## Publications

106 results found

Arun KG, Belgacem E, Benkel R,
et al., 2022, New horizons for fundamental physics with LISA, *LIVING REVIEWS IN RELATIVITY*, Vol: 25, ISSN: 2367-3613

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- Citations: 1

de Rham C, Tolley AJ, Zhang J, 2022, Causality Constraints on Gravitational Effective Field Theories, *PHYSICAL REVIEW LETTERS*, Vol: 128, ISSN: 0031-9007

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- Citations: 3

Chen CY-R, de Rham C, Margalit A,
et al., 2022, A cautionary case of casual causality, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 3

de Rham C, Garcia-Saenz S, Heisenberg L,
et al., 2022, Cosmology of Extended Proca-Nuevo, *JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS*, ISSN: 1475-7516

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- Citations: 1

Alberte L, de Rham C, Jaitly S,
et al., 2022, Reverse Bootstrapping: IR Lessons for UV Physics, *PHYSICAL REVIEW LETTERS*, Vol: 128, ISSN: 0031-9007

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- Citations: 2

de Rham C, Heisenberg L, Kumar A,
et al., 2022, Quantum stability of a new Proca theory, *Physical Review D*, Vol: 105, ISSN: 2470-0010

Gonzalez MC, de Rham C, Tolley AJ, 2021, Scattering amplitudes for binary systems beyond GR, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

de Rham C, Melville S, Noller J, 2021, Positivity bounds on dark energy: when matter matters, *JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS*, ISSN: 1475-7516

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- Citations: 10

Alberte L, de Rham C, Jaitly S,
et al., 2021, QED positivity bounds, *Physical Review D: Particles, Fields, Gravitation and Cosmology*, Vol: 103, Pages: 1-26, ISSN: 1550-2368

We apply positivity bounds directly to a U(1) gauge theory with charged scalars and charged fermions, i.e., QED, minimally coupled to gravity. Assuming that the massless t-channel pole may be discarded, we show that the improved positivity bounds are violated unless new physics is introduced at the parametrically low scale Λnew∼(emMPl)1/2, consistent with similar results for scalar field theories, far lower than the scale implied by the weak gravity conjecture. This is sharply contrasted with previous treatments which focus on the application of positivity bounds to the low energy gravitational Euler-Heisenberg effective theory only. We emphasize that the low cutoff is a consequence of applying the positivity bounds under the assumption that the pole may be discarded. We conjecture an alternative resolution that a small amount of negativity, consistent with decoupling limits, is allowed and is not in conflict with standard UV completions, including weakly coupled ones.

Xie Y, Zhang J, Silva HO,
et al., 2021, Square Peg in a Circular Hole: Choosing the Right Ansatz for Isolated Black Holes in Generic Gravitational Theories, *PHYSICAL REVIEW LETTERS*, Vol: 126, ISSN: 0031-9007

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- Citations: 4

Alberte L, de Rham C, Jaitly S,
et al., 2020, Positivity bounds and the massless spin-2 pole, *Physical Review D: Particles, Fields, Gravitation and Cosmology*, Vol: 102, Pages: 1-34, ISSN: 1550-2368

The presence of a massless spin-2 field in an effective field theory results in a t-channel pole in the scattering amplitudes that precludes the application of standard positivity bounds. Despite this, recent arguments based on compactification to three dimensions have suggested that positivity bounds may be applied to the t-channel pole subtracted amplitude. If correct, this would have deep implications for UV physics and the weak gravity conjecture. Within the context of a simple renormalizable field theory coupled to gravity we find that applying these arguments would constrain the low-energy coupling constants in a way which is incompatible with their actual values. This contradiction persists on deforming the theory. Further enforcing the t-channel pole subtracted positivity bounds on such generic renormalizable effective theories coupled to gravity would imply new physics at a scale parametrically smaller than expected, with far-reaching implications. This suggests that generically the standard positivity bounds are inapplicable with gravity, and we highlight a number of issues that impinge on the formulation of a three-dimensional amplitude which simultaneously satisfies the required properties of analyticity, positivity, and crossing symmetry. We conjecture instead a modified bound that ought to be satisfied independently of the precise details of the high energy completion.

de Rham C, Tolley AJ, 2020, Causality in curved spacetimes: The speed of light and gravity, *PHYSICAL REVIEW D*, Vol: 102, Pages: 1-33, ISSN: 1550-7998

Within the low-energy effective field theories of quantum electrodynamics and gravity, the low-energy speed of light or that of gravitational waves can typically be mildly superluminal in curved spacetimes. Related to this, small scattering time advances relative to the curved background can emerge from known effective field theory coefficients for photons or gravitons. We clarify why these results are not in contradiction with causality, analyticity or Lorentz invariance, and highlight various subtleties that arise when dealing with superluminalities and time advances in the gravitational context. Consistent low-energy effective theories are shown to self-protect by ensuring that any time advance and superluminality calculated within the regime of validity of the effective theory is necessarily unresolvable, and cannot be argued to lead to a macroscopically larger light cone. Such considerations are particularly relevant for putting constraints on cosmological and gravitational effective field theories and we provide explicit criteria to be satisfied so as to ensure causality.

de Rham C, Pozsgay V, 2020, New class of Proca interactions, *Physical Review D: Particles, Fields, Gravitation and Cosmology*, Vol: 102, Pages: 1-18, ISSN: 1550-2368

We propose a new class of Proca interactions that enjoy a nontrivial constraint and hence propagates the correct number of degrees of freedom for a healthy massive spin-1 field. We show that the scattering amplitudes always differ from those of the Generalized Proca. This implies that the new class of interactions proposed here are genuinely different from the Generalized Proca and there can be no local field redefinitions between the two. In curved spacetime, massive gravity is the natural covariantization, but we show how other classes of covariantizations can be considered.

Barausse E, Berti E, Hertog T,
et al., 2020, Prospects for fundamental physics with LISA, *General Relativity and Gravitation*, Vol: 52, Pages: 1-33, ISSN: 0001-7701

In this paper, which is of programmatic rather than quantitative nature, we aim to further delineate and sharpen the future potential of the LISA mission in the area of fundamental physics. Given the very broad range of topics that might be relevant to LISA,we present here a sample of what we view as particularly promising fundamental physics directions. We organize these directions through a “science-first” approach that allows us to classify how LISA data can inform theoretical physics in a variety of areas. For each of these theoretical physics classes, we identify the sources that are currently expected to provide the principal contribution to our knowledge, and the areas that need further development. The classification presented here should not be thought of as cast in stone, but rather as a fluid framework that is amenable to change with the flow of new insights in theoretical physics.

de Rham C, Francfort J, Zhang J, 2020, Black hole gravitational waves in the effective field theory of gravity, *Physical Review D: Particles, Fields, Gravitation and Cosmology*, Vol: 102, Pages: 024079 – 1-024079 – 14, ISSN: 1550-2368

We investigate the propagation of gravitational waves on a black hole background within the low-energy effective field theory of gravity, where effects from heavy fields are captured by higher-dimensional curvature operators. Depending on the spin of the particles integrated out, the speed of gravitational waves at low energy can be either superluminal or subluminal as compared to the causal structure observed by other species. Interestingly, however, gravitational waves are always exactly luminal at the black hole horizon, implying that the horizon is identically defined for all species. We further compute the corrections on quasinormal frequencies caused by the higher-dimensional curvature operators and highlight the corrections arising from the low-energy effective field.

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, Zhang J, 2019, Perturbations of stealth black holes in degenerate higher-order scalar-tensor theories, *Physical Review D: Particles, Fields, Gravitation and Cosmology*, Vol: 100, Pages: 124023-1-124023-12, ISSN: 1550-2368

Among the scalar-tensor modified theories of gravity, degenerate higher-order scalar-tensor (DHOST) models could play a special role for dark energy while being consistent with current observations, notably those constraining the speed of gravitational waves. Schwarzschild–de Sitter black holes were shown to be exact solutions of a particular subclass of quadratic DHOST theories, while carrying a nontrivial scalar profile that linearly evolves in time and hence potentially providing exciting new phenomenological windows to explore this model. We investigate the physical perturbations about such black holes and find that the odd-parity tensor perturbations behave in a way indistinguishable to general relativity. On the other hand, the effective metric for the (even-parity) scalar perturbations is singular, indicating that those exact black hole solutions are infinitely strongly coupled and cannot be trusted within the regime of validity of the DHOST effective field theory. We show how this strong coupling result is generalizable to a whole class of solutions with arbitrary manifolds both for DHOST and Horndeski.

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.

Rham CD, Zhang J, 2019, Perturbations of stealth black holes in DHOST theories, Publisher: arXiv

Among the Scalar-Tensor modified theories of gravity, DHOST models could playa special role for dark energy while being consistent with currentobservations, notably those constraining the speed of gravitational waves.Schwarzschild-de Sitter black holes were shown to be exact solutions of aparticular subclass of quadratic DHOST theories, while carrying a nontrivialscalar profile that linearly evolves in time and hence potentially providingexciting new phenomenological windows to explore this model. We investigate thephysical perturbations about such black holes and find that the odd-paritytensor perturbations behave in a way indistinguishable to GR. On the otherhand, the effective metric for the (even-parity) scalar perturbations issingular, indicating that those exact black hole solutions are infinitelystrongly coupled and cannot be trusted within the regime of validity of theDHOST effective field theory. We show how this strong coupling result isgeneralizable to a whole class of solutions with arbitrary manifolds both forDHOST and Horndeski.

Jiménez JB, Rham CD, Heisenberg L, 2019, Generalized proca and its constraint algebra, Publisher: arXiv

We reconsider the construction of general derivative self-interactions for amassive Proca field. The constructed Lagrangian is such that the vector fieldpropagates at most three degrees of freedom, thus avoiding the ghostly natureof a fourth polarisation. The construction makes use of the well-knowncondition for constrained systems of having a degenerate Hessian. We brieflydiscuss the casuistry according to the nature of the existing constraintsalgebra. We also explore various classes of interesting new interactions thathave been recently raised in the literature. For the sixth order Lagrangianthat satisfies the constraints by itself we prove its topological character,making such a term irrelevant. There is however a window of opportunity forexploring other classes of fully-nonlinear interactions that satisfy theconstraint algebra by mixing terms of various order.

de Rham C, 2019, The gravitational rainbow beyond Einstein gravity, *International Journal of Modern Physics D: Gravitation, Astrophysics and Cosmology*, Vol: 28, ISSN: 0218-2718

The recent direct detection of gravitational waves have been successfully used to examine the basic properties of the gravitational degrees of freedom. They set an upper bound on their mass and constrain their speed of propagation with unprecedented accuracy. Within the current realm of observational and theoretical constraints, we explore the possibility for gravity to depart from general relativity (GR) in the infrared and derive the implications on our observable Universe. We also investigate whether these types of models could ever enjoy a standard analytic UV completion.

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.

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.

Amendola L, Appleby S, Avgoustidis A,
et al., 2018, Cosmology and fundamental physics with the Euclid satellite, *Living Reviews in Relativity*, Vol: 21, Pages: 1-345, ISSN: 1433-8351

Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

de Rham C, Melville S, 2018, Gravitational rainbows: LIGO and dark energy at its cutoff, *Physical Review Letters*, Vol: 121, Pages: 1-6, ISSN: 0031-9007

The recent direct detection of gravitational waves from a neutron star merger with optical counterpart has been used to severely constrain models of dark energy that typically predict a modification of the gravitational wave speed. However, the energy scales observed at LIGO, and the particular frequency of the neutron star event, lie very close to the strong coupling scale or cutoff associated with many dark energy models. While it is true that at very low energies one expects gravitational waves to travel at a speed different than light in these models, the same is no longer necessarily true as one reaches energy scales close to the cutoff. We show explicitly how this occurs in a simple model with a known partial UV completion. Within the context of Horndeski, we show how the operators that naturally lie at the cutoff scale can affect the speed of propagation of gravitational waves and bring it back to unity at LIGO scales. We discuss how further missions including LISA and PTAs could play an essential role in testing such models.

de Rham C, Hinterbichler K, Johnson LA, 2018, On the (A)dS decoupling limits of massive gravity, *The Journal of High Energy Physics*, Vol: 154, Pages: 1-38, ISSN: 1029-8479

We consider various decoupling limits of ghost-free massive gravity on (A)dS. The first is a decoupling limit on AdS space where the mass goes to zero while the AdS radius is held fixed. This results in an interacting massive Proca vector theory with a Λ2 ∼ (MPlm)1/2 strong coupling scale which is ghost-free by construction and yet can not be put in the form of the generalized Proca theories considered so far. We comment on the existence of a potential duality between this Proca theory and a CFT on the boundary. The second decoupling limit we consider is a new limit on dS, obtained by sending the mass towards the finite partially massless value. We do this by introducing the scalar Stückelberg field which restores the partially massless symmetry. For generic values of the parameters, only a finite number of operators enter the partially massless decoupling limit and take the form of dS Galileons. If the interactions are chosen to be precisely those of the ‘candidate’ non-linear partially massless theory, the resulting strong coupling scale has a higher value and the resulting decoupling limit includes an infinite number of interactions which we give in closed form. These interactions preserve both the linear partially massless symmetry and the dS version of the Galileon shift symmetry.

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.

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