## Publications

83 results found

Tolley AJ, 2020, TT<mml:mo stretchy="true"><overbar></mml:mover> deformations, massive gravity and non-critical strings, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 3

Alberte L, de Rham C, Momeni A,
et al., 2020, EFT of interacting spin-2 fields, *The Journal of High Energy Physics*, Vol: 2020, Pages: 1-57, ISSN: 1029-8479

We consider the effective field theory of multiple interacting massive spin-2 fields. We focus on the case where the interactions are chosen so that the cutoff is the highest possible, and highlight two distinct classes of theories. In the first class, the mass eigenstates only interact through potential operators that carry no derivatives in unitary gauge at leading order. In the second class, a specific kinetic mixing between the mass eigenstates is included non-linearly. Performing a decoupling and ADM analysis, we point out the existence of a ghost present at a low scale for the first class of interactions. For the second class of interactions where kinetic mixing is included, we derive the full Λ3-decoupling limit and confirm the absence of any ghosts. Nevertheless both formulations can be used to consistently describe an EFT of interacting massive spin-2 fields which, for a suitable technically natural tuning of the EFT, have the same strong coupling scale Λ3. We identify the generic form of EFT corrections in each case. By using Galileon Duality transformations for the specific case of two massive spin-2 fields with suitable couplings, the decoupling limit theory is shown to be a bi-Galileon.

Alberte L, Rham CD, Momeni A, et al., 2019, Positivity constraints on interacting pseudo-linear spin-2 fields, Publisher: arXiv

We explore the effective field theory for single and multiple interactingpseudo-linear spin-2 fields. By applying forward limit positivity bounds, weshow that among the parameters contributing to elastic tree level scatteringamplitude, there is no region of compatibility of the leading interactions witha standard local UV completion. Our result generalizes to any number ofinteracting pseudo-linear spin-2 fields. This results have significantimplications for the organization of the effective field theory expansion forpseudo-linear fields.

de Rham C, Heisenberg L, Tolley AJ, 2019, Spin-2 fields and the weak gravity conjecture, *Physical Review D: Particles, Fields, Gravitation and Cosmology*, Vol: 100, Pages: 1-20, ISSN: 1550-2368

Recently, it has been argued that application of the weak gravity conjecture (WGC) to spin-2 fields implies a universal upper bound on the cutoff of the effective theory for a single spin-2 field. We point out here that these arguments are largely spurious, because of the absence of states carrying spin-2 Stückelberg U(1) charge, and because of incorrect scaling assumptions. Known examples such as Kaluza-Klein theory that respect the usual WGC do so because of the existence of a genuine U(1) field under which states are charged, as in the case of the Stückelberg formulation of spin-1 theories, for which there is an unambiguously defined U(1) charge. Theories of bigravity naturally satisfy a naive formulation of the WGC, MW<MPl, since the force of the massless graviton is always weaker than the massive spin-2 modes. It also follows that theories of massive gravity trivially satisfies this form of the WGC. We also point out that the identification of a massive spin-2 state in a truncated higher derivative theory, such as Einstein-Weyl-squared or its supergravity extension, bears no relationship with massive spin-2 states in the UV completion, contrary to previous statements in the literature. We also discuss the conjecture from a swampland perspective and show how the emergence of a universal upper bound on the cutoff relies on strong assumptions on the scale of the couplings between the spin-2 and other fields, an assumption which is known to be violated in explicit examples.

Alberte L, Rham CD, Momeni A, et al., 2019, Positivity constraints on interacting spin-2 fields, Publisher: arXiv

The consistency of the EFT of two interacting spin-2 fields is checked byapplying forward limit positivity bounds on the scattering amplitudes toexclude the region of parameter space devoid of a standard UV completion. Wefocus on two classes of theories that have the highest possible EFT cutoff,namely those theories modelled on ghost-free interacting theories of a singlemassive spin-2 field. We find that the very existence of interactions betweenthe spin-2 fields implies more stringent bounds on all the parameters of theEFT, even on the spin-2 self-interactions. This arises for two reasons. First,with every new field included in the low-energy EFT, comes the `knowledge' ofan extra pole to be subtracted, hence strengthening the positivity bounds.Second, while adding new fields increases the number of free parameters fromthe new interactions, this is rapidly overcome by the increased number ofpositivity bounds for different possible scattering processes. We also discusshow positivity bounds appear to favour relations between operators thateffectively raise the cutoff of the EFT.

Rham CD, Tolley AJ, 2019, The speed of gravity, Publisher: arXiv

Within the standard effective field theory of General Relativity, we showthat the speed of gravitational waves deviates, ever so slightly, fromluminality on cosmological and other spontaneously Lorentz-breakingbackgrounds. This effect results from loop contributions from massive fields ofany spin, including Standard Model fields, or from tree level effects frommassive higher spins $s \ge 2$. We show that for the choice of interactionsigns implied by S-matrix and spectral density positivity bounds suggested byanalyticity and causality, the speed of gravitational waves is in generalsuperluminal at low-energies on NEC preserving backgrounds, meaninggravitational waves travel faster than allowed by the metric to which photonsand Standard Model fields are minimally coupled. We show that departure of thespeed from unity increases in the IR and argue that the speed inevitablyreturns to luminal at high energies as required by Lorentz invariance.Performing a special tuning of the EFT so that renormalization sensitivecurvature-squared terms are set to zero, we find that finite loop correctionsfrom Standard Model fields still lead to an epoch dependent modification of thespeed of gravitational waves which is determined by the precise field contentof the lightest particles with masses larger than the Hubble parameter today.Depending on interpretation, such considerations could potentially havefar-reaching implications on light scalar models, such as axionic or fuzzy colddark matter.

de Rham C, Melville S, Tolley AJ,
et al., 2019, Positivity bounds for massive spin-1 and spin-2 fields, *The Journal of High Energy Physics*, Vol: 2019, ISSN: 1029-8479

We apply the recently developed positivity bounds for particles with spin, applied away from the forward limit, to the low energy effective theories of massive spin-1 and spin-2 theories. For spin-1 theories, we consider the generic Proca EFT which arises at low energies from a heavy Higgs mechanism, and the special case of a charged Galileon for which the EFT is reorganized by the Galileon symmetry. For spin-2, we consider generic Λ5 massive gravity theories and the special ‘ghost-free’ Λ3 theories. Remarkably we find that at the level of 2-2 scattering, the positivity bounds applied to Λ5 massive gravity theories, impose the special tunings which generate the Λ3 structure. For Λ3 massive gravity theories, the island of positivity derived in the forward limit appears relatively stable against further bounds.

de Rham C, Melville S, Tolley AJ,
et al., 2019, UV complete me: positivity bounds for particles with spin, *Journal of High Energy Physics*, Vol: 2018, ISSN: 1029-8479

For a low energy effective theory to admit a standard local, unitary, analytic and Lorentz-invariant UV completion, its scattering amplitudes must satisfy certain inequalities. While these bounds are known in the forward limit for real polarizations, any extension beyond this for particles with nonzero spin is subtle due to their non-trivial crossing relations. Using the transversity formalism (i.e. spin projections orthogonal to the scattering plane), in which the crossing relations become diagonal, these inequalities can be derived for 2-to-2 scattering between any pair of massive particles, for a complete set of polarizations at and away from the forward scattering limit. This provides a set of powerful criteria which can be used to restrict the parameter space of any effective field theory, often considerably more so than its forward limit subset alone.

Dar F, de Rham C, Deskins JT,
et al., 2019, Scalar gravitational radiation from binaries: Vainshtein mechanism in time-dependent systems, *Classical and Quantum Gravity*, Vol: 36, ISSN: 0264-9381

We develop a full four-dimensional numerical code to study scalar gravitational radiation emitted from binary systems and probe the Vainshtein mechanism in situations that break the static and spherical symmetry, relevant for binary pulsars as well as black holes and neutron stars binaries. The present study focuses on the cubic Galileon which arises as the decoupling limit of massive theories of gravity. Limitations associated with the numerical methods prevent us from reaching a physically realistic hierarchy of scales; nevertheless, within this context we observe the same power law scaling of the radiated power as previous analytic estimates, and confirm a strong suppression of the power emitted in the monopole and dipole as compared with quadrupole radiation. Following the trend to more physically realistic parameters, we confirm the suppression of the power emitted in scalar gravitational radiation and the recovery of general relativity with good accuracy. This paves the way for future numerical work, probing more generic, physically relevant situations and sets of interactions that may exhibit the Vainshtein mechanism.

Ondo NA, Tolley AJ, 2018, Deconstructing supergravity: massive supermultiplets, *Journal of High Energy Physics*, Vol: 2018, ISSN: 1029-8479

Given the success of the deconstruction program in obtaining ghost-free massive gravity from 5-D Einstein gravity, we propose a modification of the deconstruction procedure that incorporates supersymmetry at the linear level. We discuss the relevant limits of a conjectured interacting theory of a massive spin 2 supermultiplet, and determine the linear theory to be the N=1 Zinoviev theory, a supersymmetric extension of Fierz-Pauli theory. We develop a family of 1-site deconstruction procedures for fermionic fields (yielding Dirac and Majorana mass terms). The deconstruction procedure appropriate for giving fermions a Dirac mass is found to preserve half of the supersymmetry of the 5-D theory. We explicitly check this by deconstructing 5-D N=2 super-Maxwell theory down to 4-D N=1 super-Proca theory, and deconstructing linear 5-D N=2 supergravity down to 4-D N=1 Zinoviev theory, and derive the full 4-D supersymmetry algebras and Stückelberg symmetries from the 5-D superalgebras and gauge symmetries, respectively. We conjecture that this procedure should admit a generalization to fully non-linear theories.

de Rham C, Melville S, Tolley AJ, 2018, Improved positivity bounds and massive gravity, *Journal of High Energy Physics*, Vol: 2018, ISSN: 1029-8479

Theories such as massive Galileons and massive gravity can satisfy the presently known improved positivity bounds provided they are weakly coupled. We discuss the form of the EFT Lagrangian for a weakly coupled UV completion of massive gravity which closely parallels the massive Galileon, and perform the power counting of corrections to the scattering amplitude and the positivity bounds. The Vainshtein mechanism which is central to the phenomenological viability of massive gravity is entirely consistent with weak coupling since it is classical in nature. We highlight that the only implication of the improved positivity constraints is that the EFT cutoff is lower than previous assumed, and discuss the observable implications, emphasizing that these bounds are not capable of ruling out the model contrary to previous statements in the literature.

de Rham C, Melville S, Tolley AJ,
et al., 2017, Positivity bounds for scalar field theories, *Physical Review D - Particles, Fields, Gravitation and Cosmology*, Vol: 96, ISSN: 1550-2368

Assuming the existence of a local, analytic, unitary UV completion in a Poincaré invariant scalar field theory with a mass gap, we derive an infinite number of positivity requirements using the known properties of the amplitude at and away from the forward scattering limit. These take the form of bounds on combinations of the pole subtracted scattering amplitude and its derivatives. In turn, these positivity requirements act as constraints on the operator coefficients in the low energy effective theory. For certain theories these constraints can be used to place an upper bound on the mass of the next lightest state that must lie beyond the low energy effective theory if such a UV completion is to ever exist.

de Rham C, Melville S, Tolley AJ,
et al., 2017, Massive Galileon positivity bounds, *Journal of High Energy Physics*, Vol: 2017, ISSN: 1029-8479

The EFT coefficients in any gapped, scalar, Lorentz invariant field theory must satisfy positivity requirements if there is to exist a local, analytic Wilsonian UV completion. We apply these bounds to the tree level scattering amplitudes for a massive Galileon. The addition of a mass term, which does not spoil the non-renormalization theorem of the Galileon and preserves the Galileon symmetry at loop level, is necessary to satisfy the lowest order positivity bound. We further show that a careful choice of successively higher derivative corrections are necessary to satisfy the higher order positivity bounds. There is then no obstruction to a local UV completion from considerations of tree level 2-to-2 scattering alone. To demonstrate this we give an explicit example of such a UV completion.

de Rham C, Deskins JT, Tolley AJ,
et al., 2017, Graviton mass bounds, *Reviews of Modern Physics*, Vol: 89, ISSN: 0034-6861

Recently, aLIGO announced the first direct detections of gravitational waves, a direct manifestation of the propagating degrees of freedom of gravity. The detected signals GW150914 and GW151226 have been used to examine the basic properties of these gravitational degrees of freedom, particularly setting an upper bound on their mass. It is timely to review what the mass of these gravitational degrees of freedom means from the theoretical point of view, particularly taking into account the recent developments in constructing consistent massive gravity theories. Apart from the GW150914 mass bound, a few other observational bounds have been established from the effects of the Yukawa potential, modified dispersion relation, and fifth force that are all induced when the fundamental gravitational degrees of freedom are massive. These different mass bounds are reviewed, how they stand in the wake of recent theoretical developments and how they compare to the bound from GW150914 are examined.

de Rham C, Tolley AJ, Zhou S-Y, 2016, Non-compact nonlinear sigma models, *Physics Letters B*, Vol: 760, Pages: 579-583, ISSN: 0370-2693

The target space of a nonlinear sigma model is usually required to be positive definite to avoid ghosts. We introduce a unique class of nonlinear sigma models where the target space metric has a Lorentzian signature, thus the associated group being non-compact. We show that the would-be ghost associated with the negative direction is fully projected out by 2 second-class constraints, and there exist stable solutions in this class of models. This result also has important implications for Lorentz–invariant massive gravity: There exist stable nontrivial vacua in massive gravity that are free from any linear vDVZ-discontinuity and a Λ2 decoupling limit can be defined on these vacua.

de Rham C, Tolley AJ, Zhou SY, 2016, The Λ2 limit of massive gravity, *Journal of High Energy Physics*, Vol: 2016, ISSN: 1126-6708

Lorentz-invariant massive gravity is usually associated with a strong couplingscale Λ3. By including non-trivial effects from the St¨uckelberg modes, we show that aboutthese vacua, one can push the strong coupling scale to higher values and evade the linearvDVZ-discontinuity. For generic parameters of the theory and generic vacua for theSt¨uckelberg fields, the Λ2-decoupling limit of the theory is well-behaved and free of anyghost or gradient-like instabilities. We also discuss the implications for nonlinear sigmamodels with Lorentzian target spaces.

Tolley AJ, Wu DJ, Zhou SY, 2015, Hairy black holes in scalar extended massive gravity, *Physical Review D - Particles, Fields, Gravitation and Cosmology*, Vol: 92, ISSN: 1550-7998

We construct static, spherically symmetric black hole solutions in scalar extended ghost-free massive gravity and show the existence of hairy black holes in this class of extension. While the existence seems to be a generic feature, we focus on the simplest models of this extension and find that asymptotically flat hairy black holes can exist without fine-tuning the theory parameters, unlike the bi-gravity extension, where asymptotical flatness requires fine-tuning in the parameter space. Like the bi-gravity extension, we are unable to obtain asymptotically dS regular black holes in the simplest models considered, but it is possible to obtain asymptotically AdS black holes.

de Rham C, Matas A, Tolley AJ, 2015, New kinetic terms for massive gravity and multi-gravity: a no-go in vielbein form, *CLASSICAL AND QUANTUM GRAVITY*, Vol: 32, ISSN: 0264-9381

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- Citations: 24

de Rham C, Matas A, Ondo NA,
et al., 2015, Interactions of charged spin-2 fields, *Classical and Quantum Gravity*, Vol: 32, ISSN: 0264-9381

In light of recent progress in ghost-free theories of massive gravity and multi-gravity, we reconsider the problem of constructing a ghost-free theory of an interacting spin-2 field charged under a U(1) gauge symmetry. Our starting point is the theory originally proposed by Federbush, which is essentially Fierz–Pauli generalized to include a minimal coupling to a U(1) gauge field. We show the Federbush theory with a dynamical U(1) field is in fact ghost-free and can be treated as a healthy effective field theory to describe a massive charged spin-2 particle. It can even potentially have healthy dynamics above its strong-coupling scale. We then construct candidate gravitational extensions to the Federbush theory both by using dimensional deconstruction, and by constructing a general nonlinear completion. However, we find that the U(1) symmetry forces us to modify the form of the Einstein–Hilbert kinetic term. By performing a constraint analysis directly in the first-order form, we show that these modified kinetic terms inevitably reintroduce the Boulware–Deser ghost. As a by-product of our analysis, we present a new proof for ghost-freedom of bi-gravity in 2+1 dimensions (also known as Zwei-Dreibein gravity). We also give a complementary algebraic argument that the Einstein–Hilbert kinetic term is incompatible with a U(1) symmetry, for a finite number of gravitons.

de Rham C, Tolley AJ, 2015, Vielbein to the rescue? Breaking the symmetric vielbein condition in massive gravity and multigravity, *PHYSICAL REVIEW D*, Vol: 92, ISSN: 1550-7998

Nonminimal matter couplings have recently been considered in the context of massive gravity and multigravity. These couplings are free of the Boulware-Deser ghost in the decoupling limit and can thus be considered within an effective field theory setup. Beyond the decoupling limit the ghost was shown to reemerge in the metric formulation of the theory. Recently it was argued that this pathology is absent when formulated in terms of unconstrained vielbeins. We investigate this possibility and show that the Boulware-Deser ghost is always present beyond the decoupling limit in any dimension larger than 2. We also show that the metric and vielbein formulations have an identical ghost-free decoupling limit. Finally we extend these arguments to more generic multigravity theories and argue that for any dimension larger than 2 a ghost is also present in the vielbein formulation whenever the symmetric vielbein condition is spoiled and the equivalence with the metric formulation is lost.

Elder B, Joyce A, Khoury J,
et al., 2015, Positive energy theorem for P(X, phi) theories, *PHYSICAL REVIEW D*, Vol: 91, ISSN: 1550-7998

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- Citations: 4

Tolley AJ, 2015, Cosmological applications of massive gravity, *Lecture Notes in Physics*, Vol: 892, Pages: 203-224, ISSN: 0075-8450

© Springer International Publishing Switzerland 2015. Models of modified gravity in the infrared are especially appealing for their late-time cosmology. We review different models before focusing on the cosmology of massive gravity.We start by information derived from its decoupling limit where a self-acceleration solution can be found but suffers from strong coupling issues in the vector modes. This feature is carried through for most FRW self-accelerating solutions in the full theory. We emphasize the role played by inhomogeneous solutions which reduce to a self-accelerating FRW solution on distances comparable to our current Universe but are inhomogeneous at larger distances. We also give an overview of cosmological solutions in extensions of massive gravity such as bi-gravity and quasi-dilaton massive gravity.

Tolley AJ, 2015, Cosmological Applications of Massive Gravity, Modifications of Einstein's Theory of Gravity at Large Distances, Publisher: Springer International Publishing, Pages: 203-224, ISBN: 9783319100692

de Rham C, Fasiello M, Tolley AJ, 2014, Stable FLRW solutions in generalized massive gravity, *INTERNATIONAL JOURNAL OF MODERN PHYSICS D*, Vol: 23, ISSN: 0218-2718

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- Citations: 28

Khoury J, Miller GEJ, Tolley AJ, 2014, How general relativity and Lorentz covariance arise from the spatially-covariant effective field theory of the transverse, traceless graviton, *INTERNATIONAL JOURNAL OF MODERN PHYSICS D*, Vol: 23, ISSN: 0218-2718

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- Citations: 1

de Rham C, Matas A, Tolley AJ, 2014, New kinetic interactions for massive gravity?, *CLASSICAL AND QUANTUM GRAVITY*, Vol: 31, ISSN: 0264-9381

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- Citations: 57

de Rham C, Keltner L, Tolley AJ, 2014, Generalized Galileon duality, *PHYSICAL REVIEW D*, Vol: 90, ISSN: 1550-7998

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- Citations: 44

Khoury J, Miller GEJ, Tolley AJ, 2014, On the origin of gravitational Lorentz covariance, *CLASSICAL AND QUANTUM GRAVITY*, Vol: 31, ISSN: 0264-9381

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- Citations: 12

de Rham C, Fasiello M, Tolley AJ, 2014, Galileon duality, *PHYSICS LETTERS B*, Vol: 733, Pages: 46-51, ISSN: 0370-2693

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- Citations: 50

de Rham C, Matas A, Tolley AJ, 2014, Deconstructing dimensions and massive gravity, *CLASSICAL AND QUANTUM GRAVITY*, Vol: 31, ISSN: 0264-9381

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- Citations: 30

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