We investigate how the speed of propagation of physical excitations is encoded in the coefficients of five-point interactions. This leads to a superluminality bound on scalar five-point interactions, which we present here for the first time. To substantiate our result, we also consider the case of four-point interactions for which bounds from S-matrix sum rules exist and show that these are parametrically equivalent to the bounds obtained within our analysis. Finally, we extend the discussion to a class of higher-point interactions.

United States

Czechia

Francesco Serra

Leonardo Trombetta

Five-point superluminality bounds

We derive causality constraints on the simplest scalar-tensor theories in which black holes differ from what General Relativity predicts, a scalar coupled to the Gauss-Bonnet or the Chern-Simons terms. Demanding that time advances are unobservable within the regime of validity of these effective field theories, we find their cutoff must be parametrically of the same size as the inverse Schwarzschild radius of the black holes for which the non-standard effects are of order one. For astrophysical black holes within the range of current gravitational wave detectors, this means a cutoff length of the order of kilometers. We further explore the leading additional higher-dimensional operators potentially associated with the scale of UV completion and discuss their phenomenological implications for gravitational wave science.

Italy

Germany

Javi Serra

Enrico Trincherini

Causality constraints on black holes beyond GR

Scalar hair of black holes in theories with a shift symmetry are constrained by the no-hair theorem of Hui and Nicolis, assuming spherical symmetry, time-independence of the scalar field and asymptotic flatness. The most studied counterexample is a linear coupling of the scalar with the Gauss-Bonnet invariant. However, in this case the norm of the shift-symmetry current diverges at the horizon casting doubts on whether the solution is physically sound. We show that this is not an issue since is not a scalar quantity, since is not a diffinvariant current in the presence of Gauss-Bonnet. The same theory can be written in Horndeski form with a non-analytic function log . In this case the shift-symmetry current is diff-invariant, but contains powers of in the denominator, so that its divergence at the horizon is again immaterial. We confirm that other hairy solutions in the presence of non-analytic Horndeski functions are pathological, featuring divergences of physical quantities as soon as one departs from time-independence and spherical symmetry. We generalise the no-hair theorem to Beyond Horndeski and DHOST theories, showing that the coupling with Gauss-Bonnet is necessary to have hair.

Paolo Creminelli

Spain

Nicolás Loayza

Hairy black-holes in shift-symmetric theories

We analyze the infrared behavior of the two and four-point functions for the massless O(N) model in Lorentzian de Sitter spacetime, using the 1/N expansion. Our approach is based in the study of the Schwinger-Dyson equations on the sphere (Euclidean de Sitter space), using the fact that the infrared behavior in Lorentzian spacetime is determined by the pole structure of the Euclidean correlation functions. We compute the two-point function up to the NTLO in 1/N , and show that in the infrared it behaves as the superposition of two massive free propagators with effective masses of the same order, but not equal to, the dynamical mass m  dyn . We compare our results with those obtained using other approaches, and find that they are equivalent but retrieved in a considerably simpler way. We also discuss the infrared behavior of the equal-times four-point functions.

Argentina

Diana Nacir

Francisco Mazzitelli

To the sphere and back again: de Sitter infrared correlators at NTLO in 1/N

We analyze the long distance behavior of the two-point functions for an interacting scalar O(N) model in de Sitter spacetime. Following our previous work, this behavior is analyzed by analytic continuation of the Euclidean correlators, which are computed by treating the homogeneous zero mode exactly and using a partial resummation of the interactions between the zero and the non-zero modes. We focus on massless fields and present an alternative derivation of our method, which involves a double expansion in 1/N and the coupling constant of the theory. This derivation is simpler than the previous one and can be directly extended for fields with negative squared-mass. We extend our previous results by computing the long wavelength limit of the two-point functions at next-to-leading order in 1/N and at leading order in the coupling constant, which involves a further resummation of Feynman diagrams (needed when the two-point functions are analitically continued). We prove that, after this extra resummation, the two-point functions vanish in the long distance limit.

Long distance behavior of O(N)-model correlators in de Sitter space and the resummation of secular terms

Higher derivative scalar interactions can give rise to interesting cosmological scenarios. We present a complete classification of such operators that can yield sizeable effects without introducing ghosts and, at the same time, define an effective field theory robust under the inclusion of quantum corrections. A set of rules to power count consistently the coefficients of the resulting Lagrangian is provided by the presence of an approximate global symmetry. The interactions that we derive in this way contain a subset of the so-called Horndeski and beyond Horndeski theories. Our construction therefore provides a structurally robust context to study their phenomenology. Applications to dark energy/modified gravity and geodesically complete cosmologies are briefly discussed.

Netherlands

Luca Santoni

Behind Horndeski: structurally robust higher derivative EFTs

We consider an O ( N ) scalar field model with quartic interaction in d -dimensional Euclidean de Sitter space. In order to avoid the problems of the standard perturbative calculations for light and massless fields, we generalize to the O ( N ) theory a systematic method introduced previously for a single field, which treats the zero modes exactly and the nonzero modes perturbatively. We compute the two-point functions taking into account not only the leading infrared contribution, coming from the self-interaction of the zero modes, but also corrections due to the interaction of the ultraviolet modes. For the model defined in the corresponding Lorentzian de Sitter spacetime, we obtain the two-point functions by analytical continuation. We point out that a partial resummation of the leading secular terms (which necessarily involves nonzero modes) is required to obtain a decay at large distances for massless fields. We implement this resummation along with a systematic double expansion in an effective coupling constant λ $$ \sqrt{\lambda } $$ and in 1 /N . We explicitly perform the calculation up to the next-to-next-to-leading order in λ $$ \sqrt{\lambda } $$ and up to next-to-leading order in 1 /N . The results reduce to those known in the leading infrared approximation. We also show that they coincide with the ones obtained directly in Lorentzian de Sitter spacetime in the large N limit, provided the same renormalization scheme is used.