Formation of caustics in k-essence and Horndeski theory

Abstract

We study propagation of waves and appearance of caustics in k-essence and galileon theories. First we show that previously known solutions for travelling waves in k-essence and galileon models correspond to very specific fine-tuned initial conditions. On the contrary, as we demonstrate by the method of characteristics, generic initial conditions leads to a wave in k-essence which ends up with formation of caustics. Finally, we find that any wave solution in pure k-essence is also a solution for a galileon theory with the same k-essence term. Thus in the Horndeski theory with a k-essence term formation of caustics is generic. We discuss physical consequences of the caustics formation and possible ways to cure the problem.

17 pages, 3 figures, v3: References added, appendix added with a tentative approach to resolve the caustic problem; v4: typos corrected, matches published version

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• UV completions, fixing the equations and nonlinearities in $k$-essence
• Gravitational Collapse in Cubic Horndeski Theories
• Spacetime and dark matter from spontaneous breaking of Lorentz symmetry
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• Plebanski-Demianski solutions in Quadratic gravity with conformally coupled scalar fields
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• Field Theories and Fluids for an Interacting Dark Sector
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• K-essence in Horndeski models
• Emergence of ghosts in Horndeski theory
• A new nonlinear instability for scalar fields
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• Non-Affine Extensions of the Raychaudhuri Equation in the K-essence Framework
• Caustic formation in DBI models: Wave propagation on planar domain walls
• Positivity vs. Lorentz-violation: an explicit example
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