CMB geodesics

[Syksy Rasanen]

I am thinking about the shape of CMB geodesics, parametrised by the tangent vector [tex]k^\alpha[/tex]. Spatial variations of [tex]k^0[/tex] are of course known to be small, since it gives the redshift. But what about the spatial component [tex]k^i[/tex]? In other words, do we know that the CMB photons in a certain direction have originated in that direction, or can they have been bent a lot?

I guess such geodesic mixing would affect the Gaussianity (and possibly statistical isotropy), so that there are good constraints? This seems like a simple question, I hope someone can point me to a good reference...

[Antony Lewis]

CMB lensing is reviewed in astro-ph/0601594. The basic answer is that because the unlensed CMB is smooth, the complicated structure of the past light cone on very small scales doesn't matter on the (much larger) scales of most interest for the acoustic peaks; the overall size of the deflection (rms ~ 3 arcmin) is determined by large under/overdensities that are nearly linear. From data we know the acoustic-scale CMB lensing effect is within a factor of a few of that expected from linear-theory deflections; detection paper is 0705.3980.

[Tess Jaffe]

Anisotropic geometries can also lead to precisely this. Naturally, the observed near-isotropy constrains these models, as you suggest. But some of the large scale anomalies suprisingly resemble what you would get in a BIanchi type VIIh geometry where the geodesics rotate (astro-ph/0503213). Those particular models appear to be ruled out (astro-ph/0512433), but the general idea is still interesting in light of the as yet unexplained large-scale anomalies.

Each different geometry would have different observational effects, however, so I'm not sure you'll find a reference with constraints in general. But perhaps some of the references in the latter paper above might be useful.

[Syksy Rasanen]

Thanks. Some of the physical arguments in the lensing review are useful, but the quantitative things depend on assuming near-FRW geometry. I am interested in limits in the more general case of clumpy spaces, but assuming the validity of geometric optics.

For example, the smallness of [tex]\Delta T/T[/tex] shows that variations in [tex]k^0[/tex] are small, without knowing anything about the geometry between us and the last scattering surface. So I am thinking of the following: take a Gaussian, statistically isotropic CMB map which represents the initial state. Assume that the geodesics [tex]k^i[/tex] are bent, so the map gets mixed up, but keep [tex]k^0[/tex] fixed. Is it possible to parametrise and put limits on the geodesic deviation just from the statistics and isotropy of the CMB? (Of course, if the mixing is done in a way that is statistically isotropic, then it would not show up as a violation of statistical isotropy.)

I knew the Bianchi papers, they are an interesting example, but indeed only for a specific type of mixing.