# Cosmological consequences of a scalar field with oscillating equation of state. IV. Primordial nucleosynthesis and the deuterium problem

## TL;DR

This paper investigates how a scalar field with an oscillating equation of state affects primordial nucleosynthesis, demonstrating the model's compatibility with observed light element abundances and proposing a solution to the deuterium problem.

## Contribution

It introduces a stepwise scalar field model compatible with BBN constraints and provides a public code for its analysis, offering a new perspective on early Universe evolution.

## Key findings

- The model survives BBN constraints.
- Early dark energy can address the deuterium problem.
- Universe's radiation era may evolve chaotically rather than oscillating.

## Abstract

We study the primordial nucleosynthesis (BBN) in the stepwise scalar field model proposed by Ti\'an [arXiv:1912.13208, Phys. Rev. D 101, 063531 (2020)], which provides a multiaccelerating Universe solution to the cosmological coincidence problem and predicts that the scalar field may be non-negligible even in the early Universe. The observed abundances of the light elements can be used to constrain the energy density of the scalar field during the BBN era. We present a public \texttt{Matlab} code to implement the BBN calculation in the stepwise scalar field model. We show that the model can survive the BBN constraints. In particular, this model incorporates a new solution to the possible deuterium problem: very early dark energy that appears at the end of BBN. In addition, the BBN constraints, along with constraints from the cosmic late-time acceleration, suggest that the Universe in the radiation era evolves in a chaotic accelerating manner, rather than an oscillating scaling manner.