Impact of EDGES 21-cm global signal on the primordial power spectrum

We investigate the impact of the recent observation of the 21-cm global signal by EDGES on the primordial power spectrum, particularly focusing on the running parameters ${\alpha }_s$ and ${\beta }_s$ which characterize the detailed scale dependence of the primordial spectrum. When the primordial power spectrum is enhanced or suppressed on small scales, the structure formation proceeds faster or slower and changes the abundance of small size halos, which affects the sources of Lyman $\alpha$ radiation at high redshifts to alter the position of the absorption line. A recent observation of EDGES detected the 21-cm absorption line at $z=17.2$, and this result also indicates that the brightness temperature is consistent with zero for $z\lesssim 14$ and $z\gtrsim 22$, which can exclude a scenario giving the absorption line at such redshifts. We argue that the bound on the running parameters can be obtained by requiring that the absorption line should not exceed observational bounds at such redshift ranges and find that the parameter space of ${\alpha }_s$ and ${\beta }_s$ allowed by Planck may be disfavored for some values of astrophysical parameters.

Figure 1

[Left panel]: Evolution of $T_k$ (solid), $T_s$ (dashed) and $T_{\mathrm{CMB}}$ (dotted). [Right panel]: Evolution of the brightness temperature $T_b$. Cases with $(n_s,{\alpha }_s,{\beta }_s)=(0.9586,0,0)$ (red), (0.9586, 0.009, 0.025) (blue) and $(0.9586,-0.009,-0.025)$ (green) are shown. Light blue hatched regions correspond to the ones inconsistent with the EDGES result. Black hatched one indicates that there are no data in the redshift range.

Figure 2

Allowed region from the EDGES result and the peak redshift of the absorption trough $z_{\mathrm{peak}}$ are shown with a color panel for the cases with $T_{\mathrm{vir}}=5\times {10}^3\mathrm{K}$ (left), $10^4\mathrm{K}$ (middle) and $10^5\mathrm{K}$ (right). Other cosmological and astrophysical parameters are fixed as described in the text. Here $n_s$ is fixed to be $n_s=0.9530$, 0.9586 and 0.9642 which correspond to the values of $1\sigma$ lower, central and $1\sigma$ upper bound from Planck and depicted as dotted, solid and dashed lines, respectively. Red point shows Planck best fit value with 1 sigma error bars. When the peak redshift of the absorption line is in the range of $z>27$ or $T_b>-100\mathrm{mK}$ at $z=27$, no constraint can be obtained from EDGES, which is indicated by black hatched. It should be noted that the constraint depends on the values of astrophysical parameters, which will be discussed in Sec. 4.

Figure 3

Evolution of the brightness temperature for various sets of astrophysical parameters. We show the impact of minimum virial temperature, $T_{\mathrm{vir}}$ (top), fraction of baryon converted to starts, $f_{*}$ (middle) and x-ray heating efficiency, ${\zeta }_{\mathrm{X}}$ (bottom). Here, we assume $n_s=0.9586$, ${\alpha }_s=0.009$, ${\beta }_s=0.025$ for the spectral index and its runnings. Light blue hatched regions correspond to the ones inconsistent with the EDGES result. Black hatched one indicates that there are no data in the redshift range.

Figure 4

Allowed region from the EDGES result and the peak redshift of the absorption trough $z_{\mathrm{peak}}$ are shown with a color panel in the ${\alpha }_s–T_{\mathrm{vir}}$ (left) and ${\beta }_s\text{−}{T}_{\mathrm{vir}}$ (right) planes. For the left and right panels, we fix the other running parameter as ${\beta }_s=0.025$ (left) and ${\alpha }_s=0.009$ (right). Other cosmological and astrophysical parameters are fixed as in Fig. 2. In the right panel, although the allowed region is disconnected at around $({\beta }_s,T_{\mathrm{vir}})\sim (0.03,1.1\times {10}^5[\mathrm{K}])$, this is due to sparse grid sampling in the analysis. Since ${\beta }_s$ and $T_{\mathrm{vir}}$ are degenerate, the allowed regions should be connected if we adopt denser sampling.