Massless Graviton Research Articles

Black hole solutions to Einstein-Bel-Robinson gravity

In this paper, we study the physical properties of black holes in the framework of the recently proposed Einstien-Bel-Robinson gravity. We show that interestingly the theory propagates a transverse and massless graviton on a maximally symmetric background with positive energy. There is also a single ghost-free branch that returns to the Einstein case when β → 0. We find new black hole solutions to the equations, both approximate and exact, the latter being a constant curvature black hole solution, and discuss inconsistencies with metrics that were previously claimed to be approximate solutions to the equations. We obtain the conserved charges of the theory and briefly study the thermodynamics of the black hole solutions.

Vacuum energy in the effective field theory of general relativity with a scalar field

A consistency condition of general relativity as an effective field theory in Minkowskian background uniquely fixes the value of the cosmological constant. In two-loop calculations, including the interaction of gravitons with matter fields, it has been shown that this value of the cosmological constant leads to vanishing vacuum energy, under the assumption that the energy-momentum tensor of the gravitational field is given by the pseudotensor of Landau-Lifshitz’s classic textbook. Here, we demonstrate that this result also holds when the self-interaction of a scalar field is taken into account. That is, our two-loop-order calculation suggests that, in an effective field theory of metric and scalar fields, one arrives at a consistent theory with massless gravitons if the cosmological constant is fixed from the condition of vanishing vacuum energy. Vice versa, imposing the consistency condition in Minkowskian background leads to a vanishing vacuum energy. Published by the American Physical Society 2024

Unconventional conformal invariance of maximal depth partially massless fields on dS4 and its relation to complex partially massless SUSY

Deser and Waldron have shown that maximal depth partially massless theories of higher (integer) spin on four-dimensional de Sitter spacetime (dS4) possess infinitesimal symmetries generated by the conformal Killing vectors of dS4. However, it was later shown by Barnich, Bekaert, and Grigoriev that these theories are not invariant under the conformal algebra so(2, 4). To get some insight into these seemingly contradicting results we write down the full set of infinitesimal transformations of the fields generated by the fifteen conformal Killing vectors of dS4. In particular, although the infinitesimal transformations generated by the ten dS Killing vectors are well-known (these correspond to the conventional Lie derivatives), the transformations generated by the five non-Killing conformal Killing vectors were absent from the literature, and we show that they have an ‘unconventional’ form. In the spin-2 case (partially massless graviton), we show that the field equations and the action are invariant under the unconventional conformal transformations. For spin s > 2, the invariance is demonstrated only at the level of the field equations. For all spins s ≥ 2, we reproduce the result that the symmetry algebra does not close on the conformal algebra, so(2, 4). This is due to the appearance of new higher-derivative symmetry transformations in the commutator of two unconventional conformal transformations. Our results concerning the closure of the full symmetry algebra are inconclusive. Then we shift focus to the question of supersymmetry (SUSY) on dS4 and our objective is twofold. First, we uncover a non-interacting supermultiplet that consists of a complex partially massless spin-2 field and a complex spin-3/2 field on dS4. Second, we showcase the appearance of the unconventional conformal symmetries in the commutator of two SUSY transformations. Thus, this commutator closes on an algebra that is neither so(1, 4) nor so(2, 4), while its full structure is an open question. More open questions arising from our findings are also discussed.

Holographic fluids from 5D dilaton gravity

We study a solvable class of five-dimensional dilaton gravity models that continuously interpolate between anti-de Sitter (AdS5), linear dilaton (LD5) and positively curved spacetimes as a function of a continuous parameter ν. The dilaton vacuum expectation value is set by a potential localized on a flat brane. We chart the elementary properties of these backgrounds for any admissible ν, and determine stability conditions of the brane-dilaton system. We find that the spectrum of metric fluctuations can be either continuous or discrete. It features a massless graviton mode confined between the brane and the curvature singularity, and a massive radion mode tied to brane-dilaton stability. We show that, in the presence of a bulk black hole, the holographic theory living on the brane features a perfect fluid. The equation of state of the holographic fluid interpolates between radiation, pressureless matter and vacuum energy as a function of ν. This extends earlier findings on holographic fluids. Our results suggest that the thermodynamics of the fluid mirrors precisely the thermodynamics of the bulk black hole.

Natural metric-affine inflation

We consider here natural inflation in the low energy (two-derivative) metric-affine theory containing only the minimal degrees of freedom in the inflationary sector, i.e. the massless graviton and the pseudo-Nambu-Goldstone boson (PNGB). This theory contains the Ricci-like and parity-odd Holst invariants together with non-minimal couplings between the PNGB and the above-mentioned invariants. The Palatini and Einstein-Cartan realizations of natural inflation are particular cases of our construction. Explicit models of this type featuring non-minimal couplings are shown to emerge from the microscopic dynamics of a QCD-like theory with an either sub-Planckian or trans-Planckian confining scale and that is renormalizable on Minkowski spacetime. Moreover, for these models, we find regions of the parameter space where the inflationary predictions agree with the most recent observations at the 2σ level. We find that in order to enter the 1σ region it is necessary (and sufficient) to have a finite value of the Barbero-Immirzi parameter and a sizable non-minimal coupling between the inflaton and the Holst invariant (with sign opposite to the Barbero-Immirzi parameter). Indeed, in this case the potential of the canonically normalized inflaton develops a plateau as shown analytically.

Bigravity portal dark matter

We consider a model where the interaction between dark matter and the Standard Model particles is mediated by a ghost-free bigravity portal. The bigravity model invokes a massive spin-2 particle coupled to the usual massless graviton as well as generic bimetric matter couplings. The cross sections for dark matter direct detection are computed and confronted with the experimental bounds. The presence of the massive spin-2 mediator resolves the core-cusp problem, which in turn significantly constrains the dark matter coupling in such a bigravity theory. Yet, there remains a window of the parameter space where the model can be tested in the upcoming direct detection experiments such as XENONnT and PandaX-30T. The model also predicts a reheating temperature on the order of 106 GeV. Published by the American Physical Society 2024

Cosmological correlators through the looking glass: reality, parity, and factorisation

We consider the evolution of quantum fields during inflation, and show that the total-energy singularities appearing in the perturbative expansion of the late-time Wavefunction of the Universe are purely real when the external states are massless scalars and massless gravitons. Our proof relies on the tree-level approximation, Bunch-Davies initial conditions, and exact scale invariance (IR-convergence), but without any assumptions on invariance under de Sitter boosts. We consider all n-point functions and allow for the exchange of additional states of any mass and integer spin. Our proof makes use of a decomposition of the inflationary bulk-bulk propagator of massive spinning fields which preserves UV-convergence and ensures that the time-ordered contributions are purely real after we rotate to Euclidean time. We use this reality property to show that the maximally-connected parts of wavefunction coefficients, from which total-energy singularities originate, are purely real. In a theory where all states are in the complementary series, this reality extends to the full wavefunction coefficient. We then use our reality theorem to show that parity-odd correlators (correlators that are mirror asymmetric) are factorised and do not diverge when the total-energy is conserved. We pay special attention to the parity-odd four-point function (trispectrum) of inflationary curvature perturbations and use our reality/factorisation theorems to show that this observable is factorised into a product of cubic diagrams thereby enabling us to derive exact shapes. We present examples of couplings between the inflaton and massive spin-1 and spin-2 fields, with the parity-violation in the trispectrum driven by Chern-Simons corrections to the spinning field two-point function, or from parity-violating cubic interactions which we build within the Effective Field Theory of Inflation. In addition, we present a first-of-its-kind example of a parity-violating trispectrum, generated at tree-level, that arises in a purely scalar theory where the inflaton mixes linearly with an additional massive scalar field.

Constraining braneworlds with entanglement entropy

We propose swampland criteria for braneworlds viewed as effective field theories of defects coupled to semiclassical gravity. We do this by exploiting their holographic interpretation. We focus on general features of entanglement entropies and their holographic calculations. Entropies have to be positive. Furthermore, causality imposes certain constraints on the surfaces that are used holographically to compute them, most notably a property known as causal wedge inclusion. As a test case, we explicitly constrain the Dvali-Gabadadze-Porrati term as a second-order-in-derivatives correction to the Randall-Sundrum action. We conclude by discussing the implications of these criteria for the question on whether entanglement islands in theories with massless gravitons are possible in Karch-Randall braneworlds.

Reconciling absence of vDVZ discontinuity with absence of ghosts in nonlocal linearized gravity

The modern massive gravity theories resolve a historical tension between the absence of the so called vDVZ mass discontinuity and the absence of ghosts via a fine tuned gravitational potential and a sophisticated screening mechanism. Those theories have originated the modern covariant bimetric models which are local, ghost free and cosmologically viable apparently, they contain a massive plus a massless graviton in the spectrum. It seems hard to solve the mentioned tension if we do insist in a model with a minimal number of degrees of freedom, with only one massive spin-2 particle in the spectrum, even if we allow nonlocal theories. Here we show that this problem can be circumvented in linearized nonlocal theories by the introduction of exponential terms with infinite derivatives. The model admits non linear completions via nonlocal quadratic terms in curvatures. We also investigate the role of the exponential factors in linearized models where the graviton remains massless and a mass scale is introduced via nonlocal terms, they are also ghost free and approach the Einstein–Hilbert theory as we go much above the introduced mass scale.

A braneworld model in a massive gravity

A Randall–Sundrum-like braneworld scenario is constructed in a 5D extension of the Lorentz-violating massive gravity. The gauge hierarchy problem is solved in current model. The linear perturbations are calculated, and it is found that the tensor and vector perturbations are robust and free from the ghost and tachyonic instabilities, however, the scalar perturbation is a ghost filed. After Kaluza–Klein reduction, all the tensor, vector and scalar modes are massive and possess the mass splitting of order of TeV in their respective mass spectra. The massive ground states of tensor and scalar modes propagate only along the brane, however, the vector ground state is absent in the mass spectrum. By introducing the Goldberger-Wise mechanism to stabilize the extra dimension, the 4D effective theory on the brane includes a nearly massless graviton plus three towers of very massive spin-2, spin-1 and ghost spin-0 particles.

Page curves on codim-m and charged branes

This paper investigates Page curves on the branes with higher codimensions and charges. We study two kinds of doubly holographic modes, the AdS/dCFT and cone holography. In AdS/dCFT, the gravitations on the brane are massive, and the black hole on the codim-m brane is coupled with the non-gravitational bath on the AdS boundary. Following the standard approach, we derive the Page curve for eternal black holes. On the other hand, cone holography includes massless graviton on the brane, and the bath becomes gravitating. By adding suitable DGP gravity on the end-of-the-world brane, we recover non-trivial entanglement islands and Page curves, which strongly support that the island is consistent with massless gravity. Finally, we analyze the effects of charges and find that, as the charges increase, the Page time increases, and the parameter space for non-trivial Page curves widens.

Covariant quantization of the partially massless graviton field in de Sitter spacetime

Covariant quantization of the partially massless graviton field in de Sitter spacetime

Harmonic functions and gravity localization

In models with extra dimensions, matter particles can be easily localized to a ‘brane world’, but gravitational attraction tends to spread out in the extra dimensions unless they are small. Strong warping gradients can help localize gravity closer to the brane. In this note we give a mathematically rigorous proof that the internal wave-function of the massless graviton is constant as an eigenfunction of the weighted Laplacian, and hence is a power of the warping as a bound state in an analogue Schrödinger potential. This holds even in presence of singularities induced by thin branes.We also reassess the status of AdS vacuum solutions where the graviton is massive. We prove a bound on scale separation for such models, as an application of our recent results on KK masses. We also use them to estimate the scale at which gravity is localized, without having to compute the spectrum explicitly. For example, we point out that localization can be obtained at least up to the cosmological scale in string/M-theory solutions with infinite-volume Riemann surfaces; and in a known class of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 models, when the number of NS5- and D5-branes is roughly equal.

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.

Emerging Newtonian potential in pure R2 gravity on a de Sitter background

In [27] Alvarez-Gaume et al. established that pure mathcal{R} 2 theory propagates massless spin-2 graviton on a de Sitter (dS) background but not on a locally flat background. We build on this insight to derive a Newtonian limit for the theory. Unlike most previous works that linearized the metric around a locally flat background, we explicitly employ the dS background to start with. We directly solve the field equation of the action {left(2kappa right)}^{-1}int {d}^4xsqrt{-g}{mathcal{R}}^2 coupled with the stress-energy tensor of normal matter in the form Tμν = Mc2δ( overrightarrow{r} ) {delta}_{mu}^0{delta}_{nu}^0 . We obtain the following Schwarzschild-de Sitter metric d{s}^2=-left(1-frac{Lambda}{3}{r}^2-frac{kappa {c}^2}{48pi Lambda}frac{M}{r}right){c}^2d{t}^2+{left(1-frac{Lambda}{3}{r}^2-frac{kappa {c}^2}{48pi Lambda}frac{M}{r}right)}^{-1}d{r}^2+{r}^2d{varOmega}^2 which features a potential V(r)=-frac{kappa {c}^4}{96pi Lambda}frac{M}{r} with the correct Newtonian tail. The parameter Λ plays a dual role: (i) it sets the scalar curvature for the background dS metric, and (ii) it partakes in the Newtonian potential V(r). We reach two key findings. Firstly, the Newtonian limit only emerges owing to the de Sitter background. Most existing studies of the Newtonian limit in modified gravity chose to linearize the metric around a locally flat background. However, this is a false vacuum to start with for pure mathcal{R} 2 gravity. These studies unknowingly omitted the information about Λ of the de Sitter background, hence incapable of attaining a Newtonian behavior in pure mathcal{R} 2 gravity. Secondly, as Λ appears in V(r) in a singular manner, viz. V(r) ∝ Λ−1, the Newtonian limit for pure mathcal{R} 2 gravity cannot be obtained by any perturbative approach treating Λ as a small parameter.

Non-supersymmetric vacua and self-adjoint extensions

Internal intervals spanned by finite ranges of a conformal coordinate z and terminating at a pair of singularities are a common feature of many string compactifications with broken supersymmetry. The squared masses emerging in lower-dimensional Minkowski spaces are then eigenvalues of Schrödinger-like operators, whose potentials have double poles at the ends of the intervals. For one-component systems, the possible self-adjoint extensions of Schrödinger operators are described by points in AdS3 × S1, and those corresponding to independent boundary conditions at the ends of the intervals by points on the boundary of AdS3. The perturbative stability of compactifications to Minkowski space time depends, in general, on these choices of self-adjoint extensions. We apply this setup to the orientifold vacua driven by the “tadpole potential” V=T {e}^{frac{3}{2}phi } and find, in nine dimensions, a massive scalar spectrum, a unique choice of boundary conditions with stable tensor modes and a massless graviton, and a wide range of choices leading to massless and/or massive vector modes.

Massless graviton in a model of quantum gravity with emergent spacetime

Massless graviton in a model of quantum gravity with emergent spacetime

Time-symmetric quantization of relativistic fields. 1. Complex fields, massless gauge fields and gravitons

In the standard formulation of quantum field theory (QFT), where there are only positive energy particles and antiparticles, the energy and charge of the vacuum diverge, which, due to the existence of gravity, leads to the inconsistency of the theory (cosmological constant problem). In the article, it is shown that in the Stueckelberg-Feynman (SF) interpretation, where antiparticles are described as negative energy particles moving backward in time, the zero-point energy and zero-point charge of vacuum of complex fields are absent and there is no cosmological constant problem. However, until now it was believed that the SF interpretation leads to negative probabilities and incompatible with QFT. In the article, it is presented a new formulation of QFT on the basis of the SF interpretation in the form of time-symmetric quantization (TSQ), where the probability of states is positive. In TSQ, the consequences of the SF interpretation are taken into account consecutively and it is shown that: a) the negative sign of the norm of states only changes the sign of the wave function, and not the probabilities; b) the expression of backward in time integrals through the forward in time integrals changes sign; c) the time ordering of the operators is symmetric in time and writing them through the usual ordering leads to the standard diagram technique. For this reason, TSQ correctly describes the known observable effects. In TSQ, the results of unification models change, in particular, a) there is no zero-point energy even with broken supersymmetry between complex fields; b) there is no zero-point energy of modes in string theories, which allows to include gravity, but there is no a conformal anomaly and the dimension of space can be arbitrary.

Missing corner in the sky: massless three-point celestial amplitudes

We present the first computation of three-point celestial amplitudes in Minkowski space of massless scalars, photons, gluons, and gravitons. Such amplitudes were previously considered to be zero in the literature because the corresponding scattering amplitudes in the plane wave basis vanish for generic momenta due to momentum conservation. However, the delta function for the momentum conservation has support in the soft and colinear regions, and contributes to the Mellin and shadow integrals that give non-zero celestial amplitudes. We further show that when expanding in the (shadow) conformal basis for the incoming (outgoing) particle wave functions, the amplitudes take the standard form of correlators in two-dimensional conformal field theory. In particular, the three-point celestial gluon amplitudes take the form of a three-point function of a spin-one current with two spin-one primary operators, which strongly supports the relation between soft spinning particles and conserved currents. Moreover, the three-point celestial amplitudes of one graviton and two massless scalars take the form of a correlation function involving a primary operator of conformal weight one and spin two, whose level-one descendent is the supertranslation current.

From spin foams to area metric dynamics to gravitons

Although spin foams arose as quantizations of the length metric degrees of freedom, the quantum configuration space is rather based on areas as more fundamental variables. This is also highlighted by the semi-classical limit of four-dimensional spin foam models, which is described by the Area Regge action. Despite its central importance to spin foams the dynamics encoded by the Area Regge action is only poorly understood, in particular in the continuum limit. We perform here a systematic investigation of the dynamics defined by the Area Regge action on a regular centrally subdivided hypercubical lattice. This choice of lattice avoids many problems of the non-subdivided hypercubical lattice, for which the Area Regge action is singular. The regularity of the lattice allows to extract the continuum limit and its corrections, order by order in the lattice constant. We show that, contrary to widespread expectations which arose from the so-called flatness problem of spin foams, the continuum limit of the Area Regge action does describe to leading order the same graviton dynamics as general relativity. The next-to-leading order correction to the effective action for the length metric is of second order in the lattice constant, and is given by a quadratic term in the Weyl curvature tensor. This correction can be understood to originate from an underlying dynamics of area metrics. This suggests that the continuum limit of spin foam dynamics does lead to massless gravitons, and that the leading order quantum corrections can be understood to emerge from a generalization of the configuration space from length to area metrics.