This paper looks at the effect of varying \alpha on the 21cm power spectrum at high redshift. Because the Einstein coefficient varies strongly with \alpha, they claim the 21cm is potentially a very good probe.
What confuses me about the plots is the use of redshift. As usual they use that the CMB temperature goes as 1+z. However what you can observe directly from the 21cm absorption is the frequency of the radiation, and hence observationally one defines a redshift [tex]z_{obs} = \nu_0/\nu_{obs}1[/tex], where \nu_0 is the 21cm frequency today. Since \nu scales as \alpha^4, a 2% change in alpha corresponds to about an 8% change in z_{obs}. So isn't the most obvious observable really T_b as a function of z_{obs} rather than z? (i.e. the comparison plot in Fig 2 should shift the varying\alpha result sideways by ~ 8%).
[astroph/0701752] 21 cm radiation  a new probe of variation in the fine structure
Authors:  Rishi Khatri, Benjamin D. Wandelt 
Abstract:  We investigate the effect of variation in the value of the fine structure constant 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 the fine structure constant and it is so far the only probe of the fine structure constant in this redshift range. A change in the value of the fine structure constant by 1% changes the mean brightness temperature decrement of the CMB due to 21 cm absorption by > 5% over the redshift range z < 45 and z > 120. 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 more than 5%. 
[PDF] [PS] [BibTex] [Bookmark] 

 Posts: 1520
 Joined: September 23 2004
 Affiliation: University of Sussex
 Contact:

 Posts: 12
 Joined: September 24 2004
 Affiliation: IAP, UPMC, Sorbonne Universites, and Illinois
 Contact:
[astroph/0701752] 21 cm radiation  a new probe of variatio
Antony 
Thank you for this suggestion.
Observers will use the current value of the fine structure constant to connect redshift with frequency. So I agree that for observers it may be more useful to have the results plotted in terms of [tex]z_{obs}[/tex] since that shows the effect in terms of what would be observed.
On the other hand, from a theoretical perspective [tex]z_{CMB}[/tex] is the natural quantity to use in the calculations, and the effects of varying \alpha are physically more transparent when we plot as a function of [tex]z_{CMB}[/tex].
Rishi and I are weighing these advantages and disadvantages, but whatever version of the plot ends up in the printed version of the paper, we will provide access to the other version online.
Ben
Thank you for this suggestion.
Observers will use the current value of the fine structure constant to connect redshift with frequency. So I agree that for observers it may be more useful to have the results plotted in terms of [tex]z_{obs}[/tex] since that shows the effect in terms of what would be observed.
On the other hand, from a theoretical perspective [tex]z_{CMB}[/tex] is the natural quantity to use in the calculations, and the effects of varying \alpha are physically more transparent when we plot as a function of [tex]z_{CMB}[/tex].
Rishi and I are weighing these advantages and disadvantages, but whatever version of the plot ends up in the printed version of the paper, we will provide access to the other version online.
Ben