Gravitational Higgs Mechanism Research Articles

Multiscalar-Metric Gravity: Cosmological Constant Screening and Emergence of Massive-Graviton Dark Components of the Universe

In the multiscalar-metric frameworks, the issues of the vacuum energy/cosmological constant (CC) screening due to Weyl-scale enhancement of the Diff gauge symmetry, along with emergence of the massive dark gravity components through the gravitational Higgs mechanism are considered. A generic dark gravity model is developed, with two extreme versions of the model of particular interest based on general relativity (GR) and its classically equivalent Weyl transverse alternative, being compared and argued to be, generally, inequivalent. The so constructed spontaneously broken Weyl Transverse Relativity (WTR) is proposed as a viable beyond-GR effective field theory of gravity, with screening of the Lagrangian CC, superseded by the induced one, and emergence of the massive tensor and scalar gravitons as dark gravity components. A basic concept with the spontaneously broken Diff gauge symmetry/relativity—in particular, WTR vs. GR—as a principle source of the emergent dark gravity components of the Universe is put forward.

Gravitational Equivalence Theorem and Double-Copy for Kaluza-Klein Graviton Scattering Amplitudes

We analyze the structure of scattering amplitudes of the Kaluza-Klein (KK) gravitons and of the KK gravitational Goldstone bosons in the compactified 5d general relativity (GR). Using a general R ξ gauge fixing, we study the geometric Higgs mechanism for the massive spin-2 KK gravitons. We newly propose and prove a gravitational equivalence theorem (GRET) to connect the scattering amplitudes of longitudinal KK gravitons to that of the KK gravitational Goldstone bosons, which formulates the geometric gravitational Higgs mechanism at the scattering S - matrix level. We demonstrate that the GRET provides a general energy cancellation mechanism guaranteeing the N -point longitudinal KK graviton scattering amplitudes to have their leading energy dependence cancelled down by a large power factor of E 2 N N ≥ 4 up to any loop level. We propose an improved double-copy approach to construct the massive KK graviton (Goldstone) amplitudes from the KK gauge boson (Goldstone) amplitudes. With these, we establish a new correspondence between the two types of energy cancellations in the four-point longitudinal KK amplitudes at tree level: E 4 ⟶ E 0 in the KK gauge theory and E 10 ⟶ E 2 in the KK GR theory.

Gravitational Higgs mechanism and resulting observational effects

Recently, a toy model was introduced to demonstrate that screening mechanisms in alternative theories of gravitation can hide additional effects. In this model a scalar field is charged under a $U(1)$ symmetry. In sufficiently compact objects the scalar field spontaneously grows, i.e. the object scalarizes, spontaneously breaking the $U(1)$ symmetry. Exactly as in the $U(1)$ Higgs mechanism this leads to the emergence of a mass for the gauge field. The aim of this paper is to provide an example of the physical consequences if we consider this toy model as a prototype of Weak Equivalence Principle (WEP) violations. We model neutron stars with a dipolar magnetic field to compare the magnetic field behaviour of stars in Einstein-Maxwell theory on the one hand and in scalar-tensor theory with the, so-called, gravitational Higgs mechanism on the other hand.

Constraints on a gravitational Higgs mechanism

We show that it is impossible to improve the high-energy behavior of the tree-level four-point amplitude of a massive spin-2 particle by including the exchange of any number of scalars and vectors in four spacetime dimensions. This constrains possible weakly coupled ultraviolet extensions of massive gravity, ruling out gravitational analogues of the Higgs mechanism based on particles with spins less than two. Any tree-level ultraviolet extension that is Lorentz invariant and unitary must involve additional massive particles with spins greater than or equal to two, as in Kaluza-Klein theories and string theory.

Renormalizing gravity: A new insight into an old problem

It is well known that perturbative quantum gravity is nonrenormalizable. The metric or vierbein has generally been used as the variable to quantize in perturbative quantum gravity. In this paper, we show that one can use the spin connection instead, in which case it is possible to obtain a ghost-free renormalizable theory of quantum gravity. Furthermore in this approach, gravitational analogs of particle physics phenomena can be studied. In particular, we study the gravitational Higgs mechanism using spin connection as a gauge field, and show that this provides a mechanism for the effective reduction in the dimensionality of spacetime.

Constructing neutron stars with a gravitational Higgs mechanism

In scalar-tensor theories, spontaneous scalarization is a phase transition that can occur in ultra-dense environments such as neutron stars. The scalar field develops a non-trivial configuration once the stars exceeds a compactness threshold. We recently pointed out that, if the scalar exhibits some additional coupling to matter, it could give rise to significantly different microphysics in these environments. In this work we study, at the non-perturbative level, a toy model in which the photon is given a large mass when spontaneous scalarization occurs. Our results demonstrate clearly the effectiveness of spontaneous scalarization as a Higgs-like mechanism in neutron stars.

Gravitational Higgs Mechanism in Inspiraling Scalarized NS-WD Binary

We investigate the gravitational Higgs mechanism in the inspiraling scalarized neutron star - white dwarf (NS-WD) binaries, whose dynamics are described by the scalar-tensor theory. Because of the difference in binding energy of NS and WD, the orbital decay of scalarized NS-WD system actually sources an emission of dipolar gravitational scalar radiation, in addition to the tensor gravitational waves, which breaks the Lorentz invariance constructed in the framework of general relativity. The resulted gravitational scalar radiation field obtains a scalar-energy-density-dependent effective mass, arising from a gravitational scalar potential that consists of a monotonically decreasing self-interactions of gravitational scalar field and an increasing exponential coupling between the scalar field and the NS/WD matter. Owing to a thin-ring-orbit effect, the gravitational interactions encoded by the massive scalar field is screened in the region of binary orbit, with high density of stars' scalar energy, which gives us the estimation for scalar masses of about $10^{-21} eV/c^2$ and leads to a Yulkawa-like correction to the Newtonian potential of the binary system. We demonstrate that the radiated gravitational tensor waves, propagating in the Yukawa type of potential, gain a scalar-background-dependent mass term of the order of $\sim 10^{-23} eV/c^2$.

Relativistic MOND from modified energetics

We begin to investigate the question of what modifications in energy-momentum tensor can yield correct MOND regime. As a starting study, we refrain from insisting on an action principle and focus exclusively on the equations of motion. The present work, despite the absence of an explicit action functional, can be regarded to extend Milgrom's modified inertia approach to relativistic domain. Our results show that a proper MOND limit arises if energy-momentum tensor is modified to involve determinant of the metric tensor in reference to the flat metric, where the latter is dynamically generated as in gravitational Higgs mechanism. This modified energy-momentum tensor is conserved in both Newtonian and MONDian regimes.

Non-perturbative Massive de Sitter Solutions

We discuss non-perturbative dynamics of massive gravity in de Sitter space via gravitational Higgs mechanism. We argue that enhanced local symmetry and null (ghost) state at (below) the perturbative Higuchi bound are mere artifacts of not only linearization but also assuming the Fierz-Pauli mass term. We point out that, besides de Sitter, there are vacuum solutions where the space asymptotically is de Sitter both in the past and in the future, the space first contracts, this con- traction slows down, and then reverses into expansion, so there is an epoch where the space appears to be (nearly) flat, even though the vacuum energy density is non-vanishing. We confirm this by constructing a closed-form exact solution to full non-perturbative equations of motion for a special massive de Sitter case. We give a formula for the critical mass above which such solutions apparently do not exist. For the Fierz-Pauli mass term this critical mass coincides with the perturbative Higuchi bound, and the former serves as the non-perturbative reinterpretation of the latter. We argue that, notwithstanding the perturbative ghost, non-perturbatively there is no instability. Instead, there are additional vacuum solutions that may have interesting cosmological implications, which we briefly speculate on.

No vDVZ Discontinuity in Non-Fierz-Pauli Theories

In theories of massive gravity with Fierz-Pauli mass term at the linearized level, perturbative radially symmetric asymptotic solutions are singular in the zero mass limit, hence van Dam-Veltman-Zakharov (vDVZ) discontinuity. In this note, in the context of gravitational Higgs mechanism, we argue that in non-Fierz-Pauli theories, which non-perturbatively are unitary, perturbative radially symmetric asymptotic solutions have a smooth massless limit, hence no vDVZ discontinuity. Perturbative vDVZ discontinuity as an artifact of the Fierz-Pauli mass term becomes evident in the language of constrained gravity, which is the massless limit of gravitational Higgs mechanism.

Breaking generalized covariance, classical renormalization, and boundary conditions from superpotentials

Superpotentials offer a direct means of calculating conserved charges associated with the asymptotic symmetries of space-time. Yet superpotentials have been plagued with inconsistencies, resulting in nonphysical or incongruent values for the mass, angular momentum, and energy loss due to radiation. The approach of Regge and Teitelboim, aimed at a clear Hamiltonian formulation with a boundary, and its extension to the Lagrangian formulation by Julia and Silva have resolved these issues, and have resulted in a consistent, well-defined and unique variational equation for the superpotential, thereby placing it on a firm footing. A hallmark solution of this equation is the KBL superpotential obtained from the first-order Lovelock Lagrangian. Nevertheless, here we show that these formulations are still insufficient for Lovelock Lagrangians of higher orders. We present a paradox, whereby the choice of fields affects the superpotential for equivalent on-shell dynamics. We offer two solutions to this paradox: either the original Lagrangian must be effectively renormalized, or that boundary conditions must be imposed, so that space-time be asymptotically maximally symmetric. Non-metricity is central to this paradox, and we show how quadratic non-metricity in the bulk of space-time contributes to the conserved charges on the boundary, where it vanishes identically. This is a realization of the gravitational Higgs mechanism, proposed by Percacci, where the non-metricity is the analogue of the Goldstone boson.

Non-perturbative Massive Solutions in Gravitational Higgs Mechanism

We construct exact non-perturbative massive solutions in the gravitational Higgs mechanism. They confirm the conclusions of arXiv:1102.4991, which are based on non-perturbative Hamiltonian analysis for the rel- evant metric degrees of freedom, that while perturbatively unitarity may not be evident, no negative norm state is present in the full nonlinear theory. The non-perturbative massive solutions do not appear to exhibit instabil- ities and describe vacuum configurations which are periodic in time, including purely longitudinal solutions with isotropic periodically expanding and contracting spatial dimensions, cosmological strings with only one peri- odically expanding and contracting spatial dimension, and also purely non-longitudinal (traceless) periodically expanding and contracting solutions with constant spatial volume. As an aside we also discuss massive solutions in New Massive Gravity. While such solutions are present in the linearized theory, we argue that already at the next-to-linear (quadratic) order in the equations of motion (and, more generally, for weak-field configurations) there are no massive solutions.

Nonperturbative unitarity of the gravitational Higgs mechanism

In this paper we discuss massive gravity in Minkowski space via gravitational Higgs mechanism, which provides a non-perturbative definition thereof. Using this non-perturbative definition, we address the issue of unitarity by studying the full nonlinear Hamiltonian for the relevant metric degrees of freedom. While perturbatively unitarity is not evident, we argue that no negative norm state is present in the full nonlinear theory.

Brane induced gravity, its ghost and the cosmological constant problem

``Brane Induced Gravity'' is regarded as a promising framework for addressing the cosmological constant problem, but it also suffers from a ghost instability for parameter values that make it phenomenologically viable. We carry out a detailed analysis of codimension > 2 models employing gauge invariant variables in a flat background approximation. It is argued that using instead a curved background sourced by the brane would not resolve the ghost issue, unless a very specific condition is satisfied (if satisfiable at all). As for other properties of the model, from an explicit analysis of the 4-dimensional graviton propagator we extract a mass, a decay width and a momentum dependent modification of the gravitational coupling for the spin 2 mode. In the flat space approximation, the mass of the problematic spin 0 ghost is instrumental in filtering out a brane cosmological constant. The mass replaces a background curvature that would have had the same function. The optical theorem is used to demonstrate the suppression of graviton leakage into the uncompactified bulk. Then, we derive the 4-dimensional effective action for gravity and show that general covariance is spontaneously broken by the bulk-brane setup. This provides a natural realization of the gravitational Higgs mechanism. We also show that the addition of extrinsic curvature dependent terms has no bearing on linearized brane gravity.

Massive gravity in de Sitter space via the gravitational Higgs mechanism

In this paper we discuss massive gravity in de Sitter space via the gravitational Higgs mechanism, which provides a nonlinear definition thereof. The Higgs scalars are described by a nonlinear sigma model, which includes higher derivative terms required to obtain the Fierz-Pauli mass term. Using the aforesaid nonperturbative definition, we address the appearance of an enhanced local symmetry and a null norm state in the linearized massive gravity in de Sitter space at the special value of the graviton mass to the Hubble parameter ratio. By studying full nonperturbative equations of motion, we argue that there is no enhanced symmetry in the full nonlinear theory. We then argue that in the full nonlinear theory no null norm state is expected to arise at the aforesaid special value. This suggests that no ghost might be present for lower graviton mass values and the full nonlinear theory might be unitary for all values of the graviton mass and the Hubble parameter with no van Dam-Veltman-Zakharov discontinuity. We argue that this is indeed the case by studying the full nonlinear Hamiltonian for the relevant conformal and helicity-0 longitudinal modes. In particular, we argue that no negative norm state is present in the full nonlinear theory.

HIGGS MECHANISM FOR GRAVITONS

Just like the vector gauge bosons in the gauge theories, it is now known that gravitons acquire mass in the process of spontaneous symmetry breaking of diffeomorphisms through the condensation of scalar fields. The point is that we should find the gravitational Higgs mechanism such that it results in massive gravity in a flat Minkowski spacetime without non-unitary propagating modes. This is usually achieved by including higher-derivative terms in scalars and tuning the cosmological constant to be a negative value in a proper way. Recently, a similar but different gravitational Higgs mechanism has been advocated by Chamseddine and Mukhanov where one can relax the negative cosmological constant to zero or positive one. In this work, we investigate why the non-unitary ghost mode decouples from physical Hilbert space in a general spacetime dimension. Moreover, we generalize the model to possess an arbitrary potential and clarify under what conditions the general model exhibits the gravitational Higgs mechanism. By searching for solutions to the conditions, we arrive at two classes of potentials exhibiting gravitational Higgs mechanism. One class includes the model by Chamseddine and Mukhanov in a specific case while the other is a completely new model.

General tensor Lagrangians from the gravitational Higgs mechanism

The gravitational Higgs mechanism proposed by 't Hooft in arXiv:0708.3184 involves the spacetime metric gμν as well as the induced metric where ϕa (a = 0, …, 3), as we call it, break all four diffeomorphisms spontaneously via the vacuum expectation values ⟨ϕa⟩ ∝ xa. In this framework, we construct and analyze the most general action density in terms of various invariants involving the curvature tensors, connexion coefficients, and the contractions and the determinants of the two metric fields. We show that this action admits a consistent expansion about the flat background such that the resulting Lagrangian possesses several novel features not found in the linearized Einstein–Hilbert Lagrangian with Fierz–Pauli mass term (LEHL-FP): (i) its kinetic part generalizes that of LELHL-FP by weighing the corresponding structures with certain coefficients generated by invariants, (ii) the entire Lagrangian is ghost– and tachyon–free for mass terms not necessarily in the Fierz–Pauli form, and, (iii) a consistent mass term is generated with no apparent need to higher derivative couplings.

MASSIVE GRAVITY IN CURVED COSMOLOGICAL BACKGROUNDS

We study the physical propagating modes in a massive gravity model in curved cosmological backgrounds, which we have found as classical solutions in our previous paper. We show that, generically, there exist such the cosmological background solutions consistent with the equations of motion where we assume the ghost condensation ansatzes. Using the (1 + 3)-parametrization of the metric fluctuations with "unitary" gauge, we find that there is neither a scalar ghost nor a tachyon in the spectrum of the propagating modes, the tensor modes become massive owing to gravitational Higgs mechanism, and the model is free of the Boulware–Deser instability. The price we have to pay is that the scalar sector breaks the Lorentz-invariance, but there are no pathologies in the spectrum and lead to interesting phenomenology. Moreover, we present a proof of the absence of nonunitary modes for a specific ghost condensation model in a cosmological background.

CLASSICAL SOLUTIONS OF GHOST CONDENSATION MODELS

Motivated by ideas obtained from both ghost condensation and gravitational Higgs mechanism, we attempt to find classical solutions in the unitary gauge in general ghost condensation models. It is shown that depending on the form of scalar fields in an action, there are three kinds of exact solutions, which are (anti-) de Sitter space–time, polynomially expanding universes and flat Minkowski space–time. We briefly comment on gravitational Higgs mechanism in these models where we have massive gravitons of five degrees of freedom and one unitary scalar field (Nambu–Goldstone boson) after spontaneous symmetry breakdown of general coordinate reparametrization invariance. The models at hand are free from the problem associated with the non-unitary propagating mode.

Brane vector dynamics from embedding geometry

A Kaluza–Klein decomposition of higher dimensional gravity is performed in the flexible brane world scenario and the properties of the extra vectors resulting from this decomposition are explored. These vectors become massive due to a gravitational Higgs mechanism in which the brane oscillation Nambu–Goldstone bosons become the longitudinal component of the vector fields. The vector mass is found to be proportional to the exponential of the vacuum expectation value of the radion (dilaton) field and as such its magnitude is model dependent. Using the structure of the embedding geometry, the couplings of these vectors to the Standard Model, including those resulting from the extrinsic curvature, are deduced. As an example, we show that for 5D space–time the geometry of the bulk-brane world, either intrinsic or extrinsic, only depends on the extra vector and the 4D graviton. The connection between the embedding geometry and coset construction by non-linear realization is also presented.