Cosmological signatures of ultralight dark matter with an axionlike potential

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.

Figure 1

The evolution of the axion and CDM energy densities up to the present time. Although the amplitude of the axion density is initially much smaller than that of CDM, it can be noted that from $\log (a)\sim -6$ the axion density evolves exactly like CDM. The inset shows that for larger values of $\lambda$, the axion oscillations start later as compared to those of the free case, and that the transition to CDM happens more abruptly.

Figure 2

MPS at the present time for an axion field with the same values of $\lambda$ as in Fig. 1. The characteristic cutoff of the axion MPS is clearly seen, together with some differences at small scales induced by the physical parameter, $\lambda$. MPS data from BOSS DR11 (brown dots) [59] and from $\mathrm{Ly}\alpha$ forest (purple dots) [60] are shown for reference. (Inset) Zoom in of the MPS for large values of $k$. It is concluded that the presence of the parameter $\lambda$ produces a bump when $\lambda \gg 1$. The blue dashed vertical line shows the difference between the extreme case $\lambda =1.3\times {10}^5$ with respect to CDM at 50%. The red line represents the free case with a mass $m_{\varphi }^{*}=3.635\times {10}^{-22}\mathrm{eV}$, whose MPS differs at 50% from CDM just as the extreme axion case, at a wave number, $k_{50\%}=11.218h/\mathrm{Mpc}$. See the text for more details.

Figure 3

Evolution of the amplitude of the (complex) frequency $\omega =k|k_{\mathrm{eff}}|/k_J^2$ that is intrinsic to the system of linear perturbations (8), for different wave numbers $k$ but the same $\lambda ={10}^5$. We can see that the frequency becomes purely imaginary, ${\omega }^2<0$, for all the modes before the onset of the axion oscillations (marked by the black dashed vertical line), but it is just for a handful of them that a tachyonic instability (${\omega }^2\ll -1$) lasts for long enough: ${10}^{-2}<k/{\mathrm{Mpc}}^{-1}<30$. For reference, the end of the instability for each mode in the plot is indicated by the vertical dashed lines of the same color. As a result, large scales must evolve like CDM, and in the MPS of Fig. 2 there must be a bump for the aforementioned range of wave numbers together with a displacement of the cutoff towards smaller scales when compared to the free case.

Figure 4

1D MPS for the axion field compared to the $\mathrm{\Lambda }\mathrm{CDM}$ one. We show the cases $m_{\varphi }={10}^{-22}\mathrm{eV}$ for $\lambda =0,1.3\times {10}^5$ (blue lines), and $m_{\varphi }=4\times {10}^{-21}\mathrm{eV}$ for $\lambda =0,1.3\times {10}^5,3\times {10}^5$ (green lines). For reference we have included horizontal lines indicating the rough precision of current data from BOSS [61], HIRES/MIKES [62], and XQ100 [63] to show that this can be used to constraint both parameters $m_{\varphi }$ and $\lambda$.