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

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Cited by in corpus (29)

• Extended Cuscuton: Formulation
• Linear stability analysis of hairy black holes in quadratic degenerate higher-order scalar-tensor theories: Odd-parity perturbations
• General Relativity solutions in modified gravity
• First-order thermodynamics of Horndeski gravity
• Numerical relativity for Horndeski gravity
• Caustic free completion of pressureless perfect fluid and k-essence
• Cuscuton gravity as a classically stable limiting curvature theory
• Recovering P(X) from a canonical complex field
• Extended Cuscuton as Dark Energy
• Theory of Cosmological Perturbations with Cuscuton
• Wave propagation and shock formation in the most general scalar-tensor theories
• Cuscuton Inflation
• Field Theories and Fluids for an Interacting Dark Sector
• Peculiar thermal states in the first-order thermodynamics of gravity
• A new scalar-tensor realization of Hořava-Lifshitz gravity
• Cuscuta-Galileon cosmology: Dynamics, gravitational "constant"s and the Hubble Constant
• Generalized McVittie geometry in Horndeski gravity with matter
• Multi-field Cuscuton Cosmology
• Emergence of ghosts in Horndeski theory
• Cuscuton Bounce Beyond the Linear Regime: Bispectrum and Strong Coupling Constraints
• Caustic Formation upon Shift Symmetry Breaking
• Shift-symmetric $SO(N)$ multi-Galileon
• How Much NEC Breaking Can the Universe Endure?
• A new instability in clustering dark energy?
• Cosmological Dynamics and Double Screening of DBI Galileon Gravity
• K-nonizing
• Cuscuton-like contribution to dark energy evolution
• Caustic formation in DBI models: Wave propagation on planar domain walls
• Ghost condensation and Ostrogradskian instability on low derivative backgrounds