This is an interesting paper. The original idea of primordial non-Gaussanity and its relation with power spectrum can be found at Dalal, Dore, Huterer, and Shirokov, 0710.4560. I have a few questions regarding the bias and local nG:
1. The scale-dependent part of additional bias (A(k), in Eq.(4) in
1208.1491) is plotted in the attached figure "akfig.pdf". It seems that additional bias contribute more power on large scales than small scales. How do we understand this?
2. If A(k) I plotted is correct, then btot(k)=b+ Delta b(k) is shown in "btotfig1.pdf". Just want to make clearer about the relations between different choices of parameter values and the shape of the btot. There are four cases:
(a) bL>0,(b>1) and fNL>0: purple line. This means that galaxy is more correlated with matter fluctuations, and small scale galaxy fluctuation is correlated with large scale fluctuations, so btot at large scale becomes large. Is this right?
(b) bL<0 (b<1) and fNL>0: green line. Galaxy initially is anti-correlated with matter fluctuations (bL<0), therefore after evolution (extra 1 factor), Galaxy is less correlated with matter fluctuation and matter auto-correlation (0<b<1). fNL>0 means small scale gravity potential is correlated with large scale potential fluctuation, right? But how to understand these two things combined to give the large scale suppression?
In "pgfig1.pdf", we plot Pg(k), you can find that the green line and
purple line are combined with each other on k<10(−3). Why these two sets of parameter choice give same power on very large scale?
(c)bL>0(b>1) and fNL<0: brown line. Why this set of parameter choice give a suppression on large scales.
(d) bL<0(b<1) and fNL<0: blue line. galaxy is initially anti-correlated
with matter fluctuation (bL<0), and small scale and large scale potential fluctuations are anti-correlated as well. Why this set of parameter choice results in a boost on large scales as well?
Thank you guys!
[1208.1491] The Clustering of Galaxies in SDSS-III DR9 Baryon Oscillation Spectroscopic Survey: Constraints on Primordial Non-Gaussianity
|Authors:||Ashley J. Ross (Portsmouth), Will J. Percival, Aurelio Carnero, Gong-bo Zhao, Marc Manera, Alvise Raccanelli, Eric Aubourg, Dmitry Bizyaev, Howard Brewington, J. Brinkmann, Joel R. Brownstein, Antonio J. Cuesta, Luiz A. N. da Costa, Daniel J.|
|Abstract:||We analyze the density field of 264,283 galaxies observed by the Sloan Digital Sky Survey (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS) and included in the SDSS data release nine (DR9). In total, the SDSS DR9 BOSS data includes spectroscopic redshifts for over 400,000 galaxies spread over a footprint of more than 3,000 deg^2. We measure the power spectrum of these galaxies with redshifts 0.43 < z < 0.7 in order to constrain the amount of local non-Gaussianity, f_NL,local, in the primordial density field, paying particular attention to the impact of systematic uncertainties. The BOSS galaxy density field is systematically affected by the local stellar density and this influences the ability to accurately measure f_NL,local. In the absence of any correction, we find (erroneously) that the probability that f_NL,local is greater than zero, P(f_NL,local >0), is 99.5%. After quantifying and correcting for the systematic bias and including the added uncertainty, we find -45 < f_NL,local < 195 at 95% confidence, and P(f_NL,local >0) = 91.0%. A more conservative approach assumes that we have only learned the k-dependence of the systematic bias and allows any amplitude for the systematic correction; we find that the systematic effect is not fully degenerate with that of f_NL,local, and we determine that -82 < f_NL,local < 178 (at 95% confidence) and P(f_NL,local >0) = 68%. This analysis demonstrates the importance of accounting for the impact of Galactic foregrounds on f_NL,local measurements. We outline the methods that account for these systematic biases and uncertainties. We expect our methods to yield robust constraints on f_NL,local for both our own and future large-scale-structure investigations.|
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