Since the Earth isn't exactly in comoving coordinates, I would think redshift surveys have to adjust for this?
I couldn't, upon searching, immediately find which direction our CMB dipole shift was in, but I was wondering also if this direction happens to align with the asserted fine structure constant dipole shift.
This was recently independently measured to higher precision. Any thoughts?
Answer
Of course the Earth isn't at rest in the CMB frame, and of course redshift surveys correct for this. Since COBE, WMAP, Planck (perhaps before?) the dipole direction and amplitude are known to excellent precision. The Hubble factor would be anisotropic if the transformation to the CMB rest frame wasn't made, but this isn't very meaningful.
The CMB dipole is in the direction$^{1}$ (max. amplitude):
$$({\rm RA}, {\rm Dec}) \approx (11^{\rm h}11^{\rm m}, -7^\circ)$$
The paper you link puts the best-fitting direction for maximum variation in $\alpha$ at:
$$({\rm RA}, {\rm Dec}) \approx (17^{\rm h}, -60^\circ)$$
It's pretty clear that these are not anywhere near the same direction on the sky.
$^{1}$ I didn't get as far as looking up a value usable in precision work, but this one is enough to get a good idea. I used a tool for coordinate conversion, and you can also see it's in the right ballpark comparing to the values listed here.
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