Publications
97 results found
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.
Tolley AJ, 2017, Theories of modified gravity, Pages: 209-216
I briefly review modified theories of gravity, and in particular discuss massive theories of gravity and current observational bounds placed on the graviton mass.
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: 26
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 <i>P</i>(<i>X</i>, φ) theories, PHYSICAL REVIEW D, Vol: 91, ISSN: 1550-7998
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- Citations: 10
Tolley AJ, 2015, Cosmological applications of massive gravity, Lecture Notes in Physics, Vol: 892, Pages: 203-224, ISSN: 0075-8450
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, Editors: Papantonopoulos, Publisher: SPRINGER-VERLAG BERLIN, Pages: 203-224, ISBN: 978-3-319-10069-2
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- Citations: 5
de Rham C, Fasiello M, Tolley AJ, 2014, Stable FLRW solutions in generalized massive gravity, International Journal of Modern Physics D: Gravitation, Astrophysics and Cosmology, Vol: 23, Pages: 1-29, ISSN: 0218-2718
We present exact Friedmann Lemaítre Robertson Walkers (FLRW) solutions in generalized massive gravity where the mass parameters are naturally promoted to Lorentz-invariant functions of the Stückelberg fields. This new dependence relaxes the constraint that would otherwise prevent massive gravity from possessing exact FLRW solutions. It does so without the need to introduce additional degrees of freedom. We find self-accelerating cosmological solutions and show that, with a mild restriction on the region of phase space, these cosmological solutions exhibit full stability, i.e. absence of ghosts and gradient instabilities for all the tensor, vector and scalar modes, for all cosmic time. We perform the full decoupling limit analysis, including vector degrees of freedom, which can be used to confirm the existence of an active Vainshtein mechanism about these solutions.
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
We show that there can be no new Lorentz invariant kinetic interactions free from the Boulware–Deser ghost in four dimensions in the metric formulation of gravity, beyond the standard Einstein–Hilbert, up to total derivatives. We use dimensional deconstruction as a way to motivate a non-linear ansatz for potential new ghost-free kinetic interactions for massive gravity, bi-gravity and multi-gravity in four and higher dimensions. These interactions descend from Lovelock terms, and so naively one might expect the interactions to be ghost-free. However, we show that these new interactions inevitably lead to more than five propagating degrees of freedom. We then perform a general perturbative analysis in four dimensions, and show that the only term with two derivatives that does not introduce a ghost is the Einstein–Hilbert term. This result extends to all orders in perturbations.
de Rham C, Keltner L, Tolley AJ, 2014, Generalized Galileon duality, PHYSICAL REVIEW D, Vol: 90, ISSN: 1550-7998
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- Citations: 61
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: 19
de Rham C, Fasiello M, Tolley AJ, 2014, Galileon duality, Physics Letters B: Nuclear Physics and Particle Physics, Vol: 733, Pages: 46-51, ISSN: 0370-2693
We show that every Galileon theory admits a dual formulation as a Galileon theory with new operator coefficients. In n dimensions a free scalar field in Minkowski spacetime is dual to a -th order Galileon theory which exhibits the Vainshtein mechanism when coupled to sources and superluminal propagation even on-shell. This demonstrates that superluminal propagation at low energies is compatible with an analytic S-matrix and causality. For point sources, the duality interchanges the strongly coupled Vainshtein regime with the weakly coupled asymptotic regime.
de Rham C, Matas A, Tolley AJ, 2014, Deconstructing dimensions and massive gravity, Classical and Quantum Gravity, Vol: 31, ISSN: 0264-9381
We show that the ghost-free models of massive gravity and their multi-graviton extensions follow from considering higher dimensional General Relativity in Einstein–Cartan form on a discrete extra dimension, according to the dimensional deconstruction paradigm. We show that dimensional deconstruction is equivalent to a truncation of the Kaluza–Klein tower at the nonlinear level. Higher dimensional gravity is not recovered from a lower dimensional multi-graviton theory in the limit of a continuous extra dimension (infinite Kaluza–Klein tower) due to the appearance of a low strong coupling scale that depends on IR physics. This strong coupling scale, which is associated with the mass of the lowest Kaluza–Klein mode, controls the onset of the Vainshtein mechanism and is crucial to the theoretical and observational viability of the truncated theory.
Tolley AJ, 2014, Theories of modified gravity, Pages: 263-272
We review a class of theoretical models of modified gravity that incorporate the Vainshtein mechanism. These include in particular models based on massive gravity and its generalizations. We review how massive gravity models may be obtained from extra dimensions through the deconstruction framework and discuss the decoupling of bi-gravity and the associated Galileon duality it uncovers.
Fasiello M, Tolley AJ, 2013, Cosmological stability bound in massive gravity and bigravity, JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS, ISSN: 1475-7516
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- Citations: 111
Ondo NA, Tolley AJ, 2013, Complete decoupling limit of ghost-free massive gravity, JOURNAL OF HIGH ENERGY PHYSICS, ISSN: 1029-8479
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- Citations: 52
Agarwal N, Holman R, Tolley AJ, 2013, WHAT IS THE SHAPE OF THE INITIAL STATE?, INTERNATIONAL JOURNAL OF MODERN PHYSICS D, Vol: 22, ISSN: 0218-2718
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- Citations: 3
Berezhiani L, Chkareuli G, de Rham C, et al., 2013, Mixed Galileons and spherically symmetric solutions, CLASSICAL AND QUANTUM GRAVITY, Vol: 30, ISSN: 0264-9381
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- Citations: 36
de Rham C, Hinterbichler K, Rosen RA, et al., 2013, Evidence for and obstructions to nonlinear partially massless gravity, PHYSICAL REVIEW D, Vol: 88, ISSN: 1550-7998
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- Citations: 69
Agarwal N, Holman R, Tolley AJ, et al., 2013, Effective field theory and non-Gaussianity from general inflationary states, JOURNAL OF HIGH ENERGY PHYSICS, ISSN: 1029-8479
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- Citations: 66
de Rham C, Matas A, Tolley AJ, 2013, Galileon radiation from binary systems, PHYSICAL REVIEW D, Vol: 87, ISSN: 1550-7998
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- Citations: 48
Jacobs DM, Starkman GD, Tolley AJ, 2013, Brane localization and stabilization via regional physics, JOURNAL OF HIGH ENERGY PHYSICS, ISSN: 1029-8479
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- Citations: 1
Jacobs DM, Starkman GD, Tolley AJ, 2013, Brane stabilization and regionality of extra dimensions, PHYSICAL REVIEW D, Vol: 87, ISSN: 1550-7998
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- Citations: 4
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