Higher-order Gravity Theories Research Articles

Cosmic analysis of a model in higher-order gravity theory

The late-time cosmic acceleration is investigated in modified gravity theory with higher-order curvature terms of the Ricci scalar and the Gauss–Bonnet invariant. The gravitational field equation is analyzed with an appropriate parameterization of the Hubble parameter and the cosmological constraints on model parameters are derived by using the Hubble, Pantheon, and their joint dataset. It is demonstrated that the best-fit values of the model parameters are in close agreement with the recent observations. Moreover, it is shown that the deceleration parameter transits from the decelerating to an accelerating phase in the late-time universe and that the equation of state parameter converges to the quintessence region and the accelerated expansion of the universe is realized. Furthermore, the perturbation analysis has been performed concerning the Hubble parameter and the energy density to examine the stability conditions of the model under the observational constraints. The energy conditions, the statefinder diagnostic, and the description of a scalar field theory are also investigated.

Probing bounce dynamics via Higher-Order Gauss-Bonnet modifications

In this paper, we focus on the Gauss-Bonnet gravity theory, which includes higher curvature corrections to the Einstein-Hilbert action. We investigate the possibility of obtaining a bouncing cosmology in this modified theory of gravity, where the Universe contracts until a minimum scale factor and then expands again. We examines four Higher-Order Gauss-Bonnet Gravity theory models within the FLRW formalism, emphasizing the Universe’s bouncing behavior to resolve Big-Bang cosmology’s singularity problem. We establish cosmological constraints over cosmic time, investigate bounce conditions, reconstruct Higher-Order Gauss-Bonnet Gravity for a hyperbolic expansion law, and extend this reconstruction using the red-shift parameter to derive cosmological parameters signifying accelerated Universe expansion. The stability of these models is subsequently evaluated through an arbitrary speed of sound function for late-time stability assessment. Our results suggest that the Gauss-Bonnet gravity theory can provide a viable mechanism for a non-singular bounce in the early universe.

Second-order corrections to Starobinsky inflation

Higher-order theories of gravity are extensions to general relativity (GR) motivated mainly by high-energy physics searching for GR ultraviolet completeness. They are characterized by the inclusion of correction terms in the Einstein–Hilbert action that leads to higher-order field equations. In this paper, we propose investigating inflation due to the GR extension built with all correction terms up to the second-order involving only the scalar curvature R, namely, R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R^{2}$$\\end{document}, R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R^{3}$$\\end{document}, R□R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R\\square R$$\\end{document}. We investigate inflation within the Friedmann cosmological background, where we study the phase space of the model, as well as explore inflation in slow-roll leading-order. Furthermore, we describe the evolution of scalar perturbations and properly establish the curvature perturbation. Finally, we confront the proposed model with recent observations from Planck, BICEP3/Keck, and BAO data.

Five-dimensional Einstein–Gauss–Bonnet gravity compactified and applied to a colour-flavour-locked equation of state

Einstein–Gauss–Bonnet gravity in five dimensions is applied to compact stellar objects, in particular to quark stars obeying a colour-flavour-locked equation of state. Matter under such extreme conditions welcomes the use of higher-order gravity theories or the inclusion of extra dimensions in support of higher-curvature effects. In so doing, we focus on the representation of quantities in higher dimensions in standard four-dimensional spacetime via compactification. Invoking extra compact dimensions from a basic string-theoretic perspective provides for the rationalisation of physical quantities computed in higher dimensions.

Perusing Buchbinder–Lyakhovich Canonical Formalism for Higher-Order Theories of Gravity

Ostrogradsky’s, Dirac’s, and Horowitz’s techniques in terms of higher-order theories of gravity produce identical phase-space structures. The problem with these techniques is manifested in the case of Gauss–Bonnet–dilatonic coupled action in the presence of higher-order term, in which case, classical correspondence cannot be established. Here, we explore another technique developed by Buchbinder and their collaborators (BL) and show that it also suffers from the same disease. However, when expressing the action in terms of the three-space curvature, and removing ‘the total derivative terms’, if Horowitz’s formalism or even Dirac’s constraint analysis is pursued, all pathologies disappear. Here, we show that the same is true for BL formalism, which appears to be the simplest of all the techniques to handle.

The gravitational energy-momentum pseudo-tensor in higher-order theories of gravity

The problem of non-localizability and the non-uniqueness of gravitational energy in general relativity has been considered by many authors. Several gravitational pseudo-tensor prescriptions have been proposed by physicists, such as Einstein, Tolman, Landau, Lifshitz, Papapetrou, Moller, andWeinberg. We examine here the energy-momentum complex in higher-order theories of gravity applying the Noether theorem for the invariance of gravitational action under rigid translations. This, in general, is not a tensor quantity because it is not a covariant object but only an affine tensor, that is, a pseudo-tensor. Therefore we propose a possible prescription of gravitational energy and momentum density for ?k gravity governed by the gravitational Lagrangian L1 = (R + a0R2 + Pp k=1 akR?kR) ??g and generally for n-order gravity described by the gravitational Lagrangian L = L (g??, g??,i1, 1??,i1i2, g??,i1i2i3 ,..., g??,i1i2i3...in). The extended pseudo-tensor reduces to the one introduced by Einstein in the limit of general relativity where corrections vanish. Then, we explicitly show a useful calculation, i.e., the power per unit solid angle ? emitted by a massive system and carried by a gravitational wave in the direction ? x for a fixed wave number k. We fix a suitable gauge, by means of the average value of the pseudo-tensor over a spacetime domain and we verify that the local pseudo-tensor conservation holds. The gravitational energy-momentum pseudo-tensor may be a useful tool to search for possible further gravitational modes beyond the two standard ones of general relativity. Their finding could be a possible observable signatures for alternative theories of gravity.

Functional renormalization for f(Rμνρσ) quantum gravity

We derive new functional renormalisation group flows for quantum gravity, in any dimension. The key new achievement is that the equations apply for any theory of gravity whose underlying Lagrangian $\sim f(R_{\mu\nu\rho\sigma})$ is a function of the Riemann tensor and the inverse metric. The results centrally exploit the benefits of maximally symmetric spaces for the evaluation of operator traces. The framework is highly versatile and offers a wide range of new applications to study quantum gravitational effects in extensions of Einstein gravity, many of which have hitherto been out of reach. The phase diagram and sample flows for Einstein-Hilbert gravity, Gauss-Bonnet, and selected higher-order theories of gravity are given. We also provide an algorithm to find the flow for general polynomial Riemann curvature interactions. The setup vastly enhances the reach of fixed point searches, enabling novel types of search strategies including across the operator space spanned by polynomial curvature invariants, and in extensions of general relativity relevant for cosmology. Further implications, and links with unimodular versions of gravity are indicated.

EFT approach to black hole scalarization and its compatibility with cosmic evolution

We address the issue of black hole scalarization and its compatibility with cosmic inflation and big bang cosmology from an effective field theory (EFT) point of view. In practice, using a well-defined and healthy toy model which (in part) has been broadly considered in the literature, we consider how higher-order theories of gravity, up to cubic operators in Riemann curvature, fit within this context. Interestingly enough, we find that already at this minimal level, there is a nontrivial interplay between the Wilson coefficients which are otherwise completely independent, constraining the parameter space where scalarization may actually occur. Conclusively, we claim that the EFT does exhibit black hole scalarization, remaining compatible with the inflationary paradigm, and admitting general relativity as a cosmological attractor.

Anisotropic spacetimes in f(T, B) theory I: Bianchi I universe

That is the first part of a series of studies on analyzing the higher-order teleparallel theory of gravity known as the f(T, B)-theory. This work attempts to understand how the anisotropic spacetimes are involved in the f(T, B)-theory. In this work, we review the previous analysis of f(T, B)-gravity, and we investigate the global dynamics in the case of a locally rotational Bianchi I background geometry. We focus in the case of \(f\left( T,B\right) =T+F\left( B\right) \) theory and we determine the criteria where \(f\left( T,B\right) \)-theory solves the homogeneity problem. Finally, the integrability properties for the field equations are investigated by applying the Painlevé analysis. The analytic solution is expressed by a right Painlevé expansion.

Density Perturbation and Cosmological Evolution in the Presence of Magnetic Field in f R Gravity Models

In this paper, we have investigated the density perturbations and cosmological evolution in the FLRW universe in the presence of a cosmic magnetic field, which may be assumed to mimic primordial magnetic fields. Such magnetic fields have sufficient strength to influence galaxy formation and cluster dynamics, thereby leaving an imprint on the CMB anisotropies. We have considered the FLRW universe as a representative of the isotropic cosmological model in the 1 + 3 covariant formalism for f R gravity. The propagation equations have been determined and analyzed, where we have assumed that the magnetic field is aligned uniformly along the x -direction, resulting in a diagonal shear tensor. Subsequently, the density perturbation evolution equations have been studied, and the results have been interpreted. We have also indicated how these results change in the general relativistic case and briefly mentioned the expected change in higher-order gravity theories.

Canonical equivalence, quantization and inflation for higher-order theory of gravity

Canonical formulation of higher-order theory of gravity has been attempted over decades. Different routes lead to different phase-space structures of the Hamiltonian. Although, these Hamiltonians are canonically equivalent at the classical level, their quantum counterparts may not be same, due to nonlinearity. Earlier, it has been proved that ‘Dirac constraint analysis’ (after taking care of divergent terms) and ‘Modified Horowitz’ Formalism’ lead to identical phase-space structure of the Hamiltonian for the gravitational action with scalar curvature squared terms. For the sake of completeness, this paper expatiates the extension of the same work for a general fourth-order gravitational action. Canonical quantization and semiclassical approximation are performed to explore that such a quantum theory transits successfully to a classical de-Sitter Universe. Inflation is also studied. Inflationary parameters show excellent agreement with the recently released Planck’s data.

Improved gravitational-wave constraints on higher-order curvature theories of gravity

Gravitational wave observations of compact binaries allow us to test general relativity (and modifications thereof) in the strong and highly dynamical field regime of gravity. Here, we confront two extensions to general relativity, dynamical Chern-Simons, and Einstein-dilaton-Gauss-Bonnet theories, against the gravitational wave sources from the GWTC-1 and GWTC-2 catalogs by the LIGO-Virgo Collaboration. By stacking the posterior of individual events, we strengthen the constraint on the square root of the coupling parameter in Einstein-dilaton-Gauss-Bonnet gravity to $\sqrt{{\ensuremath{\alpha}}_{\mathrm{EdGB}}}<1.7\text{ }\text{ }\mathrm{km}$, but we are unable to place meaningful constraints on dynamical Chern-Simons gravity. Importantly, we also show that our bounds are robust to (i) the choice of general-relativity base waveform model, upon which we add modifications, (ii) unknown higher post-Newtonian order terms in the modifications to general relativity, (iii) the small-coupling approximation, and (iv) uncertainties on the nature of the constituent compact objects.

Cosmological curvature acceleration

Observed accelerated behavior of the Hubble flow, usually related to the existence of a mysterious unknown fluid dubbed dark energy, can be framed in natural extensions of General Relativity that work at infrared scales. This approach gives rise to a geometric view of the phenomenon that does not require any new particle to be addressed. In this review paper, without claiming for completeness, we will give the main ingredients of such an approach considering models like f(R) gravity, with R the Ricci curvature scalar, and, in general, higher-order theories of gravity including other curvature invariants. In this context, we will review also Teleparallel Equivalent General Relativity and its extensions like f(T) gravity, where T is the torsion scalar. We will show that the curvature picture and the torsion picture can be related each other giving an equivalent paradigm where the observed cosmological acceleration can be addressed by extending the gravitational sector.

Canonical equivalence, quantization and anisotropic inflation in higher order theory of gravity

We construct phase-space structure of a typical higher-order theory of gravity, in the background of anisotropic Bianchi-1 mini-superspace, following ‘modified Horowitz formalism’ as well as applying ‘Dirac algorithm’ (after taking care of the divergent terms), and establish equivalence. Canonical quantization, and semiclassical approximation are performed to expatiate the fact that such a quantum theory transits successfully to a classical de-Sitter Universe. Inflation has thereafter been studied. The numerical values of the inflationary parameters show excellent agreement with the latest released Planck’s data.

Ghost-free higher-order theories of gravity with torsion

In this manuscript we will present the theoretical framework of the recently proposed infinite derivative theory of gravity with a non-symmetric connection. We will explicitly derive the field equations at the linear level and obtain new solutions with a non-trivial form of the torsion tensor in the presence of a fermionic source, and show that these solutions are both ghost and singularity-free.

Canonical equivalence in anisotropic models for higher order theory of gravity

Different canonical formalisms for higher order theories lead to different phase-space structures of the Hamiltonian. Canonical equivalence of these Hamiltonians at the classical level does not assure the same in the quantum domain, due to nonlinearity. It has been proved in the isotropic models, that the “Dirac constraint analysis” (after taking care of divergent terms) and “Modified Horowitz Formalism” lead to identical phase-space structure of the Hamiltonian for the gravitational action with curvature squared terms. Here, we extend the same in anisotropic space-time, viz, Bianchi-I, Bianchi-III and Kantowski–Sachs models too. This is a prologue toward canonical quantization.

On rotating black holes in DHOST theories

Using the disformal solution-generating method, we construct new axisymmetric solutions in Degenerate Higher Order Scalar Tensor (DHOST) theories. The method consists in first considering a “seed” known solution in DHOST theories and then performing a disformal transformation of the metric to obtain a new solution. In vacuum, the two solutions are equivalent but they become physically inequivalent when one considers coupling to matter. In that way, we “disform” the stealth Kerr black hole solution and we obtain a first analytic rotating non-stealth solution in DHOST theories, while the associated scalar field is time-dependent with a constant kinetic density. The new solution is characterized by three parameters: the mass, the spin and the disformal parameter which encodes the deviation with respect to the Kerr geometry. We explore some geometrical properties of the novel disformed Kerr geometry which is no more Ricci flat but has the same singularity as the Kerr metric, admits an ergoregion, and is asymptotically flat. Moreover, the hidden symmetry of the Kerr solution is broken, providing an example of a non-circular geometry in a higher order theory of gravity. We also discuss geodesic motions and compute its (disformed) null directions which are interesting tools to understand the causal structure of the geometry. In addition, to illustrate again the potentiality of the disformal solution-generating method, we present another axisymmetric solution for DHOST theories obtained from a disformal transformation of the generalized Kerr solution of Einstein-Scalar gravity.

Gravitational AdS to dS phase transition in five-dimensional Einstein-Maxwell-Gauss-Bonnet gravity

In this work, we revisit a toy model proposed by Camanho {\it et.al.} [JHEP 10 (2015) 179] and extensively study the possible existence of gravitational phase transition from AdS to dS geometries by adding the Maxwell field as an impurity substitution. We show that the phase transitions proceed via the bubble nucleation of spherical thin-shells described by different branches of the solution which host a black hole in the interior. In order to demonstrate the existence of the phase transition, we examine how the free energy and temperature depend on the higher-order gravity coupling $(\lambda)$ indicating the possibility of thermalon mediated phase transition. We observe that the phase transitions of the charged case is possible in which the required (maximum) temperature is lower than that of the neutral case. Interestingly, we also discover that the critical temperature and the coupling $\lambda$ of the phase transitions are modified when having the charge. In addition, our results agree with the claim that the generalized gravitational phase transition is a generic behavior of the higher-order gravity theories even the matter field is added.

Anisotropic instability in a higher order gravity theory

We study a metric cubic gravity theory considering odd-parity modes of linear inhomogeneous perturbations on a spatially homogeneous Bianchi type I manifold close to the isotropic de Sitter spacetime. We show that in the regime of small anisotropy, the theory possesses new degrees of freedom compared to General Relativity, whose kinetic energy vanishes in the limit of exact isotropy. From the mass dispersion relation we show that such theory always possesses at least one ghost mode as well as a very short-time-scale (compared to the Hubble time) classical tachyonic (or ghost-tachyonic) instability. In order to confirm our analytic analysis, we also solve the equations of motion numerically and we find that this instability is developed well before a single e-fold of the scale factor. This shows that this gravity theory, as it is, cannot be used to construct viable cosmological models.

Spherically symmetric solutions in higher-derivative theories of gravity

Higher-order theories of gravity have received much attention from several areas including quantum gravity, string theory and cosmology. This paper proposes a higher-order gravity whose action includes all curvature scalar terms up to the second-order corrections of general relativity, namely, $R^{2}$, $R^{3}$ and $R\square R$. Then, we explore spherically symmetric and static solutions in the weak-field regime and black holes context. All solutions in the weak-field regime due to a point mass are deduced, and by making a stability analysis of these solutions, we restrict them to Yukawa-type solutions. In regard to black hole solutions, we use the Lichnerovicz method to investigate the possibility of existence of non-Schwarzschild black holes. The results obtained show that non-Schwarzschild solutions might exist. However, for reasonable values of the parameters of the theory, its horizon radii are extremely small making macroscopic black holes different from Schwarzschild unfeasible.