Dark Matter from an ultra-light pseudo-Goldsone-boson

TL;DR

This work investigates whether a partially contributing ultra-light pseudo-Goldstone-boson (PGB) with intermediate mass can act as dark matter and leave detectable imprints on cosmic structure and the CMB. It develops an analytic free-streaming framework that parallels the neutrino case, deriving the effective sound speed and Jeans scales that govern suppression in the matter power spectrum and CMB anisotropies. By fitting to SDSS, Lyman-\alpha, WMAP, and $\sigma_8$ data with a modified Boltzmann code, the paper finds an observable mass window $m_I \in [10^{-31},10^{-23}]$ eV where the PGB fraction $f_I$ is constrained to be $\lesssim 0.1$, while highlighting the potential for future surveys to improve sensitivity and reveal degeneracies with neutrinos. The results provide a concrete framework to constrain or detect DM components from ultra-light scalars and connect cosmological growth to underlying particle physics in PGB scenarios.

Abstract

Dark Matter (DM) and Dark Energy (DE) can be both described in terms of ultra-light Pseudo-Goldstone-Bosons (PGB) with masses m_{DM} ~ 10^{-23}eV and m_{DE} <= 10^{-33}eV respectively. Following Barbieri et al, we entertain the possibility that a PGB exists with mass m_I intermediate between these two limits, giving a partial contribution to DM. We evaluate the related effects on the power spectrum of the matter density perturbations and on the cosmic microwave background and we derive the bounds on the density fraction, f_I, of this intermediate field from current data, with room for a better sensitivity on f_I in the near future. We also give a simple and unified analytic description of the free streaming effects both for an ultra-light scalar and for a massive neutrino.

Figures (4)

• Figure 1: Comparison of the ratios $r^{\nu }(k)$ of numerical matter power spectra (red full curves) with the analytic approximation discussed in the text (green dashed curves). Upper panel: 3 massive neutrinos with mass 1/3 eV each, and $\Omega _{\Lambda }=0,0.3,0.7$, (ordered top to bottom according to the left plateau). Lower panel: same, with masses 1/9 eV.
• Figure 2: Comparison of the ratios $r^{\phi }(k)$ of numerical matter power spectra (red full curves) with the analytic approximation discussed in the text (green dashed curves). Upper panel: PGB with fraction $f_{I}=0.05$ and masses $m_{30}=0.1,1,10$ (ordered top to bottom according to the left plateau), and $\Omega _{\Lambda }=0$. Lower panel: same, with $\Omega _{\Lambda }=0.7$.
• Figure 3: Likelihood functions at 68,95 and 99.7% c.l. (dark to light gray) for the parameters $m_{30}\equiv m_{I}/10^{-30}eV$ and $f_{I}$ obtained marginalizing over $\tau ,\Omega _{m}h^{2},n_{s}$ and $h$, and fixing $\Omega _{b}h^{2} = 0.023$. The date employed are discussed in the text. The discreteness of the grid causes some wiggling in the function.
• Figure 4: Combined likelihood function at 68,95 and 99.7% c.l. (dark to light gray) for the parameters $m_{30}\equiv m_{I}/10^{-30}eV$ and $f_{I}$ obtained marginalizing over $\tau ,\Omega _{m}h^{2},n_{s}$ and $h$, and fixing $\Omega _{b}h^{2}= 0.023$.