillations and a singularity at finitetime appear to be present for a wide range of initial conditions. We show thatthis singularity can be avoided with a certain range of initial conditions, whichwe find by evolving the models forwards in time. In addition we show that theoscillations in the Ricci scalar are highly suppressed in the Hubble parameter and scalefactor.

Kerr–Newman–de Sitter solution on DGP brane

We find an exact solution of Kerr–Newman–de Sitter type on the braneworld (4D) of the DGP model. When a constant 4D Ricci scalar is assumed, only zero (flat) and a positive (de Sitter) values satisfy the Hamiltonian constraint equation coming from the extra dimension. With a Z2-symmetry across the brane and a stationary and axisymmetric metric ansatz on the brane, we solve the constraint equation exactly in the Kerr–Schild form with de Sitter background. In the de Sitter background this Kerr–Schild solution is well behaved under Boyer–Lindquist transformation: the constraint equation is preserved under the transformation and so is the solution. In the non-rotating limit we show that this Kerr–Newman–de Sitter solution has the characteristic of accelerated expansion of the braneworld universe.

An oscillating Universe from the linearized R 2 theory of gravity

An oscillating Universe which arises from the linearized R2 theory of gravity is discussed, showing that some observative evidences like the cosmological redshift and the Hubble law are in agreement with the model. In this context Dark Energy is seen like a pure curvature effect arising by the Ricci scalar.

On symmetric Finsler spaces

In this paper, we study symmetric Finsler spaces. We first study some geometric properties of globally symmetric Finsler spaces and prove that any such space can be written as a coset space of a Lie group with an invariant Finsler metric. Then we prove that a globally symmetric Finsler space is a Berwald space. As an application, we use the notion of Minkowski symmetric Lie algebras to give an algebraic description of symmetric Finsler spaces and obtain the formulas for flag curvature and Ricci scalar. Finally, some rigidity results of locally symmetric Finsler spaces related to the flag curvature are also given.

INFLATION WITH HIGH DERIVATIVE COUPLINGS

We study a class of generalized inflation models in which the inflaton is coupled to the Ricci scalar by a general f(φ, R) term. The scalar power spectrum, the spectral index, the running of the spectral index, the tensor mode spectrum and a new consistency relation of the model are calculated.

[formula omitted] Gravities à la Brans–Dicke

We extend f(R) theories via the addition of a fundamental scalar field. The approach is reminiscent of the dilaton field of string theory and the Brans–Dicke model. f(R) theories attracted much attention recently in view of their potential to explain the acceleration of the universe. Extending f(R) models to theories with scalars can be motivated from the low energy effective action of string theory. There, a fundamental scalar (the dilaton), has a non-minimal coupling to the Ricci scalar. Furthermore beyond tree level actions will contain terms having higher (or lower) powers of R compared to the canonical Einstein–Hilbert term. Theories with f(R) will contain an extra scalar degree on top of the ad-hoc dilaton and mixing of these two modes around a stable solution is a concern. In this work we show that no mixing condition mandates the form V1(ϕ)f(R)+V2(ϕ)R2 for the action.

Isolated horizons in higher dimensional Einstein–Gauss–Bonnet gravity

The isolated horizon framework was introduced in order to provide a local description of black holes that are in equilibrium with their (possibly dynamic) environment. Over the past several years, the framework has been extended to include matter fields (dilaton, Yang–Mills etc) in D = 4 dimensions and cosmological constant in D ⩾ 3 dimensions. In this paper, we present a further extension of the framework that includes black holes in higher dimensional Einstein–Gauss–Bonnet (EGB) gravity. In particular, we construct a covariant phase space for EGB gravity in arbitrary dimensions which allows us to derive the first law. We find that the entropy of a weakly isolated and non-rotating horizon is given by In this expression SD−2 is the (D − 2)-dimensional cross section of the horizon with an area form and the Ricci scalar is the D-dimensional Newton constant and α is the Gauss–Bonnet parameter. This expression for the horizon entropy is in agreement with those predicted by the Euclidean and Noether charge methods. Thus we extend the isolated horizon framework beyond Einstein gravity.

Coordinates with Non-Singular Curvature for a Time Dependent Black Hole Horizon

A naive introduction of a dependency of the mass of a black hole on the Schwarzschild time coordinate results in singular behavior of curvature invariants at the horizon, violating expectations from complementarity. If instead a temporal dependence is introduced in terms of a coordinate akin to the river time representation, the Ricci scalar is nowhere singular away from the origin. It is found that for a shrinking mass scale due to evaporation, the null radial geodesics that generate the horizon are slightly displaced from the coordinate singularity. In addition, a changing horizon scale significantly alters the form of the coordinate singularity in diagonal (orthogonal) metric coordinates representing the space-time. A Penrose diagram describing the growth and evaporation of an example black hole is constructed to examine the evolution of the coordinate singularity.

Quantum field backreaction corrections and remnant stable evaporating Schwarzschild-de Sitter dynamical black hole

Time-dependent backreaction corrections of the renormalized expectation value of the stress-energy tensor operator of a massless quantum scalar field, minimally coupled, in the two-dimensional spherically symmetric nondilatonic Schwarzschild-de Sitter dynamical black hole metric, is applied to determine the final state of its thermal radiation. Renormalization theory in the two-dimensional analog of a generally curved space-time reduces to a trace anomaly defined in terms of the Ricci scalar. So the regularized stress-energy tensor, in close relation to the work by Christensen and Fulling, may be obtained by the nonlocal contribution of the trace anomaly and some suitable parameters. Linear-order, time-dependent solutions of the metric backreaction equations, in close relation to the work by Bousso et al., show that the spherically symmetric nondilatonic evaporating Schwarzschild-de Sitter dynamical black hole final state, reduces to a set of remnant, stable, mini black holes where their metric should be described in terms of some permissible discrete Eddington-Finkelstein advance times. Also the results of this article are confirmed by the consequences of time-independent backreaction solutions which were derived recently by the author and may propose a new approach for quantization of gravity, in which the cosmological constant and a distinguished observer have a key role.

Acceleration of the Universe viaf(R)gravities and the stability of extra dimensions

We discuss the possibility of obtaining the present acceleration of the Universe via $f(R)$ gravity theories which recently attracted much attention. It is known that $f(R)$ theories generally have room for this. In this work we stress that the requirement for the stabilization of extra dimensions is naturally incorporated in such a generalization of Einstein gravity under rather orthodox assumptions. We have restricted our study to pure $f(R)$ gravity without additional matter sources partially in view of the fact that if the acceleration is to continue indefinitely any ordinary matter term is to redshift to irrelevancy and mostly for economy in understanding. The general conditions we find are that the manifold of the extra dimensional space is to have negative internal curvature and that the Ricci scalar of the full space-time manifold is also negative. The positive curvature case for an extra dimensional manifold is actually the most generic case. However, this necessitates a fine-tuning between the Hubble constant and the size of extra dimensions in the absence of matter sources.

Dynamics of linear perturbations inf(R)gravity

We consider predictions for structure formation from modifications to general relativity in which the Einstein-Hilbert action is replaced by a general function of the Ricci scalar. We work without fixing a gauge, as well as in explicit popular coordinate choices, appropriate for the modification of existing cosmological code. We present the framework in a comprehensive and practical form that can be directly compared to standard perturbation analyses. By considering the full evolution equations, we resolve perceived instabilities previously suggested, and instead find a suppression of perturbations. This result presents significant challenges for agreement with current cosmological structure formation observations. The findings apply to a broad range of forms of f(R) for which the modification becomes important at low curvatures, disfavoring them in comparison with the LCDM scenario. As such, these results provide a powerful method to rule out a wide class of modified gravity models aimed at providing an alternative explanation to the dark energy problem.

Modified gravity withf(R)=R2−R02

In this work we propose a modified gravity with the action $f(R)=\sqrt{{R}^{2}\ensuremath{-}{R}_{0}^{2}}$ instead of the Einstein-Hilbert action to describe the late time acceleration of the Universe. We obtain the equation of the modified gravity both in the metric and Palatini formalisms. An asymptotic solution of gravity equations corresponding to a constant Ricci scalar causes a late time acceleration of the Universe. We do a conformal transformation in the action of the modified gravity and obtain the equivalent minimally coupled scalar-tensor gravity. The equivalent Brans-Dicke gravity of this model is also studied. To examine this model with observation, the perihelion precession of the Mercury is compared with our prediction and we put an upper constraint of ${R}_{0}l{H}_{0}^{2}$. This range for ${R}_{0}$ is also in agreement with the cosmological acceleration at the present time. Finally we show that this action has instability for the small perturbations of the metric in vacuum solution in which adding a quadratic term of Ricci scalar can stabilize it.

Constraining f(R) theories with the energy conditions

A new method to constrain gravitational theories depending on the Ricci scalar is presented. It is based on the weak energy condition and yields limits on the parameters of a given theory through the current values of the derivatives of the scale factor of the Friedmann–Robertson–Walker geometry. A further constraint depending on the current value of the snap is also given. Actual constraints (and the corresponding error propagation analysis) are calculated for two examples, which show that the method is useful in limiting the possible f ( R ) theories.

Homogeneous Finsler spaces of negative curvature

We prove that a homogeneous Finsler space with non-positive flag curvature and strictly negative Ricci scalar is a simply connected manifold.