Caustics for Spherical Waves

Abstract

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.

25 pages. v2: References added and included discussion on extreme-relativistic case. v3: Matches published version in PRD, appendix expanded

References in corpus (20)

• Quantum Gravity at a Lifshitz Point
• Resummation of Massive Gravity
• Covariant Galileon
• Membranes at Quantum Criticality
• Healthy theories beyond Horndeski
• Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors
• Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
• DBI and the Galileon reunited
• Cuscuton: A Causal Field Theory with an Infinite Speed of Sound
• On causality and superluminal behavior in classical field theories. Applications to k-essence theories and MOND-like theories of gravity
• Third order equations of motion and the Ostrogradsky instability
• Cuscuton Cosmology: Dark Energy meets Modified Gravity
• Cuscuton and low energy limit of Horava-Lifshitz gravity
• Caustic avoidance in Horava-Lifshitz gravity
• Superluminality and UV Completion
• Riding on irrelevant operators
• Causality and Micro-Causality in Curved Spacetime
• TeVeS gets caught on caustics
• A geometrical approach to degenerate scalar-tensor theories
• Formation of caustics in Dirac-Born-Infeld type scalar field systems

Cited by in corpus (1)

• Wave propagation and shock formation in the most general scalar-tensor theories