# Formation, Gravitational Clustering and Interactions of Non-relativistic Solitons in an Expanding Universe

## TL;DR

This paper explores how non-relativistic scalar field solitons form, cluster, and interact under gravity in an expanding universe, revealing complex dynamics like mergers and binary formation through simulations and analytic estimates.

## Contribution

It provides new insights into the formation, stability, and gravitational clustering of solitons in an expanding universe, combining numerical and analytical methods.

## Key findings

- Rapid soliton formation driven by self-interactions
- Gravitational clustering leads to mergers and binary formation
- Analytic estimates of instability scales and soliton profiles

## Abstract

We investigate the formation, gravitational clustering and interactions of solitons in a self-interacting, non-relativistic scalar field in an expanding universe. Rapid formation of large number of solitons is driven by attractive self-interactions of the field, whereas the slower clustering of solitons is driven by gravitational forces. Driven closer together by gravity, we see a rich plethora of dynamics in the soliton "gas" including mergers, scatterings and formation of soliton binaries. The numerical simulations are complemented by analytic calculations and estimates of (i) the relevant instability length and time scales, (ii) individual soliton profiles and their stability, (iii) number density of produced solitons, and (iv) the two point correlation function of soliton positions as evidence for gravitational clustering.