Dark energy driven by an oscillating generalised axion-like quintessence field

TL;DR

The paper addresses dark energy from a generalised axion-like quintessence that can coherently oscillate around a finite potential minimum, which destabilises the usual fluid perturbation description. It develops a field-based linear perturbation framework in the Newtonian gauge that remains well defined across oscillatory and non-oscillatory phases by evolving $(\Psi,\delta\phi)$ together with matter and radiation. The key findings are that non-oscillatory tracking models suppress late-time structure growth relative to $\Lambda$CDM, while oscillatory models quickly approach $w_\phi\approx -1$ and yield growth histories nearly indistinguishable from LCDM, with dark-energy perturbations strongly suppressed. This work provides a robust, unified method to explore the full parameter space of oscillating axion-like quintessence and its observable signatures in large-scale structure.

Abstract

Generalised axion-like scalar fields provide a well-motivated framework for describing the late-time acceleration of the Universe. As the field evolves, it rolls down its potential and, depending on its mass and initial conditions, it may either still be approaching the minimum or already oscillating around it. These two dynamical regimes require distinct treatments of cosmological perturbations. In this work, we perform a detailed analysis of linear cosmological perturbations in the regime where the dark-energy scalar field undergoes coherent oscillations about the minimum of its potential. We show that the standard effective fluid description breaks down in this phase and develop a consistent field-based perturbation framework, which we use to assess the impact of oscillatory dark energy on the growth of cosmic structures.

Figures (5)

• Figure 1: Exact generalised axion-like potential $V(\phi)/V_0=\left[1-\cos(\phi/\eta)\right]^{-n}$ (solid line) and its quadratic approximation around the minimum at $\phi/\eta=\pi$ (dotted line), shown as functions of the dimensionless field variable $\phi/\eta$ for the representative case $n=1$. The potential is displayed in the compactified form $(V/V_0)/(1+V/V_0)$ in order to avoid divergences at the extrema. In this representation, the minimum of the potential corresponds to $(V/V_0)/(1+V/V_0)=1/3$.
• Figure 2: Background evolution of generalised axion-like quintessence. The left panel shows the transition from radiation and matter domination to a scalar-field-dominated accelerated phase, while the right panel shows the associated evolution of the scalar-field equation of state. The comparison highlights the qualitative difference between the non-oscillatory benchmark SF A ($\eta=1$) and the oscillatory benchmark SF B ($\eta=0.1$) at late-time.
• Figure 3: Scalar-field and matter perturbations for generalised axion-like quintessence models. The left panel shows the evolution of the scalar-field perturbations, highlighting their regular behaviour across the oscillatory regime. The right panel shows the corresponding matter density perturbations, illustrating the suppression present in the non-oscillatory case and its absence in the oscillatory case, where the dynamics closely resemble $\Lambda$CDM.
• Figure 4: Cosmological observables in generalised axion-like quintessence models. The left panel shows the matter power spectrum at $z=0$, while the right panel displays the evolution of $f\sigma_8$ at low redshift. Both observables reflect the same qualitative behaviour found at the level of linear perturbations: significant suppression in the non-oscillatory case and near-$\Lambda$CDM behaviour in the oscillatory case.
• Figure 5: Diagnostic of the breakdown of the multi-fluid description in the oscillatory regime and regularity of the metric perturbation. The left panel shows that the fluid diagnostic $\delta_\phi/(1+w_\phi)$ develops turning-point divergences only for the oscillatory benchmark. The right panel shows that this behaviour does not propagate to the metric: the gravitational potential remains well defined and well behaved, and closely follows the corresponding smooth evolution in the non-oscillatory benchmark and in $\Lambda$CDM.