### [1107.5427] Large-scale clustering of galaxies in general re

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**August 01 2011**This is a very impressive paper that appears to definitively solve the question of how GR effects affect the observed power spectrum on largest observable scales - a hot topic over the past few years. Well explained derivations and numerous examples are given to confirm the results - and those agree with (equally impressive) analyses by Baldauf et al 1106.5507, Challinor and Lewis 1105.5292, and Bonvin and Durrer 1105.5280.

The results are also in mild disagreement with the original analysis by Yoo et al 0907.0707. The issue seems to be that the linear bias relation is to be assumed in the synchronous gauge, but this then does not correspond to linear bias in the constant-redshift gauge, so appropriate care must be taken.

The bottom line is that the GR effects are small, but not completely negligible. Interestingly, they modify the large-scale P(k) in nearly the same way as nonzero primordial non-Gaussianity of the local type, with additional terms going as [tex]k^{-2}[/tex] and [tex]k^{-4}[/tex]. Fortunately, the 'effective non-G' induced by GR is (f_{\rm NL})^{\rm eff}\lesssim 0.5, which is likely to stay well below the statistical error in LSS surveys for another decade. So basically the GR effects are likely to be deep within the noise until your favorite gigantic survey produces high-quality data.

One thing I missed has to do with effects of nonzero primordial non-Gaussianity at these huge scales. Does this paper implicitly confirm the results of Wands and Slosar 0902.1084 who find that non-Gaussianity of the local form does not get additional corrections near the Hubble scale? I am a bit confused, since the NG effect in this paper appears as-usual in the *synchronous* gauge (Eq 104 here), but what does that imply about it in the constant-redshift gauge, in which we presumably operate when we utilize spectroscopic LSS surveys? Or is this equation already in the constant-redshift gauge?

Finally, given that the results agree with Challinor and Lewis, I presume that CAMB-sources already produces P(k) consistent with the one described here?

The results are also in mild disagreement with the original analysis by Yoo et al 0907.0707. The issue seems to be that the linear bias relation is to be assumed in the synchronous gauge, but this then does not correspond to linear bias in the constant-redshift gauge, so appropriate care must be taken.

The bottom line is that the GR effects are small, but not completely negligible. Interestingly, they modify the large-scale P(k) in nearly the same way as nonzero primordial non-Gaussianity of the local type, with additional terms going as [tex]k^{-2}[/tex] and [tex]k^{-4}[/tex]. Fortunately, the 'effective non-G' induced by GR is (f_{\rm NL})^{\rm eff}\lesssim 0.5, which is likely to stay well below the statistical error in LSS surveys for another decade. So basically the GR effects are likely to be deep within the noise until your favorite gigantic survey produces high-quality data.

One thing I missed has to do with effects of nonzero primordial non-Gaussianity at these huge scales. Does this paper implicitly confirm the results of Wands and Slosar 0902.1084 who find that non-Gaussianity of the local form does not get additional corrections near the Hubble scale? I am a bit confused, since the NG effect in this paper appears as-usual in the *synchronous* gauge (Eq 104 here), but what does that imply about it in the constant-redshift gauge, in which we presumably operate when we utilize spectroscopic LSS surveys? Or is this equation already in the constant-redshift gauge?

Finally, given that the results agree with Challinor and Lewis, I presume that CAMB-sources already produces P(k) consistent with the one described here?