Higher Derivative Gravity Theories Research Articles

Nontrivial vacua in higher-derivative gravitation.

A discussion of an extended class of higher-derivative classical theories of gravity is presented. A procedure is given for exhibiting the new propagating degrees of freedom, at the full non-linear level, by transforming the higher-derivative action to a canonical second-order form. For general fourth-order theories, described by actions which are general functions of the scalar curvature, the Ricci tensor and the full Riemann tensor, it is shown that the higher-derivative theories may have multiple stable vacua. The vacua are shown to be, in general, non-trivial, corresponding to deSitter or anti-deSitter solutions of the original theory. It is also shown that around any vacuum the elementary excitations remain the massless graviton, a massive scalar field and a massive ghost-like spin-two field. The analysis is extended to actions which are arbitrary functions of terms of the form $\nabla^{2k}R$, and it is shown that such theories also have a non-trivial vacuum structure.

Inflationary cosmology with aR+λT µν R µν /R Lagrangian

We consider an alternative higher order gravity theory which is non-analytic in the Ricci curvature. It has power-law inflationary behaviour. This is further evidence that inflation is a general property of higher derivative gravity theories.

One-loop renormalization of higher-derivative 2D dilaton gravity

A theory of higher-derivative 2D dilaton gravity which has its roots in the massive higher-spin mode dynamics of string theory is suggested. The divergences of the effective action to one-loop are calculated, both in the covariant and in the conformal gauge. Some technical problems which appear in the calculations are discussed. An interpretation of the theory as a particular D = 2 higher-derivative σ-model is given. for a specific case of higher-derivative 2D dilaton gravity, which is one loop multiplicatively renormalizable, static configurations corresponding to black holes are shown to exist.

Stability of the inflation in R2 cosmology with massless conformal quantum fields

A semiclassical higher-derivative theory of gravity is investigated for conformally invariant free quantum fields in homogeneous and isotropic spacetime with no cosmological constant nor classical source. In the spatially flat case the stability of the de Sitter solution is studied. Moreover, the Minkowski solution is found to be unstable.

Lorentzian wormholes in higher-derivative gravity and the weak energy condition.

The possibility of the existence of a traversible wormhole solution which does not break the weak energy condition is examined in a higher-derivative theory of gravity. No such solution is found, suggesting that a Lorentzian wormhole without the violation of the weak energy condition is incompatible with a wide class of gravitational theories. We show this in two simple examples of spherically symmetric wormhole solutions.

Black holes in higher-derivative gravity theories.

We study static spherically symmetric solutions of Einstein gravity plus an action polynomial in the Ricci scalar, $R$, of arbitrary degree, $n$, in arbitrary dimension, $D$. The global properties of all such solutions are derived by studying the phase space of field equations in the equivalent theory of gravity coupled to a scalar field, which is obtained by a field redefinition and conformal transformation. The following uniqueness theorem is obtained: provided that the coefficient of the $R^2$ term in the Lagrangian polynomial is positive then the only static spherically symmetric asymptotically flat solution with a regular horizon in these models is the Schwarzschild solution. Other branches of solutions with regular horizons, which are asymptotically anti-de Sitter, or de Sitter, are also found. An exact Schwarzschild-de Sitter type solution is found to exist in the $R+aR^2$ if $D>4$. If terms of cubic or higher order in $R$ are included in the action, then such solutions also exist in four dimensions. The general Schwarzschild-de Sitter type solution for arbitrary $D$ and $n$ is given. The fact that the Schwarzschild solution in these models does not coincide with the exterior solution of physical bodies such as stars has important physical implications which we discuss. As a byproduct, we classify all static spherically symmetric solutions of $D$-dimensional gravity coupled to a scalar field with a potential consisting of a finite sum of exponential terms.

Non-singular de Sitter universe inR+R 2?2? gravity

For the theory described by the action\(S = \int {(R + \varepsilon R^2 - 2\Lambda )} \sqrt { - g} d^4 x\) and taking the FRW flat space metric we find an exact non-singular de Sitter model universe exp(Λt2), with\(\Lambda = - \tfrac{1}{{72}}\varepsilon \). It is also proved that the standard general relativity de Sitter cosmology\(\exp (\sqrt {\tfrac{1}{3}\Lambda } t)\), Λ>0 is also a model of this higher derivative theory of gravity. If the metric is conformally flatS could describe a consistent quantum theory and its classical solutions would correspond to cosmological models in this theory.

WORMHOLE SOLUTIONS WITH GAUSS–BONNET TERM IN HIGHER DIMENSIONS

Wormhole solution is obtained in higher derivative gravity theory with Gauss–Bonnet term. The corresponding Euclidean action is finite and proportional to the coupling constant of Gauss–Bonnet term. The size of the wormhole is not fixed by the theory but large wormhole is highly suppressed.

Lorentzian wormholes in higher order gravity theories

We present a method for constructing Minkowski-signature wormholes in higher-derivative gravity theories. This is accomplished by exploiting the dynamical equivalence between standard Einstein gravity (coupled to bosonic matter fields) and a large class of higher curvature gravity theories. Specific solutions of the former are grafted together using the connected sum, and this gives rise to a wormhole whose throat is identified with the boundary layer created by the surgery. We illustrate this procedure by constructing dynamic and static wormholes for pure R 2 gravity.

KASNER-TYPE SOLUTION IN A HIGHER-DERIVATIVE GRAVITY THEORY

We study how the curvature squared terms, which may be included in the gravitational action, affects cosmology. We show, in particular, that the resulting higher-derivative gravity theory in 5 space-time dimensions admits a unique Kasner-type solution which represents three static space dimensions and one expanding space dimension.

Sedentary ghost poles in higher derivative gravity

Following Antoniadis and Tomboulis [1] we consider the gauge behaviour of the massive spin-2 ghost pole that appears in the propagator of higher derivative gravity theories. In contradistinction to [1] we observe that the pair of complex conjugate poles that appear in the resummed propagator are gauge independent. They are sedentary, that is, under a change in the gauge parameter they do not move. We derive this result using the ubiquitous Nielsen identities [11].

Higher-derivative gravity, surface terms, and string theory.

We consider adding Euler densities to the Einstein action as new gravity interactions in higher-dimensional theories. When the appropriate surface terms are included, the surface geometry is sufficient data for the boundary-value problem associated with the new Lagrangians. We also discuss the relevance of such interactions in the context of string theory.

Mass spectrum of the M 4×S D solution in Euler invariant type higher derivative gravity

The mass spectrum is computed in Euler invariant type higher derivative gravity theory in the case that the space-time is dimensionally reduced to the four-dimensional Minkowski space × D-dimensional sphere. It is shown at the linearized level that after the compactification there appear massless gravitons, massive spin-two particles, massless vectors and one massive scalar mode. All the vectors are massless and the masses of massive spin-two particles are proportional to the S D eigenvalues of the laplacian. Classical stability is shown to depend only on three parameters.

Asymptotic freedom in higher-derivative quantum gravity

We investigate the ultraviolet limit in the renormalizable higher-derivative gravity theory with a quadratic lagrangian of a general type and find the previous attempts at these investigations to be in error. The off-shell one-loop counterterms of the recently proposed unique effective action are computed in this theory, and in the case of the positive definite euclidean action the theory is shown to be asymptotically free. The possibility of restoring the unitarity due to radiative corrections is also discussed with regard to this positivity.

Remarks on a class of almost trivial solutions of the gravitational field equation: K. Kraus. Institute for Theoretical Physics Universität Marburg, Marburg, Germany

The mass spectrum is computed in Euler invariant type higher derivative gravity theory in the case that the space-time is dimensionally reduced to the four-dimensional Minkowski space × D-dimensional sphere. It is shown at the linearized level that after the compactification there appear massless gravitons, massive spin-two particles, massless vectors and one massive scalar mode. All the vectors are massless and the masses of massive spin-two particles are proportional to the SD eigenvalues of the laplacian. Classical stability is shown to depend only on three parameters.