Fourth-order Gravity Research Articles

Noether symmetry analysis for fourth-order modified gravity theory: Cosmological solution and evolution

A modified fourth-order gravity theory namely the [Formula: see text] theory is considered in flat FLRW model to investigate both classical and quantum cosmology. The field equations are reduced to second-order differential equations by considering the technique of Lagrange multiplier. Noether symmetry analysis has been used both for obtaining classical solution and the wave function of the Universe in quantum cosmology. Finally the cosmological solutions are examined from observational view point.

Energy in Fourth-Order Gravity

Energy in Fourth-Order Gravity

Beyond Schwarzschild–de Sitter spacetimes. III. A perturbative vacuum with nonconstant scalar curvature in R+R2 gravity

In violation of the generalized Lichnerowicz theorem advocated by Nelson and others, quadratic gravity admits vacua with non-constant scalar curvature. In a recent publication [Phys. Rev. D 106, 104004 (2022)], we revitalized a program that Buchdahl originated but prematurely abandoned circa 1962 [Nuovo Cimento 23, 141 (1962)], and uncovered a novel exhaustive class of static spherically symmetric vacua for pure $R^2$ gravity. The Buchdahl-inspired metrics we obtained therein are exact solutions which exhibit non-constant scalar curvature. A product of fourth-order gravity, the metrics entail a new (Buchdahl) parameter $k$ which allows the Ricci scalar to vary on the manifold. The metrics are able to defeat the generalized Lichnerowicz theorem by evading an overly strong restriction on the asymptotic falloff in the Ricci scalar as assumed in the theorem. The Buchdahl parameter $k$ is a new characteristic of pure $R^2$ gravity, a higher-derivative theory. By venturing that the Buchdahl parameter should be a universal hallmark of higher-derivative gravity at large, in this paper we seek to extend the concept to the quadratic action $R^2+\gamma\,(R-2\Lambda)$. We are able to determine that the quadratic field equation admits a perturbative vacuo that is valid up to the order $O(k^2)$. Conforming with our guiding intuition, the Ricci scalar is non-constant, including the asymptotically flat case, as long as $k\neq0$ and $\gamma\neq0$. The existence of such an asymptotically flat vacuo with non-constant scalar curvature defeats the generalized Lichnerowicz theorem in its entirety. Our finding thus warrants restoring the $R^2$ term in the full quadratic action, $\gamma\,R+\beta\,R^2-\alpha\,C^{\mu\nu\rho\sigma}C_{\mu\nu\rho\sigma}$, when applying the L\"u-Perkins-Pope-Stelle ansatz. Implications to the L\"u-Perkins-Pope-Stelle solution are discussed herein.

Multicritical phase transitions in Lovelock AdS black holes

We demonstrate that black holes in order $N\ensuremath{\ge}4$ Lovelock gravity can exhibit multicritical phase behavior. We show an explicit example of a quadruple point in $d=10$ fourth-order Lovelock gravity and a quintuple point in $d=14$ sixth-order Lovelock gravity. We also demonstrate that multicriticality can be realized for uncharged, nonrotating black holes by highlighting a new type of multicritical point between black holes and thermal radiation. We discuss the methodology used and make comparisons to other black hole multicritical points in terms of the Gibbs phase rule.

Mesozoic magmatic arc in East Asian continental margin triggered by Paleo-Pacific plate subduction: Constraints from gravity and magnetic anomalies

The Mesozoic East Asian Continental Margin (EACM) is generally considered as a continental magmatic arc triggered by Paleo-Pacific Plate subduction. However, the magmatic arc was not evident for a long time. This paper tries to use the gravity and magnetic responses along the magmatic arc to deeply explore its spatio-temporal distribution. Based on the gravity and magnetic anomalies of the Mesozoic magmatic arc on the EACM and combined with the integration of previous geological and geochronological studies, it is found that the tectonic features of the magmatic arc are more obvious in the fourth-order approximation/detail gravity anomaly fields by using wavelet multi-scale analysis. Furthermore, the residual crustal gravity anomalies containing the medium-wavelength components of the complete Bouguer gravity anomalies are analyzed for the identification of the Jurassic magmatic arcs. Finally, line-drawing analysis is performed on the fourth-order detail gravity anomaly field to explore the response of the Mesozoic magmatic arcs to Paleo-Pacific subduction on the EACM. Our results support that the magmatic arcs on the EACM mainly developed in the Late Triassic-Early Cretaceous Andean Active Continental Margin and in the late Early Cretaceous-Eocene transtensional continental margin. Our study contributes to the formation and refinement of the Paleo-Pacific Plate subduction mechanism and the Mesozoic tectonic evolutionary model of the EACM, and also provides geophysical evidence for the reconstruction of dynamic processes of the EACM.

Bouncing Cosmology in Fourth-Order Gravity

The Big Bang initial singularity problem can be solved by means of bouncing solutions. In the context of extended theories of gravity, we will look for covariant effective actions whose field equations contain up to fourth-order derivatives of the metric tensor. In finding such bouncing solutions, we will make use of an order reduction technique based on a perturbative approach. Reducing the order of the field equations to second-order, we are able to find solutions which are perturbatively close to General Relativity. We will build the covariant effective actions of the resulting order reduced theories.

Physical black holes in fourth-order gravity

The existence of black holes is a central prediction of general relativity and thus serves as a basic consistency test for modified theories of gravity. In spherical symmetry, only two classes of dynamic solutions are compatible with the formation of an apparent horizon in finite time of a distant observer. Moreover, the formation of black holes follows a unique scenario involving both types of solutions. To be compatible with their existence, any self-consistent theory of modified gravity must satisfy several constraints. We derive properties of the modified gravity terms of $\mathfrak{f}(R)$ and generic fourth-order gravity theories and find that they naturally accommodate both classes of solutions. Consequently, the observation of an apparent horizon by itself may not suffice to distinguish between general relativity and modifications including up to fourth-order derivatives in the metric.

A positive energy theorem for fourth-order gravity

A positive energy theorem for fourth-order gravity

A Note on Singularity Avoidance in Fourth-Order Gravity

We consider the fourth-order differential theory of gravitation to treat the problem of singularity avoidance: studying the short-distance behaviour in the case of black-holes and the big-bang we are going to see a way to attack the issue from a general perspective.

No-go theorem for inflation in an extended Ricci-inverse gravity model

In this paper, we propose an extension of the Ricci-inverse gravity, which has been proposed recently as a very novel type of fourth-order gravity, by introducing a second order term of the so-called anticurvature scalar as a correction. The main purpose of this paper is that we would like to see whether the extended Ricci-inverse gravity model admits the homogeneous and isotropic Friedmann–Lemaitre–Robertson–Walker metric as its stable inflationary solution. However, a no-go theorem for inflation in this extended Ricci-inverse gravity is shown to appear through a stability analysis based on the dynamical system method. As a result, this no-go theorem implies that it is impossible to have such stable inflation in this extended Ricci-inverse gravity model.

Effective actions for loop quantum cosmology in fourth-order gravity

Loop quantum cosmology (LQC) is a theory which renders the Big Bang initial singularity into a quantum bounce, by means of short-range repulsive quantum effects at the Planck scale. In this work, we are interested in reproducing the effective Friedmann equation of LQC, by considering a generic f(R, P, Q) theory of gravity, where R=g^{mu nu }R_{mu nu } is the Ricci scalar, P=R_{mu nu }R^{mu nu }, and Q=R_{alpha beta mu nu }R^{alpha beta mu nu } is the Kretschmann scalar. An order reduction technique allows us to work in f(R, P, Q) theories which are perturbatively close to General Relativity, and to deduce a modified Friedmann equation in the reduced theory. Requiring that the modified Friedmann equation mimics the effective Friedmann equation of LQC, we are able to derive several functional forms of f(R, P, Q). We discuss the necessary conditions to obtain viable bouncing cosmologies for the proposed effective actions of f(R, P, Q) theory of gravity.

Virial theorem in scalar tensor fourth order gravity

In this paper, we study, in the Newtonian limit, the virial theorem in the context of a scalar tensor fourth order gravity. In particular, we show, that for a isolated galaxy in viral equilibrium, a specific class of scalar tensor fourth order gravity, i.e. f(R,phi )+omega (phi ),phi _{;alpha },phi ^{;alpha } in not suitable to explain the large fraction of dark matter necessary to have the flatness of the galaxies rotation curves experimentally observed.

Exact solution to perturbative conformal cosmology from recombination until the current era

In a previous paper (P. D. Mannheim, Phys. Rev. D 102, 123535 (2020)) we studied cosmological perturbation theory in the cosmology associated with the fourth-order derivative conformal gravity theory, and provided an exact solution to the theory in the recombination era. In this paper we present an exact solution that holds all the way from recombination until the current era.

No-go theorem for inflation in Ricci-inverse gravity

In this paper, we study the so-called Ricci-inverse gravity, which is a very novel type of fourth-order gravity proposed recently. In particular, we are able to figure out both isotropically and anisotropically inflating universes to this model. More interestingly, these solutions are shown to be free from a singularity problem. However, stability analysis based on the dynamical system method shows that both isotropic and anisotropic inflation of this model turn out to be unstable against field perturbations. This result implies a no-go theorem for both isotropic and anisotropic inflation in the Ricci-inverse gravity.

Constraints on extended gravity models through gravitational wave emission

Using recent experimental results of detection of gravitational waves from the binary black hole signals by Advanced LIGO and Advanced Virgo, we investigate the propagation of gravitational waves in the context of fourth order gravity nonminimally coupled to a massive scalar field. Gravitational radiation admits extra massive modes of oscillation and we assume that the amplitude of these modes is comparable to that of the massless mode. We derive the propagation equation and effective mass for each degree of freedom and we infer, from the current observational data, constraints on the free parameters of the gravity models we considered. In particular, for f(R)=R-R2/R0, the constraint obtained from the speed of gravitational waves is not compatible with the one set by Solar System tests, which implies that amplitude of the massive modes could not be detectable with current experiments on Earth.

Ghost problems from Pauli–Villars to fourth-order quantum gravity and their resolution

We review the history of the ghost problem in quantum field theory from the Pauli–Villars regulator theory to currently popular fourth-order derivative quantum gravity theories. While these theories all appear to have unitarity-violating ghost states with negative norm, we show that in fact these ghost states only appear because the theories are being formulated in the wrong Hilbert space. In these theories, the Hamiltonians are not Hermitian but instead possess an antilinear symmetry. Consequently, one cannot use inner products that are built out of states and their Hermitian conjugates. Rather, one must use inner products built out of states and their conjugates with respect to the antilinear symmetry, and these latter inner products are positive. In this way, one can build quantum theories of gravity in four spacetime dimensions that are unitary.

Cosmological singularities in conformal Weyl gravity

In this work, we study the issue of the past and future cosmological singularities in the context of the fourth-order conformal Weyl gravity. In particular, we investigate the emergent universe scenario proposed by Ellis et al., and find the stability conditions of the corresponding Einstein static state using the fixed point approach. We show that depending on the values of the parameters of the conformal Weyl gravity theory, there are possibilities for having initially stable emergent states for an FRW universe with both the positive and negative spatial curvatures. This represents that the conformal Weyl gravity can be free of the initial singularity problem. Then, following Barrow et al., we address the possible types of the finite-time future cosmological singularities. We discuss how these singularities also can be avoided in the context of this theory.

Electromagnetic field and dark dynamical scalars for spherical systems

This paper studies the effects of inhomogeneous fluid configurations on the evolution of relativistic spheres within the context of electromagnetic field and fourth order gravity. We assume a compact distribution of spherical structure that evolves due to the curvature influences coming from f (R) gravity model and non-ideal matter source. After calculating the corresponding f (R) equations of motion, an explicit formulation among Weyl scalar, dark dynamical scalars and material variables is developed. With f (R) curvature and charged fluid terms, all the non-zero dynamical variables are presented from the orthogonal decomposition the Riemann curvature tensor. The Raychaudhuri, Weyl scalar and shearing equations are formulated through modified scalar functions with and without varying Ricci scalar for perfect and imperfect spherical systems.

Stability issues of black hole in non-local gravity

We discuss stability issues of Schwarzschild black hole in non-local gravity. It is shown that the stability analysis of black hole for the unitary and renormalizable non-local gravity with γ2=−2γ0 cannot be performed in the Lichnerowicz operator approach. On the other hand, for the unitary and non-renormalizable case with γ2=0, the black hole is stable against the metric perturbations. For non-unitary and renormalizable local gravity with γ2=−2γ0=const (fourth-order gravity), the small black holes are unstable against the metric perturbations. This implies that what makes the problem difficult in stability analysis of black hole is the simultaneous requirement of unitarity and renormalizability around the Minkowski spacetime.

A first-order approach to conformal gravity

We investigate whether a spontaneously-broken gauge theory of the group may be a viable alternative to general relativity. The basic ingredients of the theory are an gauge field and a Higgs field W in the adjoint representation of the group with the Higgs field producing the symmetry breaking . The action for gravity is polynomial in and the field equations are first-order in derivatives of these fields. The new symmetry in the gravitational sector is interpreted in terms of an emergent local scale symmetry and the existence of ‘conformalized’ general relativity and fourth-order Weyl conformal gravity as limits of the theory is demonstrated. Maximally symmetric spacetime solutions to the full theory are found and stability of the theory around these solutions is investigated; it is shown that regions of the theory’s parameter space describe perturbations identical to that of general relativity coupled to a massive scalar field and a massless one-form field. The coupling of gravity to matter is considered and it is shown that Lagrangians for all fields are naturally gauge-invariant, polynomial in fields and yield first-order field equations; no auxiliary fields are introduced. Familiar Yang–Mills and Klein–Gordon type Lagrangians are recovered on-shell in the general-relativistic limit of the theory. In this formalism, the general-relativistic limit coincides with a spontaneous breaking of scale invariance and it is shown that this generates mass terms for Higgs and spinor fields.