arXiv subjects

Claudia de Rham

Publications and source records attributed to Claudia de Rham.

At least 55 records · Page 3Linked to original sources

arXiv2020

Black Hole Gravitational Waves in the Effective Field Theory of Gravity

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.

hep-th↗

arXiv2020

Causality in Curved Spacetimes: The Speed of Light & Gravity

Within the low-energy effective field theories of QED 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 lightcone. 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.

hep-th↗

arXiv2020

Positivity Constraints on Interacting Pseudo-Linear Spin-2 Fields

We explore the effective field theory for single and multiple interacting pseudo-linear spin-2 fields. By applying forward limit positivity bounds, we show that among the parameters contributing to elastic tree level scattering amplitude, there is no region of compatibility of the leading interactions with a standard local UV completion. Our result generalizes to any number of interacting pseudo-linear spin-2 fields. These results have significant implications for the organization of the effective field theory expansion for pseudo-linear fields.

hep-th↗

arXiv2019

Positivity Constraints on Interacting Spin-2 Fields

The consistency of the EFT of two interacting spin-2 fields is checked by applying forward limit positivity bounds on the scattering amplitudes to exclude the region of parameter space devoid of a standard UV completion. We focus on two classes of theories that have the highest possible EFT cutoff, namely those theories modelled on ghost-free interacting theories of a single massive spin-2 field. We find that the very existence of interactions between the spin-2 fields implies more stringent bounds on all the parameters of the EFT, 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' of an extra pole to be subtracted, hence strengthening the positivity bounds. Second, while adding new fields increases the number of free parameters from the new interactions, this is rapidly overcome by the increased number of positivity bounds for different possible scattering processes. We also discuss how positivity bounds appear to favour relations between operators that effectively raise the cutoff of the EFT.

hep-th↗

arXiv2019

EFT of Interacting Spin-2 Fields

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 $Λ_3$ 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 $Λ_3$. 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.

hep-th↗

arXiv2019

The Speed of Gravity

Within the standard effective field theory of General Relativity, we show that the speed of gravitational waves deviates, ever so slightly, from luminality on cosmological and other spontaneously Lorentz-breaking backgrounds. This effect results from loop contributions from massive fields of any spin, including Standard Model fields, or from tree level effects from massive higher spins $s \ge 2$. We show that for the choice of interaction signs implied by S-matrix and spectral density positivity bounds suggested by analyticity and causality, the speed of gravitational waves is in general superluminal at low-energies on NEC preserving backgrounds, meaning gravitational waves travel faster than allowed by the metric to which photons and Standard Model fields are minimally coupled. We show that departure of the speed from unity increases in the IR and argue that the speed inevitably returns to luminal at high energies as required by Lorentz invariance. Performing a special tuning of the EFT so that renormalization sensitive curvature-squared terms are set to zero, we find that finite loop corrections from Standard Model fields still lead to an epoch dependent modification of the speed of gravitational waves which is determined by the precise field content of the lightest particles with masses larger than the Hubble parameter today. Depending on interpretation, such considerations could potentially have far-reaching implications on light scalar models, such as axionic or fuzzy cold dark matter.

hep-th↗

arXiv2019

Perturbations of Stealth Black Holes in DHOST Theories

Among the Scalar-Tensor modified theories of gravity, 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 GR. 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.

hep-th↗

arXiv2019

Spin-2 and the Weak Gravity Conjecture

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 Stuckelberg $U(1)$ 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 Stuckelberg 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, $M_W< M_{\rm Pl}$, 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.

hep-th↗

arXiv2019

Generalized Proca and its Constraint Algebra

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

hep-th↗

arXiv2019

Positivity Bounds for Massive Spin-1 and Spin-2 Fields

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 $Λ_5$ massive gravity theories and the special `ghost-free' $Λ_3$ theories. Remarkably we find that at the level of 2-2 scattering, the positivity bounds applied to $Λ_5$ massive gravity theories impose the special tunings which generate the $Λ_3$ structure. For $Λ_3$ massive gravity theories, the island of positivity derived in the forward limit appears relatively stable against further bounds.

hep-th↗

arXiv2018

Gravitational Rainbows: LIGO and Dark Energy at its Cutoff

The recent direct detection of a neutron star merger with optical counterpart has been used to severely constrain models of dark energy that typically predict a modification of the speed of gravitational waves. We point out that 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 those scales. We discuss how further missions including LISA and PTAs could play an essential role in testing such models.

hep-th↗

arXiv2018

Scalar Gravitational Radiation from Binaries: Vainshtein Mechanism in Time-dependent Systems

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.

hep-th↗

arXiv2018

On the (A)dS Decoupling Limits of Massive Gravity

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 $Λ_2\sim (M_{\rm Pl} m)^{1/2}$ 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.

hep-th↗

arXiv2017

Improved Positivity Bounds and Massive Gravity

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 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.

hep-th↗

arXiv2017

UV complete me: Positivity Bounds for Particles with Spin

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.

hep-th↗

arXiv2017

Unitary null energy condition violation in $P(X)$ cosmologies

A non-singular cosmological bounce in the Einstein frame can only take place if the Null Energy Condition (NEC) is violated. We explore situations where a single scalar field drives the NEC violation and derive the constraints imposed by demanding tree level unitarity on a cosmological background. We then focus on the explicit constraints that arise in P(X) theories and show that constraints from perturbative unitarity make it impossible for the NEC violation to occur within the region of validity of the effective field theory without also involving irrelevant operators that arise at a higher scale that would enter from integrating out more massive degrees of freedom. Within the context of P(X) theories we show that including such operators allows for a bounce that does not manifestly violate tree level unitarity, but at the price of either imposing a shift symmetry or involving technically unnatural small operator coefficients within the low-energy effective field theory.

hep-th↗

arXiv2017

Graviton Mass Bounds

Recently, aLIGO has 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. We review these different mass bounds and examine how they stand in the wake of recent theoretical developments and how they compare to the bound from GW150914.

astro-ph.CO↗

arXiv2017

Caustics for Spherical Waves

We study the development of caustics in shift-symmetric scalar field theories by focusing on simple waves with an $SO(p)$-symmetry in an arbitrary number of space dimensions. We show that the pure Galileon, the DBI-Galileon, and the extreme-relativistic Galileon naturally emerge as the unique set of caustic-free theories, highlighting a link between the caustic-free condition for simple $SO(p)$-waves and the existence of either a global Galilean symmetry or a global (extreme-)relativistic Galilean symmetry.

hep-th↗