# Fourier-series expansion of the dark-energy equation of state

## TL;DR

This paper introduces a Fourier series-based model for the dark energy equation of state, showing it fits observational data better than standard models and challenges single scalar field theories.

## Contribution

It generalizes previous dark energy models using Fourier series and demonstrates its statistical preference over ΛCDM with observational data.

## Key findings

- Fourier series expansion of w(z) is preferred over ΛCDM at >3σ significance.
- The model slightly outperforms ΛCDM according to Akaike criteria.
- The shape of w(z) challenges single scalar field dark energy models.

## Abstract

The dark energy component of the universe still remains as a mystery, however, several papers based on observational data have shown that its equation of state may have an oscillatory behaviour. In this paper, we provide a general description for the dark-energy equation-of-state $w(z)$ in the form of Fourier series. This description generalises some previous dynamical dark energy models and is in agreement with the $w(z)$ reconstructions. We make use of a modified version of a simple and fast Markov Chain Monte Carlo code to constraint the model parameters. For the analysis we use data from supernovae type-Ia , baryon acoustic oscillations, $H(z)$ measurements and cosmic microwave background. We provide a comparison of the proposed model with $\Lambda$CDM, $w$CDM and the standard Taylor approximation. The Fourier series expansion of $w(z)$ is preferred from $\Lambda$CDM at more than $3\sigma$ significance level based on the improvement in the fit alone. We use the Akaike criteria to perform the model comparison and found that, even though there are extra parameters, there is a slight preference of the Fourier series compared with the $\Lambda$CDM model. The preferred shape of $w(z)$ found here puts in jeopardy the single scalar field models, as they as they cannot reproduce the crossing the phantom divide line $w=-1$.