Causality constraints on corrections to Einstein gravity

Abstract

We study constraints from causality and unitarity on $2\to 2$ graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass $M$ of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit $G\to 0$, and prove the scaling with $M$ expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.

arXiv comment35 pages + appendices + refs, 14 figures

References in corpus (52)

• Modified Gravity and Cosmology
• A bound on chaos
• Causality, Analyticity and an IR Obstruction to UV Completion
• The phantom menaced: constraints on low-energy effective ghosts
• Causality Constraints on Corrections to the Graviton Three-Point Coupling
• Beyond $\Lambda$CDM: Problems, solutions, and the road ahead
• Analyticity in Spin in Conformal Theories
• Testing General Relativity in Cosmology
• Black Holes and Large N Species Solution to the Hierarchy Problem
• TikZ-Feynman: Feynman diagrams with TikZ
• Theorems on gravitational time delay and related issues
• Light-ray operators in conformal field theory
• The EFT-Hedron
• Positive Moments for Scattering Amplitudes
• New positivity bounds from full crossing symmetry
• Positivity Bounds for Scalar Theories
• Sharp Boundaries for the Swampland
• A spacetime derivation of the Lorentzian OPE inversion formula
• Extremal Effective Field Theories
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• UV complete me: Positivity Bounds for Particles with Spin
• Unitarity, stability and loops of unstable ghosts
• Quantum Gravity Constraints from Unitarity and Analyticity
• Causality as an emergent macroscopic phenomenon: The Lee-Wick O(N) model
• Positivity Bounds for Massive Spin-1 and Spin-2 Fields
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• AdS Bulk Locality from Sharp CFT Bounds
• Shocks, Superconvergence, and a Stringy Equivalence Principle
• Causality, Unitarity, and the Weak Gravity Conjecture
• The Boostless Bootstrap: Amplitudes without Lorentz boosts
• Into the EFThedron and UV constraints from IR consistency
• QED positivity bounds
• Rigorous Bounds on Light-by-Light Scattering
• Gravitational-Wave Constraints on an Effective Field-Theory Extension of General Relativity
• All higher-curvature gravities as Generalized quasi-topological gravities
• Causality Constraints on Gravitational Effective Field Theories
• Reverse Bootstrapping: IR lessons for UV physics
• Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds
• Crossing Symmetry in the Planar Limit
• A Bound on Massive Higher Spin Particles
• Sums of squares and varieties of minimal degree
• Positivity Constraints on Interacting Spin-2 Fields
• Generalized positivity bounds on chiral perturbation theory
• Causality, Unitarity and Symmetry in Effective Field Theory
• Quantum field theory and the Bieberbach conjecture
• Positivity and Geometric Function Theory Constraints on Pion Scattering
• Positivity Bounds without Boosts
• SMEFTs living on the edge: determining the UV theories from positivity and extremality
• QFT, EFT and GFT
• Generalized elastic positivity bounds on interacting massive spin-2 theories
• Analyticity and Crossing Symmetry of Superstring Loop Amplitudes
• Hyperbolicity Constraints in Extended Gravity Theories

Cited by in corpus (49)

• Extremal Kerr black holes as amplifiers of new physics
• Rigorous bounds on transport from causality
• Graviton partial waves and causality in higher dimensions
• Gravitational Regge bounds
• Implications of the Weak Gravity Conjecture for Tidal Love Numbers of Black Holes
• Gravitational Causality and the Self-Stress of Photons
• What is the $i\epsilon$ for the S-matrix?
• Massive Gravity is not Positive
• Shedding black hole light on the emergent string conjecture
• Quasinormal modes and their excitation beyond general relativity
• The Stringy S-matrix Bootstrap: Maximal Spin and Superpolynomial Softness
• UV-Complete Gravity Amplitudes and the Triple Product
• Holographic cameras: an eye for the bulk
• Bell inequalities in 2-2 scattering
• Running Love Numbers and the Effective Field Theory of Gravity
• The Hydrohedron: Bootstrapping Relativistic Hydrodynamics
• Finite energy sum rules for gravitational Regge amplitudes
• Bounds on photon scattering
• The EFT Bootstrap at Finite $M_{PL}$
• Causality and quasi-normal modes in the GREFT
• Positivity Bounds on parity-violating scalar-tensor EFTs
• Positivity Bounds on Massive Vectors
• Effective Field Theory Islands from Perturbative and Nonperturbative Four-Graviton Amplitudes
• Black Hole Extremality in Nonlinear Electrodynamics: A Lesson for Weak Gravity and Festina Lente Bounds
• Non-Forward UV/IR Relations
• Feynman Integrals from Positivity Constraints
• Multipositivity Bounds for Scattering Amplitudes
• Positivity Bounds in Scalar Effective Field Theories at One-loop Level
• Gravity-Induced Photon Interactions and Infrared Consistency in any Dimensions
• Gravitational Positivity for Phenomenologists: Dark Gauge Boson in the Swampland
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Lectures in Quantum Gravity
• EFT & Species Scale: Friends or foes?
• Conservative Dynamics of Relativistic Binaries Beyond Einstein Gravity
• Five-point Superluminality Bounds
• Positively Identifying HEFT or SMEFT
• A Celestial Route to AdS Bulk Locality
• Amplitudes and partial wave unitarity bounds
• Positivity bounds in scalar-QED EFT at one-loop level
• Strings from Almost Nothing
• IR side of bounds on Theories with Spontaneously Broken Lorentz Symmetry
• Spectral Constraints on Theories of Colored Particles and Gravity
• Positivity and partial wave unitarity bounds on ALP theories via amplitude methods
• Unitarity, Causality, and Solar System Bounds May Significantly Limit the Use of Gravitational Waves to Test General Relativity
• Saturating unitarity bounds at U-duality symmetric points
• Quasinormal modes and their excitation beyond general relativity. II: isospectrality loss in gravitational waveforms
• Entire Four-Graviton EFT from the Duality Between Color and Kinematics
• The Rise of Linear Trajectories
• Completeness from Gravitational Scattering