Ultra-Light Scalar Fields and the Growth of Structure in the Universe

TL;DR

This study analyzes ultra-light scalar fields with masses in $10^{-33}\,\text{eV}$ to $10^{-22}\,\text{eV}$ and their influence on cosmic structure growth. Using a perturbation framework in synchronous gauge, complemented by analytic (including WKB) and numerical methods, it tracks the background evolution and the growth of perturbations as these fields transition from dark-energy–like to matter-like behaviour, with a potential shift in $a_{eq}$ if a substantial ALP fraction is present. A key result is the identification of a scale-dependent sound speed $c_s^2=\frac{k^2}{4m^2a^2}$ that produces free-streaming below $k_R=ma$, and a central suppression scale $k_m\propto m^{1/3}$ that yields a step-like feature in the matter power spectrum $P(k)$, parameterized by the ALP fraction $f$ and redshift. These findings imply observable imprints on the matter power spectrum and linked cosmological probes (e.g., ISW, weak lensing, BAO, Lyman-$\alpha$), contributing to the broader string axiverse scenario by allowing constraints on ultra-light axion-like dark matter.

Abstract

Ultra-light scalar fields, with masses of between m=10^{-33} eV and m=10^{-22} eV, can affect the growth of structure in the Universe. We identify the different regimes in the evolution of ultra-light scalar fields, how they affect the expansion rate of the universe and how they affect the growth rate of cosmological perturbations. We find a number of interesting effects, discuss how they might arise in realistic scenarios of the early universe and comment on how they might be observed.

Figures (11)

• Figure 1: $\phi_0$ versus $a$ for $m = 10^3$, various $\Omega_c$, $\Omega_{\Lambda} = 0$
• Figure 2: A fit for $\phi_0$ versus $a$ for $m=10^5$, $\Omega_c = 0.8$, $\Omega_{\Lambda} = 0$. The solid line is the result of numerically integrating the equations of motion, whilst the dotted line is the analytic fit of Eqn. \ref{['eqn:phibessel']}.
• Figure 3: $\log \rho$ versus $\log a$ for $m = 10^3$, $\Omega_c = 0.8$, $\Omega_{\Lambda} = 0$
• Figure 4: $p$ versus $a$ for $m = 10^3$, $\Omega_c = 0.8$, $\Omega_{\Lambda} = 0$. Insert: ALPs $+$ CDM divided by standard CDM alone
• Figure 5: $T^2(k)$ for $m = 10^{-29}\, \mathrm{eV}$, $\Omega_{\Lambda} = 0$