A Coefficient correlation between 2 cosmological probes

AI Thread Summary
The discussion centers on determining the correlation coefficient between two cosmological probes, specifically a spectroscopic probe (A) and a photometric probe (B). The user seeks clarification on whether the correlation coefficient is closer to 0 or 1 based on the dominance of Poisson noise in the spectroscopic probe compared to its cosmological component. The document referenced suggests that the cosmological part is significantly larger than the noise, implying a correlation closer to 1, but the user expresses uncertainty about this conclusion. The conversation emphasizes the importance of clearly articulating complex concepts in cosmology for better understanding. Overall, the correlation analysis remains a critical aspect of evaluating the relationship between these probes.
fab13
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TL;DR Summary
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

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I put in attachment the capture in PDF for more lisibility
 

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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.
 

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