21-cm Radiation: A New Probe of Variation in the Fine-Structure Constant

We investigate the effect of variation in the value of the fine-structure constant ($\alpha$) at high redshifts (recombination $>z>30$) on the absorption of the cosmic microwave background (CMB) at 21 cm hyperfine transition of the neutral atomic hydrogen. We find that the 21 cm signal is very sensitive to the variations in $\alpha$ and it is so far the only probe of the fine-structure constant in this redshift range. A change in the value of $\alpha$ by 1% changes the mean brightness temperature decrement of the CMB due to 21 cm absorption by $>5\%$ over the redshift range $z<50$. There is an effect of similar magnitude on the amplitude of the fluctuations in the brightness temperature. The redshift of maximum absorption also changes by $\sim 5\%$.

Figure 1

The fractional change in ${\kappa }_{10}^{HH}$ with respect to the unperturbed value.

Figure 2

Upper panel shows $T_b$ with different values of $\alpha$. Bottom panel shows the fractional change $[T_b(\alpha )-T_b]/T_b$.

Figure 3

Upper panel shows the angular power spectrum $\sqrt{l(l+1)C_l/2\pi }$ at several redshifts. Bottom panel shows $[\sqrt{C_l(\delta \alpha =-2\%)}-\sqrt{C_l}]/\sqrt{C_l}$ for the same redshifts.