Cosmological implications of ultra-light axion-like fields

TL;DR

This work analyzes ultra-light axion-like fields with potentials $V_n(\phi)\propto[1-\cos(\phi/f)]^{n}$ as cosmological components that can behave as early dark energy, dark matter, or radiation depending on $n$ and the onset of dynamics. The authors develop a generalized fluid formalism parameterized by the redshift $z_c$ at which the field becomes dynamical and the fractional density $f_{z_c}$, including perturbations for $n=2,3$ via an effective sound speed $c_s^2$, and map these model parameters to the underlying theory parameters $(n,\Theta_i,\mu,\alpha)$. They compute CMB and matter power spectra with CLASS and constrain ULAs using Planck, BAO and JLA data, finding that ULAs are degenerate with dark energy for $1+z_c\lesssim 10$ and that stringent bounds on $f_{z_c}$ apply for $3\times10^4 \gtrsim 1+z_c \gtrsim 10$, with constraints relaxing at higher $z_c$. Perturbations help distinguish ULA effects from other components, but current data do not support ULAs as a robust resolution to the Hubble tension or the EDGES 21 cm anomaly, though a modest easing of the H0 tension is possible in some parameter regions. Overall, the generalized fluid approach provides a state-of-the-art, scalable framework to analyze anharmonic ULAs in cosmology and to confront them with upcoming high-precision data.

Abstract

Cosmological observations are used to test for imprints of an ultra-light axion-like field (ULA), with a range of potentials $V(φ)\propto[1-\cos(φ/f)]^n$ set by the axion-field value $φ$ and decay constant $f$. Scalar field dynamics dictate that the field is initially frozen and then begins to oscillate around its minimum when the Hubble parameter drops below some critical value. For $n\!=\!1$, once dynamical, the axion energy density dilutes as matter; for $n\!=\!2$ it dilutes as radiation and for $n\!=\!3$ it dilutes faster than radiation. Both the homogeneous evolution of the ULA and the dynamics of its linear perturbations are included, using an effective fluid approximation generalized from the usual $n=1$ case. ULA models are parameterized by the redshift $z_c$ when the field becomes dynamical, the fractional energy density $f_{z_c} \equiv Ω_a(z_c)/Ω_{\rm tot}(z_c)$ in the axion field at $z_c$, and the effective sound speed $c_s^2$. Using Planck, BAO and JLA data, constraints on $f_{z_c}$ are obtained. ULAs are degenerate with dark energy for all three potentials if $1+z_c \lesssim 10$. When $3\times10^4 \gtrsim 1+z_c \gtrsim 10 $, $f_{z_c}$ is constrained to be $ \lesssim 0.004 $ for $n=1$ and $f_{z_c} \lesssim 0.02 $ for the other two potentials. The constraints then relax with increasing $z_c$. These results strongly constrain ULAs as a resolution to cosmological tensions, such as discrepant measurements of the Hubble constant, or the EDGES measurement of the global 21 cm signal.

Figures (12)

• Figure 1: The evolution of the background field with $\mu = 10^6$, $\alpha = 0.05$, and $\Theta_i = \pi-0.1$ for the three forms of the axion potential explored in this paper.
• Figure 2: The evolution of a series of scales associated with ULA perturbations. Note that while $k>a \varpi$ the mode has $c_s^2 \simeq 1$.
• Figure 3: Evolution of the density contrast for the three forms of the ULA potential considered in this paper and with $z_c=10^{4}$, $f_{z_c}=0.01$, and $\Theta_i = \pi/2$. The vertical dashed black line shows $a_c$, while the vertical dashed colored lines show Horizon crossing for each mode.
• Figure 4: Residuals of the (lensed) CMB TT power spectrum (first panel), EE power spectrum (second panel), lensing power spectrum (third) and matter power spectrum (fourth panel) computed for several values of the potential exponent $n=(1,2,3)$ and $1+z_c = 10^5$. Residuals are taken with respect to the $\Lambda$CDM model, with parameters given by the best fit of Planck TT,TE,EE+lowP Ade:2015xua. Axion densities are set at their constraints at 95% C.L.. The grey bands show Planck 1$\sigma$ sensitivity.
• Figure 5: Same legend as Fig. \ref{['fig:Cl_residuals_zc10']} for $1+z_c = 10$.