Evolution of linear wave dark matter perturbations in the radiation-dominated era

Abstract

Linear perturbations of the wave dark matter, or ψ dark matter (ψDM), of particle mass ∼ 10 −22 eV in the radiation-dominant era are analyzed, and the matter power spectrum at the photonmatter equality is obtained. We identify four phases of evolution for ψDM perturbations, where the dynamics can be vastly different from the counterparts of cold dark matter (CDM). While in late stages after mass oscillation long-wave ψDM perturbations are almost identical to CDM perturbations, some subtle differences remain, let alone intermediate-to-short waves that bear no resemblance with those of CDM throughout the whole evolutionary history. The dissimilarity is due to quantum mechanical effects which lead to severe mode suppression. We also discuss the axion model with a cosine field potential. The power spectrum of axion models are generally almost identical to those of ψDM, but in the extreme case when the initial axion angle is near the field potential top, this axion model predict a power excess over a range of wave number and a higher spectral cutoff than ψDM as if ψDM had a higher particle mass.

Scalar field dark matter with a cosh potential, revisited

“…This type of models are known as axion-like particles (ALP) [28], and their anharmonic nature produces observable signatures. The most noticeable effect appears for the evolution of linear density perturbations: there is an overgrowth of the density contrast with respect to the CDM case, which is characterized as a bump in the mass power spectrum (MPS) [29][30][31].…”

Evolution of perturbation and power spectrum in a two-component ultralight axionic universe

“…To eliminate the rapid mass oscillation in the Klein-Gordon equation, Eq. (2), after the onset of mass oscillations, the Schödinger equation is adopted [25,26]. For the background angle, it can be approximated to be as Θ i ≈ Θ 0,i a −3/2 cos(ω Θ,i t) with Θ 0,i being a constant and…”

“…The evolution of the neutrino perturbation behaves the same as the photon perturbation at the first half cycle of oscillation and damps abruptly after crossing the null [28]. In our computation, we set the neutrino perturbation to be zero after crossing the null [25].…”

“…Ultralight axion perturbations in the radiation epoch have been analyzed in [25,26], while those in the matter era can be found in [27]. Our computation follows much on these papers, especially [25] and [26], which is engaged in the evolution for complete perturbed equations (full evolution). However, the full-evolution approach is formidably time-consuming to compute due to the stiffness of the differential equations.…”

Testing extreme-axion wave-like dark matter using the BOSS Lyman-alpha forest data

“…One of the common features of wave dark matter power spectra is the suppression of small-scale structures below the Compton length prior to the matter-radiation equality (Hu et al 2000;Zhang & Chiueh 2017a) and the existence of a Jeans length due to the uncertainty principle in the matter dominant era (Woo & Chiueh 2009). The EAψDM power spectra, however, have one more degree of freedom other than the boson mass m b , the initial misaligned field angle θ, which gives rise to a broad spectral bump immediately longward of the spectral suppression (see Fig.…”