## Publications

112 results found

Rham CD, Garcia-Saenz S, Heisenberg L, et al., 2023, To Half--Be or Not To Be?

It has recently been argued that half degrees of freedom could emerge inLorentz and parity invariant field theories, using a non-linear Proca fieldtheory dubbed Proca-Nuevo as a specific example. We provide two proofs, usingthe Lagrangian and Hamiltonian pictures, that the theory possesses a pair ofsecond class constraints, leaving $D-1$ degrees of freedom in $D$ spacetimedimensions, as befits a consistent Proca model. Our proofs are explicit andstraightforward in two dimensions and we discuss how they generalize to anarbitrary number of dimensions. We also clarify why local Lorentz and parityinvariant field theories cannot hold half degrees of freedom.

Rham CD, Kożuszek J, Tolley AJ, et al., 2023, A dynamical formulation of ghost-free massive gravity

We present a formulation of ghost-free massive gravity with flat referencemetric that exhibits the full non-linear constraint algebraically, in a waythat can be directly implemented for numerical simulations. Motivated by thepresence of higher order operators in the low-energy effective description ofmassive gravity, we show how the inclusion of higher-order gradient(dissipative) terms leads to a well-posed formulation of its dynamics. Whilethe formulation is presented for a generic combination of the minimal andquadratic mass terms on any background, for concreteness, we then focus on thenumerical evolution of the minimal model for spherically symmetricgravitational collapse of scalar field matter. This minimal model does notcarry the relevant interactions to switch on an active Vainshtein mechanism, atleast in spherical symmetry, thus we do not expect to recover usual GRbehaviour even for small graviton mass. Nonetheless we may ask what the outcomeof matter collapse is for this gravitational theory. Starting with smallinitial data far away from the centre, we follow the matter through anon-linear regime as it falls towards the origin. For sufficiently weak datathe matter disperses. However for larger data we generally find that theclassical evolution breaks down due to the theory becoming infinitely stronglycoupled without the presence of an apparent horizon shielding this behaviourfrom an asymptotic observer.

de Rham C, Engelbrecht L, Heisenberg L,
et al., 2022, Positivity bounds in vector theories, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Rham CD, Jaitly S, Tolley AJ, 2022, Constraints on Regge behaviour from IR physics

We consider positivity constraints applicable to the Effective Field Theory(EFT) of gravity in arbitrary dimensions. By considering scattering ofindefinite initial and final states, we highlight the existence of agravitational scattering amplitude for which full crossing symmetry is manifestand utilize the recently developed crossing symmetric dispersion relations toderive compact non-linear bounds. We show that the null constraints built intothese dispersion relations lead to a finite energy sum rule for gravity whichmay be extended to a one-parameter family of continuous moment sum rules. Thesesum rules enforce a UV-IR relation which imposes constraints on both the Reggetrajectory and residue. We also highlight a situation where the Reggetrajectory is uniquely determined in terms of the sub-Regge scale amplitude.Generically the Regge behaviour may be split into an IR sensitive partcalculable within a given EFT which mainly depends on the lightest fields inNature, and an IR independent part which are subject to universal positivityconstraints following from unitarity and analyticity.

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: 8

González MC, De Rham C, Pozsgay V,
et al., 2022, Causal effective field theories, *Physical Review D*, Vol: 106, ISSN: 2470-0010

Physical principles such as unitarity, causality, and locality can constrain the space of consistent effective field theories (EFTs) by imposing two-sided bounds on the allowed values of Wilson coefficients. In this paper, we consider the bounds that arise from the requirement of low energy causality alone, without appealing to any assumptions about UV physics. We focus on shift-symmetric theories, and consider bounds that arise from the propagation around both a homogeneous and a spherically symmetric scalar field background. We find that low energy causality, namely the requirement that there are no resolvable time advances within the regime of validity of the EFT, produces two-sided bounds in agreement with compact positivity constraints previously obtained from 2→2 scattering amplitude dispersion relations using full crossing symmetry.

Baker T, Barausse E, Chen A, et al., 2022, Testing gravitational wave propagation with multiband detections

Effective field theories (EFT) of dark energy (DE) -- built to parameterisethe properties of DE in an agnostic manner -- are severely constrained bymeasurements of the propagation speed of gravitational waves (GW). However, GWfrequencies probed by ground-based interferometers lie around the typicalstrong coupling scale of the EFT, and it is likely that the effectivedescription breaks down before even reaching that scale. We discuss how thisleaves the possibility that an appropriate ultraviolet completion of DEscenarios, valid at scales beyond an EFT description, can avoid presentconstraints on the GW speed. Instead, additional constraints in the lowerfrequency LISA band would be harder to escape, since the energies involved areorders of magnitude lower. By implementing a method based on GW multibanddetections, we show indeed that a single joint observation of a GW150914-likeevent by LISA and a terrestrial interferometer would allow one to constrain thespeed of light and gravitons to match to within $10^{-15}$. Multiband GWobservations can therefore firmly constrain scenarios based on the EFT of DE,in a robust and unambiguous way.

de Rham C, Tolley AJ, Zhang J, 2022, Causality constraints on gravitational effective field theories, *Physical Review Letters*, Vol: 128, Pages: 1-6, ISSN: 0031-9007

We consider the effective field theory of gravity around black holes, and show that the coefficients of the dimension-8 operators are tightly constrained by causality considerations. Those constraints are consistent with—but tighter than—previously derived causality and positivity bounds and imply that the effects of one of the dimension-8 operators by itself cannot be observable while remaining consistent with causality. We then establish in which regime one can expect the generic dimension-8 and lower order operators to be potentially observable while preserving causality, providing a theoretical prior for future observations. We highlight the importance of “infrared causality” and show that the requirement of “asymptotic causality” or net (sub)luminality would fail to properly diagnose violations of causality.

Rham CD, Kundu S, Reece M, et al., 2022, Snowmass White Paper: UV Constraints on IR Physics

Fundamental principles of local quantum field theory or of quantum gravitycan enforce consistency requirements on the space of consistent low-energyeffective field theories. We survey the various techniques that have been usedto put UV constraints on IR physics, including those from causalityconsiderations in the form of S-matrix positivity and bootstrap bounds,scattering time delays, conformal field theory and holographic methods,together with those that arise from landscape/swampland criteria such as theweak gravity conjecture. We review recent applications of these constraints tocorrections to Standard Model physics, corrections to Einstein gravity, andcosmological theories and highlight promising future directions.

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: 8

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: 2

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: 8

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

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- Citations: 1

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

Batista RA, Amin MA, Barenboim G, et al., 2021, EuCAPT White Paper: Opportunities and Challenges for Theoretical Astroparticle Physics in the Next Decade

Astroparticle physics is undergoing a profound transformation, due to aseries of extraordinary new results, such as the discovery of high-energycosmic neutrinos with IceCube, the direct detection of gravitational waves withLIGO and Virgo, and many others. This white paper is the result of acollaborative effort that involved hundreds of theoretical astroparticlephysicists and cosmologists, under the coordination of the European Consortiumfor Astroparticle Theory (EuCAPT). Addressed to the whole astroparticle physicscommunity, it explores upcoming theoretical opportunities and challenges forour field of research, with particular emphasis on the possible synergies amongdifferent subfields, and the prospects for solving the most fundamental openquestions with multi-messenger observations.

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: 18

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: 6

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.

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