Ghost-free Theory Research Articles

Massive bigravity as a presymplectic BV-AKSZ sigma-model

We propose a presymplectic BV-AKSZ sigma model encoding the ghost-free massive bigravity theory action as well as its Batalin-Vilkovisky extension in terms of the finite-dimensional graded geometry of the target space. A characteristic feature of the construction is that the target space is realised as a quasi-regular submanifold of a linear graded manifold which, in turn, is a direct product of two copies of the shifted Poincaré or (anti-)de Sitter Lie algebra. This graded manifold comes equipped with a natural presymplectcic structure and the compatible pre-Q structure which is a sum of the Chevalley-Eilenberg differentials of each copy of the Lie algebra and the interaction term. The constraints determining the submanifold are the supergeometrical realisation of the known Deser-van Nieuwenhuizen condition and its descendant.

Dijet spectrum in nonlocal and asymptotically nonlocal theories

Asymptotically nonlocal field theories approximate ghost-free nonlocal theories at low energies, yet are theories of finite order in the number of derivatives. These theories have an emergent nonlocal scale that regulates loop diagrams and can provide a solution to the hierarchy problem. Asymptotic nonlocality has been studied previously in scalar theories, Abelian and non-Abelian gauge theories with complex scalars, and linearized gravity. Here we extend that work by considering an asymptotically nonlocal generalization of QCD, which can be used for realistic phenomenological investigations. In particular, we derive Feynman rules relevant for the study of the production of dijets at hadron colliders and compute the parton-level cross sections at leading order. We use these to determine a bound on the scale of new physics from Large Hadron Collider data, both for a typical choice of model parameters, and in the nonlocal limit. Published by the American Physical Society 2024

Exact Solution for Rotating Black Holes in Parity-Violating Gravity

Abstract It has recently been pointed out that one can construct invertible conformal transformations with a parity-violating conformal factor, which can be employed to generate a novel class of parity-violating ghost-free metric theories from general relativity. We obtain exact solutions for rotating black holes in such theories by performing the conformal transformation on the Kerr solution in general relativity, which we dub conformal Kerr solutions. We explore the geodesic motion of a test particle in the conformal Kerr spacetime. While null geodesics remain the same as those in the Kerr spacetime, timelike geodesics exhibit interesting differences due to an effective external force caused by the parity-violating conformal factor.

Massless and partially massless limits in Quadratic Gravity

In the context of perturbative quantum field theory, the addition of quadratic-curvature invariants to the Einstein-Hilbert action makes it possible to achieve strict renormalizability in four dimensions. The additional terms R2 and CμνρσCμνρσ are multiplied by dimensionless coefficients that are related to the masses of the extra gravitational degrees of freedom and to the interaction couplings. The aim of this paper is to study the limit of the theory in which the Weyl-squared coefficient tends to infinity. Remarkably, the result of this limit turns out to be sensitive to the presence of a cosmological constant: when the latter is zero we have a massless limit for the spin-2 ghost, while when the cosmological constant is different from zero we obtain a partially massless limit. We show that the renormalizability property and the ghost-like nature of the massive spin-2 field ensure that the two limits do not hit strong couplings, unlike standard ghost-free theories of massive gravity. In particular, in the partially massless limit the interactions mediated by the spin-2 sector vanish. We argue that our results can be useful for understanding the high-energy limit of Quadratic Gravity.

A stringy massive double copy

We derive a massive double copy construction within string theory. To this end, we use massive vectors of the open string spectrum that appear in compactifications to four dimensions and construct massive spin-2 tensors as closed string states, thereby mimicking the structure of the massless graviton. We then compute three-point amplitudes for the scattering of massless and massive spin-2 closed string states and reveal the double copy structure of the latter. With these results being finite in the string scale, we are further able to reproduce the cubic Lagrangian of ghost-free bimetric theory around flat spacetime for bulk massive spin-2 states originating in products of vectors of extended brane supersymmetry.

Ghost free theory in unitary gauge: a new candidate

We propose an algebraic analysis using a 3+1 decomposition to identify conditions for a clever cancellation of the higher derivatives, which plagued the theory with Ostrogradsky ghosts, by exploiting some existing degeneracy in the Lagrangian. We obtain these conditions as linear equations (in terms of coefficients of the higher derivative terms) and demand that they vanish, such that the existence of nontrivial solutions implies that the theory is degenerate. We find that, for the theory under consideration, no such solutions exist for a general inhomogeneous scalar field, but that the theory is degenerate in the unitary gauge. We, then, find modified FLRW equations and narrow down conditions for which there could exist a de Sitter inflationary epoch. We further find constraints on the coefficients of the remaining higher-derivative interaction terms, based on power-counting renormalizability and tree-level unitarity up to the Planck scale.

Effective description of generalized disformal theories

Generalized disformal transformations enable us to construct the generalized disformal Horndeski theories, which form the most general class of ghost-free scalar-tensor theories to this date. We extend the effective field theory (EFT) of cosmological perturbations to incorporate these generalized disformal Horndeski theories. The main difference from the conventional EFT is that our extended EFT involves operators with higher spatial derivatives of the lapse function. Our EFT also accommodates the generalized disformal transformation of U-DHOST theories.

Cosmological evolution in bimetric gravity: observational constraints and LSS signatures

Bimetric gravity is an interesting alternative to standard GR given its potential to provide a concrete theoretical framework for a ghost-free massive gravity theory. Here we investigate a class of Bimetric gravity models for their cosmological implications. We study the background expansion as well as the growth of matter perturbations at linear and second order. We use low-redshift observations from SnIa (Pantheon+ and SH0ES), Baryon Acoustic Oscillations (BAO), the growth (fsigma _{8}) measurements and the measurement from Megamaser Cosmology Project to constrain the Bimetric model. We find that the Bimetric models are consistent with the present data alongside the Lambda CDM model. We reconstructed the “ effective dark energy equation of state”(omega _{de}) and “Skewness”(S_{3}) parameters for the Bimetric model from the observational constraints and show that the current low-redshift data allow significant deviations in omega _{de} and S_{3} parameters with respect to the Lambda CDM behaviour. We also look at the ISW effect via galaxy-temperature correlations and find that the best fit Bimetric model behaves similarly to Lambda CDM in this regard.

Asymptotically nonlocal gravity

Asymptotically nonlocal field theories interpolate between Lee-Wick theories with multiple propagator poles, and ghost-free nonlocal theories. Previous work on asymp- totically nonlocal scalar, Abelian, and non-Abelian gauge theories has demonstrated the existence of an emergent regulator scale that is hierarchically smaller than the lightest Lee-Wick partner, in a limit where the Lee-Wick spectrum becomes dense and decoupled. We generalize this construction to linearized gravity, and demonstrate the emergent regula- tor scale in three examples: by studying the resolution of the singularity (i) at the origin in the classical solution for the metric of a point particle, and (ii) in the nonrelativistic gravitational potential computed via a one-graviton exchange amplitude; (iii) we also show how this derived scale regulates the one-loop graviton contribution to the self energy of a real scalar field. We comment briefly on the generalization of our approach to the full, nonlinear theory of gravity.

Gravitational-wave energy and other fluxes in ghost-free bigravity

One of the key ingredients for making binary waveform predictions in a beyond-general-relativity (GR) theory of gravity is understanding the energy and angular momentum carried by gravitational waves and any other radiated fields. Identifying the appropriate energy functional is unclear in Hassan-Rosen bigravity, a ghost-free theory with one massive and one massless graviton. The difficulty arises from the new degrees of freedom and length scales which are not present in GR, rendering an Isaacson-style averaging calculation ambiguous. In this article we compute the energy carried by gravitational waves in bigravity starting from the action, using the canonical current formalism. The canonical current agrees with other common energy calculations in GR, and is unambiguous (modulo boundary terms), making it a convenient choice for quantifying the energy of gravitational waves in bigravity or any diffeomorphism-invariant theories of gravity. This calculation opens the door for future waveform modeling in bigravity to correctly include backreaction due to emission of gravitational waves.

Consistency of matter coupling in modified gravity

Matter coupling in modified gravity theories is a nontrivial issue when the gravitational Lagrangian possesses a degeneracy structure to avoid the problem of the Ostrogradsky ghost. Recently, this issue was addressed for bosonic matter fields in the generalized disformal Horndeski class, which is so far the most general class of ghost-free scalar-tensor theories obtained by performing a higher-derivative generalization of invertible disformal transformations on Horndeski theories. In this paper, we clarify the consistency of fermionic matter coupling in the generalized disformal Horndeski theories. We develop the transformation law for the tetrad associated with the generalized disformal transformation to see how it affects the fermionic matter coupling. We find that the consistency of the fermionic matter coupling requires an additional condition on top of the one required for the bosonic case. As a result, we identify a subclass of the generalized disformal Horndeski class which allows for consistent coupling of ordinary matter fields, including the standard model particles.

Large spin-2 signals at the cosmological collider

We study the theory and phenomenology of massive spin-2 fields during the inflation with nonzero background chemical potential, and extend the cosmological collider physics to tensor modes. We identify a unique dimension-5 and parity-violating chemical potential operator for massive spin-2 fields, which leads to a ghost-free linear theory propagating one scalar mode and two tensor modes. The chemical potential greatly boosts the production of one tensor mode even for very heavy spin-2 particles, and thereby leads to large and distinct cosmological collider signals for massive spin-2 particles. The large signals show up at the tree-level in both the curvature trispectrum and the tensor-curvature mixed bispectrum.

Multihorizons black hole solutions, photon sphere, and perihelion shift in weak ghost-free Gauss-Bonnet theory of gravity

Among the modified gravitational theories, the ghost-free Gauss-Bonnet (GFGB) theory of gravity has been considered from the viewpoint of cosmology. The best way to check its applicability could be to elicit observable predicts which give guidelines or limitations on the theory, which could be contrasted with the actual observations. In the present study, we derive consistent field equations for GFGB and by applying the equations to a spherically symmetric space-time, we obtain new spherically symmetric black hole (BH) solutions. We study the physical properties of these BH solutions and show that the obtained space-time possesses multihorizons and the Gauss-Bonnet invariants in the space-time are not trivial. We also investigate the thermodynamical quantities related to these BH solutions and we show that these quantities are consistent with what is known in the previous works. Finally, we study the geodesic equations of these solutions which give the photon spheres and we find the perihelion shift for weak GFGB. In addition, we calculate the first-order GFGB perturbations in the Schwarzschild solution and new BH solutions and show that we improve and extend existing results in the past literature on the spherically symmetric solutions.

Avoidance of Strong Coupling in General Relativity Solutions with a Timelike Scalar Profile in a Class of Ghost-Free Scalar-Tensor Theories

Modified gravity theories can accommodate exact solutions, for which the metric has the same form as the one in general relativity, i.e., stealth solutions. One problem with these stealth solutions is that perturbations around them exhibit strong coupling when the solutions are realized in degenerate higher-order scalar-tensor theories. We show that the strong coupling problem can be circumvented in the framework of the so-called U-DHOST theories, in which the degeneracy is partially broken in such a way that higher-derivative terms are degenerate only in the unitary gauge. In this sense, the scordatura effect is built-in in U-DHOST theories in general. There is an apparent Ostrogradsky mode in U-DHOST theories, but it does not propagate as it satisfies a three-dimensional elliptic differential equation on a spacelike hypersurface. We also clarify how this nonpropagating mode, i.e., the "shadowy" mode shows up at the nonlinear level.

Hamiltonian analysis of nonlocal F(R) gravity models

We construct a Hamiltonian for the nonlocal F(R) theory in the present work. By this construction, we demonstrate the nature of the ghost degrees of freedom. Finally, we find conditions that give rise to ghost-free theories.

Invertible disformal transformations with higher derivatives

We consider a higher-derivative generalization of disformal transformations in $D$-dimensional spacetime and clarify the conditions under which they form a group with respect to the matrix product and the functional composition. These conditions allow us to systematically construct the inverse transformation in a fully covariant manner. Applying the invertible generalized disformal transformation to known ghost-free scalar-tensor theories, we obtain a novel class of ghost-free scalar-tensor theories, whose action contains the third- or higher-order derivatives of the scalar field as well as nontrivial higher-order derivative couplings to the curvature tensor.

Extracting bigravity from string theory

The origin of the graviton from string theory is well understood: it corresponds to a massless state in closed string spectra, whose low-energy effective action, as extracted from string scattering amplitudes, is that of Einstein-Hilbert. In this work, we explore the possibility of such a string-theoretic emergence of ghost-free bimetric theory, a recently proposed theory that involves two dynamical metrics, that around particular backgrounds propagates the graviton and a massive spin-2 field, which has been argued to be a viable dark matter candidate. By choosing to identify the latter with a massive spin-2 state of open string spectra, we compute tree-level three-point string scattering amplitudes that describe interactions of the massive spin-2 with itself and with the graviton. With the mass of the external legs depending on the string scale, we discover that extracting the corresponding low-energy effective actions in four spacetime dimensions is a subtle but consistent process and proceed to appropriately compare them with bimetric theory. Our findings consist in establishing that string and bimetric theory provide to lowest order the same set of two-derivative terms describing the interactions of the massive spin-2 with itself and with the graviton, albeit up to numerical coefficient discrepancies, a fact that we analyze and interpret. We conclude with a mention of future investigations.

Quantum phase space description of a cosmological minimal massive bigravity model

Bimetric gravity theories describes gravitational interactions in the presence of an extra spin-2 field. The Hassan-Rosen (HR) nonlinear massive minimal bigravity theory is a ghost-free bimetric theory formulated with respect a flat, dynamical reference metric. In this work the deformation quantization formalism is applied to a HR cosmological model in the minisuperspace. The quantization procedure is performed explicitly for quantum cosmology in the minisuperspace. The Friedmann-Lema\^itre-Robertson-Walker (FLRW) model with flat metrics is worked out and the computation of the Wigner functions for theHartle-Hawking, Vilenkin and Linde wavefunctions are done numerically and, in the Hartle-Hawking case, also analytically. From the stability analysis in the quantum minisuper phase space it is found an interpretation of the mass of graviton as an emergent cosmological constant and as a measure of the deviation of classical behavior of the Wigner functions. Also, from the Hartle-Hawking case, an interesting relation between the curvature and the mass of graviton in a cusp catastrophe surface is discussed

Geometric mean of bimetric spacetimes

We use the geometric mean to parametrize metrics in the Hassan–Rosen ghost-free bimetric theory and pose the initial-value problem. The geometric mean of two positive definite symmetric matrices is a well-established mathematical notion which can be under certain conditions extended to quadratic forms having the Lorentzian signature, say metrics g and f. In such a case, the null cone of the geometric mean metric h is in the middle of the null cones of g and f appearing as a geometric average of a bimetric spacetime. The parametrization based on h ensures the reality of the square root in the ghost-free bimetric interaction potential. Subsequently, we derive the standard n + 1 decomposition in a frame adapted to the geometric mean and state the initial-value problem, that is, the evolution equations, the constraints, and the preservation of the constraints equation.

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.