Absorption in the 21 cm Hydrogen Line at $z>10$ as a Sensitive Tool for the Construction of a Cosmological Model on Small Scales

TL;DR

This study investigates how a narrow Gaussian bump in the density-perturbation spectrum on small scales affects the global 21 cm absorption signal at $z>10$. Using N-body simulations to model halo formation and star-formation history, the authors show that the bump enhances early structure formation, advancing the Ly$\alpha$ background and the WF coupling that sets the spin temperature. They find the absorption trough boundary shifts to higher redshift in the presence of the bump (e.g., $z\sim24$ minimum for certain parameters), offering a potential method to reconstruct the small-scale power spectrum $P(k)$ for $k>1\,\mathrm{Mpc}^{-1}$ from future 21 cm observations. Due to astrophysical uncertainties (e.g., $f_*$, $f_{esc}$) and mixed observational results (EDGES vs SARAS), the work remains qualitative but outlines a promising avenue for constraining early-universe perturbations with meter-wave radio data from experiments like EDGES, SARAS, and SKA.

Abstract

The cosmic microwave background absorption intensity in the 21 cm line of neutral hydrogen in the presence of additional power in the form of a "bump" in the spectrum of cosmological density perturbations is calculated. The main absorption-amplifying effect is the earlier birth of the first stars forming an ultraviolet radiation background. This radiation reduces the spin temperature of neutral hydrogen and, thus, amplifies the absorption in the 21 cm line. A comparison of various cosmological models (with and without a bump in the density perturbation spectrum) shows that it is possible to determine the probable position of the bump in the perturbation spectrum and, thus, to reconstruct the spectrum of cosmological perturbations on scales $k>1$~Mpc${}^{-1}$ from the position of the absorption frequency profile.

Figures (3)

• Figure 1: Fraction of matter in the Universe in virialized dark matter halos versus redshift $z$. The red color indicates the curves constructed from the results of our numerical simulations; the criterion for the selection of halos was their virial temperature above $10^4$ K. The solid curve corresponds to the density perturbation spectrum with a bump; the dashed curve corresponds to the spectrum of the standard $\Lambda$CDM model. The blue color indicates the curves constructed from the Press–Schechter formalism for the minimum-mass boundary $M_b=10^8M_\odot$. The parameters of the bump are $A=20$, $k_0=4.69$ Mpc$^{-1}$ and $\sigma_0=0.1$ (the $gauss\_1$ model).
• Figure 2: The temperature shift due to the absorption in neutral hydrogen. Top: in the presence of a bump with $A=20$, $k_0=4.69$ Mpc$^{-1}$ and $\sigma_0=0.1$ (the $gauss\_1$ model) (solid curves) and without a bump (the standard $\Lambda$CDM model) (dashed curves). The parameter $f_{\rm esc}=0.025$, 0.05, and 0.1 (the blue, red, and green curves, respectively). In all three cases $f_*=0.1$. Bottom: the same, but for $f_{\rm esc} = 0.05$ and three cases: $f_*=0.025$, 0.05, and 0.1 (the green, blue, and red curves, respectively).
• Figure 3: Comparison of the EDGES data (the brown dashed curve, Bowman et al. 2018) and our simulations with $f_{\rm esc}=0.05$ and $f_*=0.025$, 0.05 and 0.1.