Coefficient correlation between 2 cosmological probes

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fab13
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TL;DR
I would like to assess the importance of spectroscopic Poisson noise compared to the cosmological contribution of Dark matter
Hello,

I have the demonstration below. A population represents the spectroscopic proble and B the photometric probe. I would like to know if, from the equation (13), the correlation coeffcient is closed to 0 or to 1 since I don't know if ##\mathcal{N}_{\ell}^{A}## Poisson noise of spectroscopic dominates or not the cosmological part ##b_A\,C_{\ell}^{DM}## with ##b_A## the cosmological bias of spectroscopic probe.

In this document, the authot states that cosmological part ##b_A\,C_{\ell}^{DM}## is very larger compared to ##\mathcal{N}_{\ell}^{A}## : this causes the correlation coefficient to be closed to 1 but I have doubts.

Any help is welcome

Handwritten-style LaTeX derivation of the correlation between two galaxy population maps, equations (1) to (13), defining a^A and a^B, covariance terms, and the correlation Corr(a^A, a^B) simplifying to 1/sqrt(1 + N^A/(b_A^2 C^M)).
 

Discussion

This is like your fourth thread on this.

If you aren't violating the PF rules on personal theories, you might want to try and make your point more clearly and concisely.