DBI domain walls stay shock-free in the hyperbolic regime across 2D flat space and extended physical setups, with caustics forming only upon loss of hyperbolicity and exhibiting cusp profiles.
Caustic free completion of pressureless perfect fluid and k-essence
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abstract
Both k-essence and the pressureless perfect fluid develop caustic singularities at finite time. We further explore the connection between the two and show that they belong to the same class of models, which admits the caustic free completion by means of the canonical complex scalar field. Specifically, the free massive/self-interacting complex scalar reproduces dynamics of pressureless perfect fluid/shift-symmetric k-essence under certain initial conditions in the limit of large mass/sharp self-interacting potential. We elucidate a mechanism of resolving caustic singularities in the complete picture. The collapse time is promoted to complex number. Hence, the singularity is not developed in real time. The same conclusion holds for a collection of collisionless particles modelled by means of the Schroedinger equation, or ultra-light axions (generically, coherent oscillations of bosons in the Bose--Einstein condensate state).
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Higher-derivative extension of dark matter yields an imperfect fluid that matches pressureless dust on homogeneous backgrounds but generates acceleration and vorticity to avoid caustic singularities in inhomogeneous cosmologies.
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Hard to shock DBI: wave propagation on planar domain walls
DBI domain walls stay shock-free in the hyperbolic regime across 2D flat space and extended physical setups, with caustics forming only upon loss of hyperbolicity and exhibiting cusp profiles.
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Imperfect dark matter with higher derivatives
Higher-derivative extension of dark matter yields an imperfect fluid that matches pressureless dust on homogeneous backgrounds but generates acceleration and vorticity to avoid caustic singularities in inhomogeneous cosmologies.