Higher Derivative Gravity Theories Research Articles

Accelerating universe in modified theories of gravity

We study cosmologies in modified theories of gravity considering Lagrangian density $f(R)$ which is a polynomial function of scalar curvature $(R)$ in the Einstein-Hilbert action in vacuum. The field equation obtained from the modified action corresponding to a Robertson-Walker metric is highly nonlinear and not simple enough to obtain analytic solution. Consequently we adopt a numerical technique to study the evolution of the Friedmann-Robertson-Walker universe. A number of evolutionary phases of the Universe including the present accelerating phase are found to exist in the higher derivative theories of gravity. The cosmological solutions obtained here are new and interesting. We study a modified theory of gravity as a toy model to explore the past and the present, and to predict the future evolution. It is found that all the models analyzed here can reproduce the current accelerating phase of expansion of the Universe. The duration of the present accelerating phase is found to depend on the coupling constants of the gravitational action. The physical importance of the coupling parameters considered in the action are also discussed.

Anisotropically inflating universes in a scalar-tensor theory

We show that a Brans-Dicke model admits some anisotropically inflating solutions which are identical to the solutions found in a higher derivative pure gravity theory. These inflating solutions were shown to break the cosmic no-hair theorem such that they do not approach the de Sitter universe at large times. The stability conditions of these solutions in this scalar-tensor theory are shown explicitly in this paper. It is shown that there exist unstable modes of the anisotropic perturbations. Therefore the inflating solutions are unstable in the scalar-tensor theory.

Resolution of curvature singularities in higher derivative gravity

We consider possible resolutions of singularities in a contracting anisotropic universe for a class of higher derivative gravity theories. We give evidence that for our models the big crunch singularity may be replaced by a nearly flat Minkowski-like phase before the Universe reenters an anisotropic expansion in a time-symmetric manner.

Viscous cosmologies with variableΛin higher derivative gravity

We obtain cosmological solutions in higher derivative theories of gravity in the presence of an imperfect fluid and a time varying cosmological parameter ($\ensuremath{\Lambda}$). We explore both power-law and exponential expansion of the universe considering an imperfect fluid described by the Eckart, truncated, and full causal theories proposed by Israel and Stewart. We discuss the physical and geometrical features of the models in the presence of a known time varying $\ensuremath{\Lambda}$. The interesting feature of the models is that they admit accelerating universes in some specific cases. The evolution of the temperature of the universe in the framework of the full causal theory is also determined.

Phase transitions in higher derivative gravity and gauge theory: R-charged black holes

This is a continuation of our earlier work where we constructed a phenomenologically motivated effective action of the boundary gauge theory at finite temperature and finite gauge coupling on S3 × S1. In this paper, we argue that this effective action qualitatively reproduces the gauge theory representing various bulk phases of R-charged black hole with Gauss-Bonnet correction. We analyze the system both in canonical and grand canonical ensemble.

Towards a holographic dual of SQCD: holographic anomalies and higher derivative gravity

We consider the holographic dual of SQCD in the conformal phase. It is based on a higher derivative gravity theory, which ensures the correct field theory anomalies. This is then related to a six-dimensional gravity theory via S1 compactification. Some speculations are then made about the correspondence, Seiberg duality and the nature of confinement from a holographic perspective.

Rotating attractors

We prove that, in a general higher derivative theory of gravity coupled to abelian gauge fields and neutral scalar fields, the entropy and the near horizon background of a rotating extremal black hole is obtained by extremizing an entropy function which depends only on the parameters labeling the near horizon background and the electric and magnetic charges and angular momentum carried by the black hole. If the entropy function has a unique extremum then this extremum must be independent of the asymptotic values of the moduli scalar fields and the solution exhibits attractor behaviour. If the entropy function has flat directions then the near horizon background is not uniquely determined by the extremization equations and could depend on the asymptotic data on the moduli fields, but the value of the entropy is still independent of this asymptotic data. We illustrate these results in the context of two derivative theories of gravity in several examples. These include Kerr black hole, Kerr-Newman black hole, black holes in Kaluza-Klein theory, and black holes in toroidally compactified heterotic string theory.

Anisotropic higher derivative gravity and inflationary universe

Stability analysis of the Kantowski-Sachs type universe in pure higher derivative gravity theory is studied in details. The non-redundant generalized Friedmann equation of the system is derived by introducing a reduced one dimensional generalized KS type action. This method greatly reduces the labor in deriving field equations of any complicate models. Existence and stability of inflationary solution in the presence of higher derivative terms are also studied in details. Implications to the choice of physical theories are discussed in details in this paper.

Higher-derivative gravity in brane world models

We investigate brane world models in higher-derivative gravity theories where thegravitational Lagrangian is an arbitrary function of the Ricci scalar. Making use of theconformal equivalence of such gravity models and Einstein–Hilbert gravity with a scalarfield, we deduce the main features of higher-derivative gravity brane worlds. Wesolve for a gravity model that has corrections quadratic in the Ricci scalar andfind it is possible to have a vanishing bulk cosmological constant. An analysis oftensor and scalar perturbations shows that gravity is localized on the brane, theNewtonian limit is recovered and the brane–bulk system appears to be stabilized.

Fluctuations, ghosts, and the cosmological constant

For a large region of parameter space involving the cosmological constant and mass parameters, we discuss fluctuating spacetime solutions that are effectively Minkowskian on large time and distance scales. Rapid, small amplitude oscillations in the scale factor have a frequency determined by the size of a negative cosmological constant. A field with modes of negative energy is required. If it is gravity that induces a coupling between the ghost-like and normal fields, we find that this results in stochastic rather than unstable behavior. The negative energy modes may also permit the existence of Lorentz invariant fluctuating solutions of finite energy density. Finally we consider higher derivative gravity theories and find oscillating metric solutions in these theories without the addition of other fields.

New bulk scalar field solutions in brane worlds

We use nonlinear perturbation theory to obtain new solutions for brane world models thatincorporate a massive bulk scalar field. We then consider tensor perturbations and showthat Newtonian gravity is recovered on the brane for both a light scalar field and fora bulk field with large negative mass. This latter result points to the viabilityof higher-derivative theories of gravity in the context of bulk extra dimensions.

(Anti–)de Sitter black holes in higher derivative gravity and dual conformal field theories

Thermodynamics of five-dimensional Schwarzschild Anti-de Sitter (SAdS) and SdS black holes in the particular model of higher derivative gravity is considered. The free energy, mass (thermodynamical energy) and entropy are evaluated. There exists the parameters region where BH entropy is zero or negative. The arguments are given that corresponding BH solutions are not stable. We also present the FRW-equations of motion of time (space)-like branes in SAdS or SdS BH background. The properties of dual CFT are discussed and it is shown that it has zero Casimir energy when BH entropy (effective gravitational constant) is zero. The Cardy-Verlinde formula for CFT dual to SAdS or SdS BH is found in the universal form.

Propagator, tree-level unitarity and effective nonrelativistic potential for higher-derivative gravity theories in D dimensions

A prescription for computing the propagator for D-dimensional higher-derivative gravity theories, based on the Barnes–Rivers operators, is presented. A systematic study of the tree-level unitarity of these theories is developed and the agreement of their linearized versions with Newton’s law is investigated by computing the corresponding effective nonrelativistic potential. Three-dimensional quadratic gravity with a gravitational Chern–Simons term is also analyzed. A discussion on the issue of light bending within the framework of both D-dimensional quadratic gravity and three-dimensional quadratic gravity with a Chern–Simons term is provided as well.

Consistency of higher derivative gravity in the brane background

We consider the theory of higher derivative gravity with non-factorizable Randall-Sundrum type space-time and obtain the metric solutions which characterize the $p$-brane world-volume as a curved or planar defect embedded in the higher dimensions. We consider the string inspired effective actions of the dilatonic Gauss-Bonnet type in the brane background and show its consistency with the RS brane-world scenario and the conformal weight of the dilaton couplings in the string theory with apppropriate choice of Regge slope ($\alpha'$) or Gauss-Bonnet coupling ($\alpha$) or both. We also discuss a time dependent dilaton solution for a string-inspired fourth-derivative gravity.

Algorithm for Computing the Propagator for Higher Derivative Gravity Theories

A simple algorithm for computing the propagator for higher derivative gravitytheories based on the Barnes–Rivers operators is presented. The prescription isused, among other things, to obtain the propagator for quadratic gravity in anunconventional gauge. We also find the propagator for both gravity and quadraticgravity in an interesting gauge recently baptized the “Einstein” gauge[Hitzer and Dehnen, Int. J. Theor. Phys.36 (1997), 559].

Higher-derivative Quantum Cosmology

The quantum cosmology of a higher-derivative gravity theory arising from the heterotic string effective action is reviewed. A new type of Wheeler–DeWitt equation is obtained when the dilaton is coupled to the quadratic curvature terms. Techniques for solving the Wheeler–DeWitt equation with appropriate boundary conditions shall be described, and implications for semiclassical theories of inflationary cosmology will be outlined.

Higher Derivative Gravity in Generalized Covariant Derivative Formalism

Field strength (‘curvature’ tensor in mathematical terms) is one of the key concepts in gauge theory. To develop a new unified theory of the gauge and Higgs fields, a “field strength” is introduced for the Higgs field by generalizing covariant derivatives for chiral multi-spinor fields so as to include the Dirac γ-matrices. 1), 2) The new theory, formulated without changing the usual notion of geometry and spacetime, has been shown to reproduce essential results of the Connes theory, 3) based on non-commutative geometry in the multi-leaved Minkowski spacetime. As a natural development of the theory, we investigate here the possible unification of gravity with the U(1) gauge and Higgs fields. Under a torsion-free condition, we arrive at a 1-loop renormalizable and asymptotically-free theory of higher derivative gravity. 4) 9) For brevity’s sake, we restrict ourselves to consideration of a fermion field ψ(x) interacting with the electromagnetic field Aμ(x), a scalar field φ(x), and a gravitational field. The fermionic Lagrangian of the system is given by

Photon propagation in Einstein and higher derivative gravity

We derive the wave equation obeyed by electromagnetic fields in curved space-time. We find that there are Riemann and Ricci curvature coupling terms to the photon polarisation which result in a polarisation-dependent deviation of the photon trajectories from null geodesics. Photons are found to have an effective mass in an external gravitational field and their velocity in an inertial frame is, in general, less than c. A physically relevant consequence of the analysis is that the curvature corrections to the propagation of electromagnetic radiation (in an homogenous and isotropic space-time) keep the velocities subluminal provided the strong energy condition is satisfied. We further show that the claims of superluminal velocities in higher derivative gravity theories are erroneous and arise due to the neglect of Riemann and Ricci coupling terms in the wave equation of Einstein gravity.

Dilatonic black holes in higher curvature string gravity. II. Linear stability

We demonstrate linear stability of the dilatonic Black Holes appearing in a string-inspired higher-derivative gravity theory with a Gauss- Bonnet curvature-squared term. The proof is accomplished by mapping the system to a one-dimensional Schrodinger problem which admits no bound states. This result is important in that it constitutes a linearly stable example of a black hole that bypasses the `no-hair conjecture'. However, the dilaton hair is `secondary'in the sense that it is not accompanied by any new quantum number for the black hole solution.

Nonlinear lagrangians and the isotropy of the universe

We analyse the question of whether, in higher derivative gravity theories, the present isotropic state of the universe could have been obtained by starting from “arbitrary” initial conditions. We show that the Collins-Hawking conclusion holds in this extended case, that is, the set of spatially homogeneous cosmologies which can approach isotropy at late times is of measure zero in the space of all spatially homogeneous universe models. This involves an examination of a generalized form of the Raychaudhuri equation valid in a general higher-order theory of gravity in four spacetime dimensions. We show that this equation is conformally equivalent to what we call a Raychaudhuri system, that is, to the usual Raychaudhuri equation in general relativity coupled to a scalar-wave equation satisfied by the scalar field generated by the conformal transformation with the usual effective potential. This result is also used to prove directly in higher-order gravity the known forms of cosmic no-hair theorems in the Sitter and power-law inflation in general relativity. Generalizations to arbitrary dimensionality and also the addition of other curvature invariants are discussed.