[Paper Review] Cosmological signatures of ultralight dark matter with an axionlike potential

Francisco X. Linares Cedeño, Alma X. González‐Morales+1 more|arXiv (Cornell University)|Mar 29, 2017

Dark Matter and Cosmic PhenomenaPhysics and Astronomy98 references55 citations

TL;DR

This paper investigates ultralight axion dark matter with a realistic trigonometric potential using the CLASS Boltzmann code to simulate cosmological evolution. It finds that nonlinearities in the potential delay axion field oscillations and induce a tachyonic instability that imprints a bump in the small-scale power spectrum, offering testable signatures for Ly-α forest observations and implications for axion star stability.

ABSTRACT

Nonlinearities in a realistic axion field potential may play an important role in the cosmological dynamics. In this paper we use the Boltzmann code CLASS to solve the background and linear perturbations evolution of an axion field and contrast our results with those of CDM and the free axion case. We conclude that there is a slight delay in the onset of the axion field oscillations when nonlinearities in the axion potential are taken into account. Besides, we identify a tachyonic instability of linear modes resulting in the presence of a bump in the power spectrum at small scales. Some comments are in turn about the true source of the tachyonic instability, how the parameters of the axionlike potential can be constrained by Ly-$\alpha$ observations, and the consequences in the stability of self-gravitating objects made of axions.

Motivation & Objective

• To study the cosmological evolution of ultralight axion dark matter with a realistic trigonometric potential, rather than the simplified quadratic potential.
• To investigate how nonlinearities in the axion potential affect background dynamics and linear perturbations compared to free axion and CDM models.
• To identify observable signatures—particularly in the small-scale power spectrum—arising from tachyonic instabilities due to the non-quadratic potential.
• To assess constraints on axion parameters using Ly-α forest observations and implications for the stability of self-gravitating axion objects.
• To provide accurate numerical solutions via an amended version of the CLASS code, incorporating full dynamical system evolution of scalar field and perturbations.

Proposed method

• Transformed the background and linear perturbation equations into a dynamical system using polar coordinates and new variables (θ, y₁, α, ϑ) to describe scalar field evolution and perturbations.
• Used the Boltzmann code CLASS with modifications to numerically solve the dynamical system for axion field evolution and perturbations across cosmic time.
• Implemented initial conditions based on constraints from field oscillation onset and axion density parameter, using a shooting procedure to match Ωφ0 at z=0.
• Solved the linearized Klein-Gordon equation for Fourier modes of the field perturbation ϕ(k,t), incorporating metric perturbations via ¯h.
• Tracked the evolution of density contrast variables δ₀ and δ₁ to analyze structure formation and instability growth.
• Compared results across different values of the decay constant parameter λ = 3/(κ²f²), spanning realistic to extreme regimes.

Experimental results

Research questions

• RQ1 How do nonlinearities in the axion potential affect the onset and evolution of field oscillations in the cosmological context?
• RQ2 What observable signatures arise in the matter power spectrum due to tachyonic instabilities induced by the trigonometric potential?
• RQ3 To what extent can Ly-α forest observations constrain the parameters of the axionlike potential?
• RQ4 How does the presence of a non-quadratic potential affect the stability of self-gravitating axion objects?
• RQ5 How do the cosmological dynamics of axion dark matter with a trigonometric potential differ from those of free axions and CDM?

Key findings

• Nonlinearities in the axion potential delay the onset of field oscillations compared to the free axion case, with the delay increasing for larger values of the decay parameter λ.
• A tachyonic instability develops in linear perturbations, leading to a characteristic bump in the small-scale matter power spectrum.
• The amplitude and scale of the power spectrum bump depend on the axion potential parameters, particularly λ and the axion mass mφ.
• For a fiducial model with mφ = 10⁻²² eV, the bump appears at k ≈ 10⁻² Mpc⁻¹, with the instability growing rapidly in the early matter era.
• The instability is rooted in the curvature of the potential near the minimum, where the effective mass becomes negative for certain modes.
• Constraints from Ly-α forest observations can potentially rule out or refine the allowed parameter space for f and mφ, especially for λ > 10⁴.