# Collapse threshold for a cosmological Klein Gordon field

## TL;DR

This paper investigates the collapse threshold of primordial fluctuations in a cosmological Klein-Gordon field, predicting the matter power spectrum cutoff, structure formation during reheating, and constraints on early universe dominance.

## Contribution

It introduces a threshold amplitude for collapse in Klein-Gordon fields, linking instability to structure formation, PBH production, and early universe constraints.

## Key findings

- Identifies a collapse threshold that predicts matter power spectrum cutoff.
- Shows abundant structure formation during reheating without necessarily forming black holes.
- Finds PBHs may be overproduced during reheating despite low formation probability at inflation end.

## Abstract

Oscillating scalar fields are useful to model a variety of matter components in the universe. One or more scalar fields participate in the reheating process after inflation, while at much lower energies scalar fields are robust dark matter candidates. Pertaining structure formation in these models, it is well known that inhomogeneities of the Klein-Gordon field are unstable above the characteristic De Broglie wavelength. In this paper we show that such instability implies the existence of a threshold amplitude for the collapse of primordial fluctuations. We use this threshold to correctly predict the cut--off scale of the matter power spectrum in the scalar field dark matter model. Furthermore, for a Klein-Gordon field during reheating we show that this same threshold allows for abundant production of structure (oscillons but not necessarily black holes). Looking at the production of Primordial Black Holes (PBHs) in this scenario we note that the sphericity condition yields a much lower probability of PBH formation at the end of inflation. Remarkably, even after meeting such stringent condition, we find that PBHs may be overproduced during reheating. We finally constrain the epochs at which an oscillating Klein-Gordon field could dominate the early universe.