This is a tour de force paper in which authors cobble together a secondorder perturbation code using Mathematica (publicly available here: http://icg.port.ac.uk/~pitrouc/cmbquick.htm). This allows them to calculate, for the first time, what is the CMB bispectrum induced by 2nd order perturbation theory. I have read the paper only cursorily and there are a few interesting things to note:
a) The main result is that the effective fnl, measured by future expts will be ~5. I think people have arrived to this number before, but this is the first time it has been shown explicitly.
b) 2nd perturbation theory induces spectral distortions and so results depend on what you define to be your temperature. They use something they call "bolometric temperature", defined as "temperature of the black body which carries the same energy density as the observed distribution". But it is a subtle issue. It would be interesting if one would measure deviations from black body as a function of position and then do the powerspectrum of that!
c) They use a "flat sky" approximation and claim to be a good approx for l>10... I am somewhat confused about that.
d) There is no discussion of the second order corrections to the power spectrum, at least not from my quick reading of the paper. They do make seem to make rather rough approximations when calculating power spectrum, like flat sky and thin shell, but they never show a plot of C_\ell s. The point is that corrections are probably of the order of 10^{5}, but it'd be still interesting to show explicitly that they're negligible.
[1003.0481] The cosmic microwave background bispectrum from the nonlinear evolution of the cosmological perturbations
Authors:  Cyril Pitrou, JeanPhilippe Uzan, Francis Bernardeau 
Abstract:  This article presents the first computation of the complete bispectrum of the cosmic microwave background temperature anisotropies arising from the evolution of all cosmic fluids up to second order, including neutrinos. Gravitational couplings, electron density fluctuations and the second order Boltzmann equation are fully taken into account. Comparison to limiting cases that appeared previously in the literature are provided. These are regimes for which analytical insights can be given. The final results are expressed in terms of equivalent fNL for different configurations. It is found that for moments up to lmax=2000, the signal generated by nonlinear effects is equivalent to fNL~5 for both localtype and equilateraltype primordial nonGaussianity. 
[PDF] [PS] [BibTex] [Bookmark] 

 Posts: 183
 Joined: September 24 2004
 Affiliation: Brookhaven National Laboratory
 Contact:

 Posts: 1407
 Joined: September 23 2004
 Affiliation: University of Sussex
 Contact:
Re: [1003.0481] The cosmic microwave background bispectrum
It might certainly be interesting to see changes to the power spectrum from around LSS, but in general calculating C_l requires at least 3rd order perturbation theory since 2nd order squared is the same order as 3rd order times first order: in fact the lensing contributions from 2x2 terms are large and mostly cancel with 3x1 terms, so a C_l ignoring 3rd order terms should differ significantly from the lineartheory result.
I recall there was some controversy about the effect of perturbed recombination, e.g. 0903.0871 and 0812.3658, which this paper appears not to comment on on the grounds that the relevant terms are not gauge invariant. However I would have thought with a suitably clear definition of which terms one is calculating it should be possible to make a meaningful comparison.
I recall there was some controversy about the effect of perturbed recombination, e.g. 0903.0871 and 0812.3658, which this paper appears not to comment on on the grounds that the relevant terms are not gauge invariant. However I would have thought with a suitably clear definition of which terms one is calculating it should be possible to make a meaningful comparison.