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I am studying about cosmological parameters and I have seen there is one parameter defined as $$S_8 = \sigma_{8}*\sqrt{\frac{\Omega_{m}}{0.3}},$$ but I don't understand why is there a need of defining this parameter if we already have $\sigma_{8}$ and $\Omega_{m}$. What extra information does this parameter give us and why is it important?

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  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Jun 12, 2022 at 11:34
  • $\begingroup$ I suggest that you post a reference in which the S8 variable is discussed. $\endgroup$
    – Buzz
    Jun 14, 2022 at 21:04

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In weak lensing studies of $σ_8$ as a function of $\Omega_m$ it is observed a "banana" shape, centered around $\Omega_m$ ~ 0.3 with a square-root shape; the "banana" can be linearized into a "cucumber" by using the definition of $S_8$. The statistical analysis of the data is easier for the linear-like $S_8$ than for the non-linear $\sigma_8$.

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