CMBR anisotropies, FAQ, & universal rotation (kind of)

[Lino]

There have been many posting (questions and answers) on universal rotation and there is a fine posting with references on the FAQ. Thanks to everyone for these. I don't pretend to understand the detail (especially of the maths), but I do understand most of the principles. However, there is one element that I am having difficults with and would appreciate any pointers / references that might help.

The articles / references on the use of CMDR anisotropies to limit (potential) rotation, contain a lot of maths, and (I think) focus on the calculations of various aspects (rather than the type / meaning of the anisotropies). Can you recommend any references / articles that discuss the anisotropies, rather than focus on specific calculations?

On a slightly different note, from the articles / papers that I have read, (I think that) there is a general assumption that we (the observer) are positioned on, or close to, the axis of rotation / origin, in comparison to the distance to the edge / source of the CMBR. This strikes me as a very dangerious assumption (it just doesn't seem to be consistent with the homogeneous principle). Am I missing something here?

Thanks inanticipation,

Noel.

 

[bcrowell]

On a slightly different note, from the articles / papers that I have read, (I think that) there is a general assumption that we (the observer) are positioned on, or close to, the axis of rotation / origin, in comparison to the distance to the edge / source of the CMBR. This strikes me as a very dangerious assumption (it just doesn't seem to be consistent with the homogeneous principle). Am I missing something here?

General relativity allows rotation without a center of rotation. In these models, there is no center of rotation. So not only is there no assumption that we're at the center, there isn't even any center.

 

[Lino]

Ben,

Thanks for responding and this is what I thought aswell. I am obviously missing / mis interputing something, and maybe you can enlighten me! The below quote is from a paper by Shi Chun / Su / CHu entitled Is the Universe Rotating - 2009 (text from below equation B6 in appendix II).

[... For simplicity, we assume that we are located on the rotating axis. Therefore, ηλ = λ and rλ = −λ sin φ due to the cylindrical symmetry. Although the general case that we may be off the rotating axis is more realistic, the constraint here can be regarded as a good approximation provided that our distance to the rotating axis is small compared to that of the last scattering surface. ...]

I don't know how else to read this, but I thought that the / your answer might help me understand the 'shape' of the rotation.


Regards,


Noel.

 

[bcrowell]

I see. I obviously didn't read the paper carefully enough. Thanks for pointing this out!

The two papers that I'm aware of that try to calculate observational constraints on the rotation are these:
Barrow, Juszkiewicz, and Sonoda, "Universal rotation: how large can it be?," Mon. Not. R. Astr. Soc. 213 (1985) 917, http://adsabs.harvard.edu/full/1985MNRAS.213..917B
Su and Chu, "Is the universe rotating?," 2009, http://arxiv.org/abs/0902.4575

Barrow's model is homogeneous, so there is no position for the axis of rotation, only a direction for the axis of rotation. Su's can be either inhomogeneous or, as a special case, homogeneous (p. 4).

Re this point...

On a slightly different note, from the articles / papers that I have read, (I think that) there is a general assumption that we (the observer) are positioned on, or close to, the axis of rotation / origin, in comparison to the distance to the edge / source of the CMBR.

...my original reply was wrong. However, I also don't think you've interpreted it correctly. There can be both homogeneous models, like Barrow's or the homogeneous special case of Su's, and inhomogeneous models, like Su's general case, so there is no general assumption throughout the literature that there is inhomogeneity. When Su and Chu consider the general inhomogeneous case, they explicitly consider effects that can arise if we're off axis (see p. 8). The part of Appendix II that you quoted is talking about an assumption made purely for the sake of computational convenience, and immediately afterward they discuss how to generalize it to the case where we're not on axis.

This strikes me as a very dangerious assumption (it just doesn't seem to be consistent with the homogeneous principle).

Homogeneity is broken by the general case of Su and Chu's model. It's broken regardless of whether the observer is on axis or not. Homogeneity is only an approximation. If it were a perfect approximation, there would be zero CMB anisotropy.

 

[Lino]

Thanks again Ben. The ' I also don't think you've interpreted it correctly' is exactly what I expected ... although I can't pretend to understand the details ... yet!

I'll keep trying to working through that, but if you do come across any discussions (rather than calculations)on the CMBR anisotropies, I would much appreciate it if you could let me know.


Regards,


Noel.