arXiv subjects

Claudia de Rham

Publications and source records attributed to Claudia de Rham.

At least 91 records · Page 5Linked to original sources

arXiv2013

Deconstructing Dimensions and Massive Gravity

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.

hep-th↗

arXiv2013

Quantum Corrections in Massive Gravity

We compute the one-loop quantum corrections to the potential of ghost-free massive gravity. We show how the mass of external matter fields contribute to the running of the cosmological constant, but do not change the ghost-free structure of the massive gravity potential at one-loop. When considering gravitons running in the loops, we show how the structure of the potential gets destabilized at the quantum level, but in a way which would never involve a ghost with a mass smaller than the Planck scale. This is done by explicitly computing the one-loop effective action and supplementing it with the Vainshtein mechanism. We conclude that to one-loop order the special mass structure of ghost-free massive gravity is technically natural.

hep-th↗

arXiv2013

Galileons in the Sky

We review the different frameworks in which Galileon scalar fields have been seen to emerge such an in DGP, New Massive Gravity and Ghost-free massive Gravity and emphasize their relation with the Lovelock invariant in braneworld models. The existence of a non-renormalization theorem for Galileon scalar fields makes them especially attractive candidates for inflation as well as for late-time acceleration. In particular we review the self-accelerating and degravitating branches of solutions present in Galileon models when arising from Massive Gravity and discuss their phenomenology.

astro-ph.CO↗

arXiv2013

Evidence for and Obstructions to Non-Linear Partially Massless Gravity

Non-linear partially massless (PM) gravity, if it exists, is a theory of massive gravity in which the graviton has four propagating degrees of freedom. In PM gravity, a scalar gauge symmetry removes one of the five modes of the massive graviton. This symmetry ties the value of the cosmological constant to the mass of the graviton, which in turn can be kept small in a technically natural way. Thus PM gravity could offer a compelling solution to the old cosmological constant problem. In this work we look for such a theory among the known ghost-free massive gravity models with a de Sitter reference metric. We find that despite the existence of strong supporting evidence for the existence of a PM theory of gravity, technical obstructions arise which preclude its formulation using the standard massive gravity framework.

hep-th↗

arXiv2013

Superluminality in the Bi- and Multi- Galileon

We re-explore the Bi- and Multi-Galileon models with trivial asymptotic conditions at infinity and show that propagation of superluminal fluctuations is a common and unavoidable feature of these theories, unlike previously claimed in the literature. We show that all Multi-Galileon theories containing a Cubic Galileon term exhibit superluminalities at large distances from a point source, and that even if the Cubic Galileon is not present one can always find sensible matter distributions in which there are superluminal modes at large distances. In the Bi-Galileon case we explicitly show that there are always superluminal modes around a point source even if the Cubic Galileon is not present. Finally, we briefly comment on the possibility of avoiding superluminalities by modifying the asymptotic conditions at infinity.

hep-th↗

arXiv2013

Vainshtein Mechanism in Binary Pulsars

We compute the scalar gravitational radiation from a binary pulsar system in the simplest model that exhibits the Vainshtein mechanism. The mechanism is successful in screening the effect from scalar fields conformally coupled to matter, although gravitational radiation is less suppressed relative to its general relativity predictions than static fifth forces effects within the pulsar system. This is due to a combination of two effects: firstly the existence of monopole and dipole radiation; secondly the Vainshtein suppression comes from the hierarchy of scales between the inverse frequency scale and the Vainshtein radius, rather than the orbital radius of the pulsar system. Extensions of these results will have direct relevance to infrared modifications of gravity, such as massive gravity theories, which are known to exhibit a Vainshtein mechanism. Generalization to Galileon models with higher order interactions are likely to provide stronger constraints.

gr-qc↗

arXiv2013

Massive Gravity on de Sitter and Unique Candidate for Partially Massless Gravity

We derive the decoupling limit of Massive Gravity on de Sitter in an arbitrary number of space-time dimensions d. By embedding d-dimensional de Sitter into d+1-dimensional Minkowski, we extract the physical helicity-1 and helicity-0 polarizations of the graviton. The resulting decoupling theory is similar to that obtained around Minkowski. We take great care at exploring the partially massless limit and define the unique fully non-linear candidate theory that is free of the helicity-0 mode in the decoupling limit, and which therefore propagates only four degrees of freedom in four dimensions. In the latter situation, we show that a new Vainshtein mechanism is at work in the limit m^2\to 2 H^2 which decouples the helicity-0 mode when the parameters are different from that of partially massless gravity. As a result, there is no discontinuity between massive gravity and its partially massless limit, just in the same way as there is no discontinuity in the massless limit of massive gravity. The usual bounds on the graviton mass could therefore equivalently well be interpreted as bounds on m^2-2H^2. When dealing with the exact partially massless parameters, on the other hand, the symmetry at m^2=2H^2 imposes a specific constraint on matter. As a result the helicity-0 mode decouples without even the need of any Vainshtein mechanism.

hep-th↗

arXiv2012

Galileon Radiation from Binary Systems

We calculate the power emitted in scalar modes for a binary systems, including binary pulsars, with a conformal coupling to the most general Galileon effective field theory by considering perturbations around a static, spherical background. While this method is effective for calculating the power in the cubic Galileon case, here we find that if the quartic or quintic Galileon dominate, for realistic pulsar systems the classical perturbative expansion about spherically symmetric backgrounds breaks down (although the quantum effective theory is well-defined). The basic reason is that the equations of motion for the fluctuations are then effectively one dimensional. This leads to many multipoles radiating with equal strength, as opposed to the normal Minkowski spacetime and cubic Galileon cases, where increasing multipoles are suppressed by increasing powers of the orbital velocity. We consider two cases where perturbation theory gives trust-worthy results: (1) when there is a large hierarchy between the masses of two orbiting objects, and (2) when we choose scales such that the quartic Galileon only begins to dominate at distances smaller than the inverse pulsar frequency. Implications for future calculations with the full Galileon that account for the Vainshtein mechanism are considered.

hep-th↗

arXiv2012

Non-Renormalization and Naturalness in a Class of Scalar-Tensor Theories

We study the renormalization of some dimension-4, 7 and 10 operators in a class of nonlinear scalar-tensor theories. These theories are invariant under: (a) linear diffeomorphisms which represent an exact symmetry of the full non-linear action, and (b) global field-space Galilean transformations of the scalar field. The Lagrangian contains a set of non-topological interaction terms of the above-mentioned dimensionality, which we show are not renormalized at any order in perturbation theory. We also discuss the renormalization of other operators, that may be generated by loops and/or receive loop-corrections, and identify the regime in which they are sub-leading with respect to the operators that do not get renormalized. Interestingly, such scalar-tensor theories emerge in a certain high-energy limit of the ghost-free theory of massive gravity. One can use the non-renormalization properties of the high-energy limit to estimate the magnitude of quantum corrections in the full theory. We show that the quantum corrections to the three free parameters of the model, one of them being the graviton mass, are strongly suppressed. In particular, we show that having an arbitrarily small graviton mass is technically natural.

hep-th↗

arXiv2012

Mode Spectrum of the Electromagnetic Field in Open Universe Models

We examine the mode functions of the electromagnetic field on spherically symmetric backgrounds with special attention to the subclass which allows for the foliation as open Friedmann-Lemaitre (FL) spacetime. It is well-known that in certain scalar field theories on open FL background there can exist so-called supercurvature modes, their existence depending on parameters of the theory. Looking at specific open universe models, such as open inflation and the Milne universe, we find that no supercurvature modes are present in the spectrum of the electromagnetic field. This excludes the possibility for superadiabatic evolution of cosmological magnetic fields within these models without relying on new physics or breaking the conformal invariance of electromagnetism.

gr-qc↗

arXiv2012

Cosmology of the Galileon from Massive Gravity

We covariantize the decoupling limit of massive gravity proposed in arXiv:1011.1232 and study the cosmology of this theory as a proxy, which embodies key features of the fully non-linear covariant theory. We first confirm that it exhibits a self-accelerating solution, similar to what has been found in arXiv:1010.1780, where the Hubble parameter corresponds to the graviton mass. For a certain range of parameters fluctuations relative to the self-accelerating background are stable and form an attractor solution. We also show that a degravitating solution can not be constructed in this covariantized proxy theory in a meaningful way. As for cosmic structure formation, we find that the helicity-0 mode of the graviton causes an enhancement relative to LCDM. For consistency we also compare proxy theories obtained starting from different frames in the decoupling limit and discuss the possibility of obtaining a non-representative proxy theory by choosing the wrong starting frame.

hep-th↗

arXiv2011

Chronology Protection in Galileon Models and Massive Gravity

Galileon models are a class of effective field theories that have recently received much attention. They arise in the decoupling limit of theories of massive gravity, and in some cases they have been treated in their own right as scalar field theories with a specific nonlinearly realized global symmetry (Galilean transformation). It is well known that in the presence of a source, these Galileon theories admit superluminal propagating solutions, implying that as quantum field theories they must admit a different notion of causality than standard local Lorentz invariant theories. We show that in these theories it is easy to construct closed timelike curves (CTCs) within the {\it naive} regime of validity of the effective field theory. However, on closer inspection we see that the CTCs could never arise since the Galileon inevitably becomes infinitely strongly coupled at the onset of the formation of a CTC. This implies an infinite amount of backreaction, first on the background for the Galileon field, signaling the break down of the effective field theory, and subsequently on the spacetime geometry, forbidding the formation of the CTC. Furthermore the background solution required to create CTCs becomes unstable with an arbitrarily fast decay time. Thus Galileon theories satisfy a direct analogue of Hawking's chronology protection conjecture.

hep-th↗

arXiv2011

Helicity Decomposition of Ghost-free Massive Gravity

We perform a helicity decomposition in the full Lagrangian of the class of Massive Gravity theories previously proven to be free of the sixth (ghost) degree of freedom via a Hamiltonian analysis. We demonstrate, both with and without the use of nonlinear field redefinitions, that the scale at which the first interactions of the helicity-zero mode come in is $Λ_3=(M_Pl m^2)^{1/3}$, and that this is the same scale at which helicity-zero perturbation theory breaks down. We show that the number of propagating helicity modes remains five in the full nonlinear theory with sources. We clarify recent misconceptions in the literature advocating the existence of either a ghost or a breakdown of perturbation theory at the significantly lower energy scales, $Λ_5=(M_Pl m^4)^{1/5}$ or $Λ_4=(M_Pl m^3)^{1/4}$, which arose because relevant terms in those calculations were overlooked. As an interesting byproduct of our analysis, we show that it is possible to derive the Stueckelberg formalism from the helicity decomposition, without ever invoking diffeomorphism invariance, just from a simple requirement that the kinetic terms of the helicity-two, -one and -zero modes are diagonalized.

hep-th↗

arXiv2011

Comments on (super)luminality

Recently, in an interesting work arXiv:1106.3972 a solution of the equations of motion of massive gravity was discussed, and it was shown that one of the fluctuations on that solution is superluminal. It was also stated that this rules out massive gravity. Here we find that the solution itself is rather unphysical. For this we show that there is another mode on the same background which grows and overcomes the background in an arbitrarily short period of time, that can be excited by a negligible cost in energy. This solution is triggered by the parameter governing the superluminality. Furthermore, we also show that the solution, if viewed as a perfect fluid, has no rest frame, or that the Lorentz transformation that is needed to boost to the rest frame is superluminal itself. The stress-tensor of this fluid has complex eigenvalues, and could not be obtained from any physically sensible matter. Moreover, for the same setup we find another background solution, fluctuations of which are all stable and subluminal. Based on these results, we conclude that the superluminality found in arXiv:1106.3972 is an artifact of using an inappropriate background, nevertheless, this solution represents an instructive example for understanding massive gravity. For instance, on this background the Boulware-Deser ghost is absent, even though this may naively appear not to be the case.

hep-th↗

arXiv2011

Ghost free Massive Gravity in the Stückelberg language

Massive Gravity in four dimensions has been shown to be free of the Boulware-Deser (BD) ghost in the ADM language for a specific choice of mass terms. We show here how this is consistent with the Stückelberg language beyond the decoupling limit, and how the constraint required to remove the BD ghost arises in this framework nonperturbatively, without the use of field redefinitions. We emphasize a subtlety in obtaining this constraint, that has been overlooked in previous literature. In both the ADM and Stückelberg formalisms the vanishing of the determinant of a Hessian guarantees the absence of the BD ghost.

hep-th↗

arXiv2011

Galileon inflation

Galileon inflation is a radiatively stable higher derivative model of inflation. The model is determined by a finite number of relevant operators which are protected by a covariant generalization of the Galileon shift symmetry. We show that the nongaussianity of the primordial density perturbation generated during an epoch of Galileon inflation is a particularly powerful observational probe of these models and that, when the speed of sound is small, fNL can be larger than the usual result fNL ~ 1/c_s^2.

hep-th↗

arXiv2011

de Sitter Galileon

We generalize the Galileon symmetry and its relativistic extension to a de Sitter background. This is made possible by studying a probe-brane in a flat five-dimensional bulk using a de Sitter slicing. The generalized Lovelock invariants induced on the probe brane enjoy the induced Poincaré symmetry inherited from the bulk, while living on a de Sitter geometry. The non-relativistic limit of these invariants naturally maintain a generalized Galileon symmetry around de Sitter while being free of ghost-like pathologies. We comment briefly on the cosmology of these models and the extension to the AdS symmetry as well as generic FRW backgrounds.

hep-th↗

arXiv2011

Nonlinear Dynamics of 3D Massive Gravity

We explore the nonlinear classical dynamics of the three-dimensional theory of "New Massive Gravity" proposed by Bergshoeff, Hohm and Townsend. We find that the theory passes remarkably highly nontrivial consistency checks at the nonlinear level. In particular, we show that: (1) In the decoupling limit of the theory, the interactions of the helicity-0 mode are described by a single cubic term -- the so-called cubic Galileon -- previously found in the context of the DGP model and in certain 4D massive gravities. (2) The conformal mode of the metric coincides with the helicity-0 mode in the decoupling limit. Away from this limit the nonlinear dynamics of the former is described by a certain generalization of Galileon interactions, which like the Galileons themselves have a well-posed Cauchy problem. (3) We give a non-perturbative argument based on the presence of additional symmetries that the full theory does not lead to any extra degrees of freedom, suggesting that a 3D analog of the 4D Boulware-Deser ghost is not present in this theory. Last but not least, we generalize "New Massive Gravity" and construct a class of 3D cubic order massive models that retain the above properties.

hep-th↗