# Caustic free completion of pressureless perfect fluid and k-essence

## TL;DR

This paper demonstrates a method to avoid caustic singularities in pressureless perfect fluids and k-essence models by using a complex scalar field, promoting collapse time to a complex number to prevent real-time singularities.

## Contribution

It introduces a caustic-free completion for pressureless perfect fluids and k-essence using a complex scalar field, unifying their dynamics and resolving singularities.

## Key findings

- Caustic singularities are avoided via complex scalar field completion.
- Collapse time becomes complex, preventing real-time singularities.
- Method applies to collisionless particles and ultra-light axions.

## 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).