Higher Derivative Gravity Theories Research Articles

Second order higher-derivative corrections in Double Field Theory

HSZ Double Field Theory is a higher-derivative theory of gravity with exact and manifest T-duality symmetry. The first order corrections in the massless sector were shown to be governed solely by Chern-Simons deformations of the three-form field strength. We compute the full action with up to six derivatives mathcal{O}left({alpha}^{prime 2}right) for the universal sector containing the metric, two-form and dilaton fields. The Green-Schwarz transformation of the two-form field remains uncorrected to second order. In addition to the expected Chern-Simons-squared and Riemann-cubed terms the theory contains a cubic Gauss-Bonnet interaction, plus other six-derivative unambiguous terms involving the three-form field strength whose presence indicates that the theory must contain further higher-derivative corrections.

BTZ black holes and flat space cosmologies in higher derivative theories

We consider BTZ black holes and flat space cosmologies in generic higher derivative gravity theories in 2 + 1 dimensions. Our goal is to prove the match between the bulk Iyer–Wald entropy and the field theory entropy for various symmetry algebras (CFT2, Warped CFT2, BMS3). We also discuss phase transitions in higher curvature theories, and argue that, in the flat case, there is strictly speaking no phase transition in the grand canonical ensemble.

Holographic entanglement entropy, field redefinition invariance, and higher derivative gravity theories

It is established that physical observables in local quantum field theories should be invariant under invertible field redefinitions. It is then expected that this statement should be true for the entanglement entropy and moreover that, via the gauge/gravity correspondence, the recipe for computing entanglement entropy holographically should also be invariant under local field redefinitions in the gravity side. We use this fact to fix the recipe for computing holographic entanglement entropy (HEE) for $f(R,R_{\mu\nu})$ theories which could be mapped to Einstein gravity. An outcome of our prescription is that the surfaces that minimize the corresponding HEE functional for $f(R,R_{\mu\nu})$ theories always have vanishing trace of extrinsic curvature and that the HEE may be evaluated using the Wald entropy functional. We show that similar results follow from the FPS and Dong HEE functionals, for Einstein manifold backgrounds in $f(R,R_{\mu\nu})$ theories.

Generalised boundary terms for higher derivative theories of gravity

In this paper we wish to find the corresponding Gibbons-Hawking-York term for the most general quadratic in curvature gravity by using Coframe slicing within the Arnowitt-Deser-Misner (ADM) decomposition of spacetime in four dimensions. In order to make sure that the higher derivative gravity is ghost and tachyon free at a perturbative level, one requires infinite covariant derivatives, which yields a generalised covariant infinite derivative theory of gravity. We will be exploring the boundary term for such a covariant infinite derivative theory of gravity.

Super-renormalizable or finite Lee–Wick quantum gravity

We propose a class of multidimensional higher derivative theories of gravity without extra real degrees of freedom besides the graviton field. The propagator shows up the usual real graviton pole in k2=0 and extra complex conjugates poles that do not contribute to the absorptive part of the physical scattering amplitudes. Indeed, they may consistently be excluded from the asymptotic observable states of the theory making use of the Lee–Wick and Cutkosky, Landshoff, Olive and Polkinghorne prescription for the construction of a unitary S-matrix. Therefore, the spectrum consists of the graviton and short lived elementary unstable particles that we named “anti-gravitons” because of their repulsive contribution to the gravitational potential at short distance. However, another interpretation of the complex conjugate pairs is proposed based on the Calmet's suggestion, i.e. they could be understood as black hole precursors long established in the classical theory. Since the theory is CPT invariant, the conjugate complex of the micro black hole precursor can be interpreted as a white hole precursor consistently with the 't Hooft complementarity principle. It is proved that the quantum theory is super-renormalizable in even dimension, i.e. only a finite number of divergent diagrams survive, and finite in odd dimension. Furthermore, turning on a local potential of the Riemann tensor we can make the theory finite in any dimension. The singularity-free Newtonian gravitational potential is explicitly computed for a range of higher derivative theories. Finally, we propose a new super-renormalizable or finite Lee–Wick standard model of particle physics.

Warped AdS3 black holes in higher derivative gravity theories

We consider warped AdS_3 black holes in generic higher derivatives gravity theories in 2+1 dimensions. The asymptotic symmetry group of the phase space containing these black holes is the semi-direct product of a centrally extended Virasoro algebra and an affine u(1) Kac-Moody algebra. Previous works have shown that in some specific theories, the entropy of these black holes agrees with a Cardy-like entropy formula derived for warped conformal field theories. In this paper, we show that this entropy matching continues to hold for the most general higher derivative theories of gravity. We also discuss the existence of phase transitions.

RG flow and thermodynamics of causal horizons in higher-derivative AdS gravity

In arXiv:1508.01343 [hep-th], one of the authors proposed that in AdS/CFT the gravity dual of the boundary $c$-theorem is the second law of thermodynamics satisfied by causal horizons in AdS and this was verified for Einstein gravity in the bulk. In this paper we verify this for higher derivative theories. We pick up theories for which an entropy expression satisfying the second law exists and show that the entropy density evaluated on the causal horizon in a RG flow geometry is a holographic c-function. We also prove that given a theory of gravity described by a local covariant action in the bulk a sufficient condition to ensure holographic c-theorem is that the second law of causal horizon thermodynamics be satisfied by the theory. This allows us to explicitly construct holographic c-function in a theory where there is curvature coupling between gravity and matter and standard null energy condition cannot be defined although second law is known to hold. Based on the duality between c-theorem and the second law of causal horizon thermodynamics proposed in arXiv:1508.01343 [hep-th] and the supporting calculations of this paper we conjecture that every Unitary higher derivative theory of gravity in AdS satisfies the second law of causal horizon thermodynamics. If this is not true then c-theorem will be violated in a unitary Lorentz invariant field theory.

Gravity waves in three dimensions

We find the explicit forms of the anti-de Sitter plane, anti-de Sitter spherical, and pp waves that solve both the linearized and exact field equations of the most general higher derivative gravity theory in three dimensions. As a sub-class, we work out the six derivative theory and the critical version of it where the masses of the two spin-2 excitations vanish and the spin-0 excitations decouple.

Mass Gap for Black-Hole Formation in Higher-Derivative and Ghost-Free Gravity.

We study a spherical gravitational collapse of a small mass in higher-derivative and ghost-free theories of gravity. By boosting a solution of linearized equations for a static point mass in such theories we obtain in the Penrose limit the gravitational field of an ultrarelativistic particle. Taking a superposition of such solutions we construct a metric of a collapsing null shell in the linearized higher-derivative and ghost-free gravity. The latter allows one to find the gravitational field of a thick null shell. By analyzing these solutions we demonstrate that in a wide class of the higher dimensional theories of gravity as well as for the ghost-free gravity there exists a mass gap for mini-black-hole production. We also found conditions when the curvature invariants remain finite at r=0 for the collapse of the thick null shell.

Quantum fluctuations and thermal dissipation in higher derivative gravity

In this paper, based on the AdS2/CFT1 prescription, we explore the low frequency behavior of quantum two point functions for a special class of strongly coupled CFTs in one dimension whose dual gravitational counterpart consists of extremal black hole solutions in higher derivative theories of gravity defined over an asymptotically AdS spacetime. The quantum critical points thus described are supposed to correspond to a very large value of the dynamic exponent (z→∞). In our analysis, we find that quantum fluctuations are enhanced due to the higher derivative corrections in the bulk which in turn increases the possibility of quantum phase transition near the critical point. On the field theory side, such higher derivative effects would stand for the corrections appearing due to the finite coupling in the gauge theory. Finally, we compute the coefficient of thermal diffusion at finite coupling corresponding to Gauss Bonnet corrected charged Lifshitz black holes in the bulk. We observe an important crossover corresponding to z=5 fixed point.

Standard model and graviweak unification with (super)renormalizable gravity. Part I: Visible and invisible sectors of the universe

We develop a self-consistent Spin (4, 4)-invariant model of the unification of gravity with weak SU(2) gauge and Higgs fields in the visible and invisible sectors of our universe. We consider a general case of the graviweak unification, including the higher-derivative super-renormalizable theory of gravity, which is a unitary, asymptotically-free and perturbatively consistent theory of the quantum gravity.

Viscosity bound for anisotropic superfluids in higher derivative gravity

In the present paper, based on the principles of gauge/gravity duality we analytically compute the shear viscosity to entropy (η/s) ratio corresponding to the super fluid phase in Einstein Gauss-Bonnet gravity. From our analysis we note that the ratio indeed receives a finite temperature correction below certain critical temperature (T < T c ). This proves the non universality of η/s ratio in higher derivative theories of gravity. We also compute the upper bound for the Gauss-Bonnet coupling (λ) corresponding to the symmetry broken phase and note that the upper bound on the coupling does not seem to change as long as we are close to the critical point of the phase diagram. However the corresponding lower bound of the η/s ratio seems to get modified due to the finite temperature effects.

Chaotic inflation in higher derivative gravity theories

In this paper, we investigate chaotic inflation from a scalar field subjected to a potential in the framework of $$f(R^2, P, Q)$$ -gravity, where we add a correction to Einstein’s gravity based on a function of the square of the Ricci scalar $$R^2$$ , the contraction of the Ricci tensor $$P$$ , and the contraction of the Riemann tensor $$Q$$ . The Gauss–Bonnet case is also discussed. We give the general formalism of inflation, deriving the slow-roll parameters, the $$e$$ -fold number, and the spectral indices. Several explicit examples are furnished; namely, we will consider the cases of a massive scalar field and a scalar field with quartic potential and some power-law function of the curvature invariants under investigation in the gravitational action of the theory. A viable approach to inflation according with observations is analyzed.

Renormalization and unitarity in higher derivative and nonlocal gravity theories

We review and discuss higher derivative and nonlocal theories of quantum gravity focusing on their UV and unitarity properties. We first consider the general fourth-order gravitational action, then actions containing derivatives up to any given fixed order, and discuss their UV divergences, fixed points and concomitant unitarity issues. This leads to a more general discussion of "asymptotic safety" and unitarity, which motivates the introduction of nonlocal theories containing derivatives to all orders arising from the expansion of entire functions. For such theories good UV behavior is visible at any finite truncation, but unitarity emerges only when derivatives to all orders are included.

Super-renormalizable and finite gravitational theories

We hereby introduce and extensively study a class of non-polynomial higher derivative theories of gravity that realize a ultraviolet (UV) completion of Einstein general relativity. These theories are unitary (ghost free) and at most only one-loop divergences survive. The outcome is a class of theories super-renormalizable in even dimension and finite in odd dimension. Moreover, we explicitly prove in D=4 that there exists an extension of the theory that is completely finite and all the beta functions vanish even at one-loop. These results can be easily extended in extra dimensions and it is likely that the higher dimensional theory can be made finite, too. Therefore we have the possibility for “finite quantum gravity” in any dimension.

On entanglement entropy functionals in higher-derivative gravity theories

In arXiv:1310.5713 and arXiv:1310.6659 a formula was proposed as the entanglement entropy functional for a general higher-derivative theory of gravity, whose lagrangian consists of terms containing contractions of the Riemann tensor. In this paper, we carry out some tests of this proposal. First, we find the surface equation of motion for general four-derivative gravity theory by minimizing the holographic entanglement entropy functional resulting from this proposed formula. Then we calculate the surface equation for the same theory using the generalized gravitational entropy method of arXiv:1304.4926. We find that the two do not match in their entirety. We also construct the holographic entropy functional for quasi-topological gravity, which is a six-derivative gravity theory. We find that this functional gives the correct universal terms. However, as in the four-derivative case, the generalized gravitational entropy method applied to this theory does not give exactly the surface equation of motion coming from minimizing the entropy functional.

Extended massive gravity in three dimensions

Using a first order Chern-Simons-like formulation of gravity we systematically construct higher-derivative extensions of general relativity in three dimensions. The construction ensures that the resulting higher-derivative gravity theories are free of scalar ghosts. We canonically analyze these theories and construct the gauge generators and the boundary central charges. The models we construct are all consistent with a holographic c-theorem which, however, does not imply that they are unitary. We find that Born-Infeld gravity in three dimensions is contained within these models as a subclass.

Do we have unitary and (super)renormalizable quantum gravity below the Planck scale?

We explore how the stability of metric perturbations in higher derivative theories of gravity depends on the energy scale of initial seeds of such perturbations and on a typical energy scale of the gravitational vacuum background. It is shown that, at least in the cases of specific cosmological backgrounds, that the unphysical massive ghost which is present in the spectrum of such theories is not growing up as a physical excitation and remains in the vacuum state, until the initial frequency of the perturbation is close to the Planck order of magnitude. In this situation the existing versions of renormalizable and superrenormalizable theories can be seen as very satisfactory effective theories of Quantum Gravity below the Planck scale.

BRST QUANTIZATION OF A SIXTH-ORDER DERIVATIVE SCALAR FIELD THEORY

We study a sixth-order derivative scalar field model in Minkowski spacetime as a toy model of higher-derivative critical gravity theories. This model is consistently quantized when using the Becchi–Rouet–Stora–Tyutin (BRST) quantization scheme even though it does not show gauge symmetry manifestly. Imposing a BRST quartet generated by two scalars and ghosts, there remains a nontrivial subspace with positive norm. This might be interpreted as a Minkowskian dual version of the unitary truncation in the logarithmic conformal field theory.

Spin–spin interactions in massive gravity and higher derivative gravity theories

We show that, in the weak field limit, at large separations, in sharp contrast to General Relativity (GR), all massive gravity theories predict distance-dependent spin alignments for spinning objects. For all separations GR requires anti-parallel spin orientations with spins pointing along the line joining the sources. Hence total spin is minimized in GR. On the other hand, while massive gravity at small separations (mgr⩽1.62) gives the same result as GR, for large separations (mgr>1.62) the spins become parallel to each other and perpendicular to the line joining the objects. Namely, the potential energy is minimized when the total spin is maximized in massive gravity for large separations. We also compute the spin–spin interactions in quadratic gravity theories and find that while at large separations GR result is intact, at small separations, spins become perpendicular to the line joining sources and anti-parallel to each other.