Definition of [itex]\sigma_8[/itex]

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SUMMARY

The discussion centers on the definition of \(\sigma_8\) in relation to the matter power spectrum. Specifically, \(\sigma_8\) is defined as \(\sigma_8 = \mathcal{P}(k=1/8 \,h/\text{Mpc})\), where \(\mathcal{P}\) represents the power spectrum. A reference provided is from the second edition of "Fundamentals of Cosmology" by James Rich, which clarifies the use of \(r=8\) in equation (7.32). The participants confirm that \(\sigma_8\) pertains specifically to the matter power spectrum, distinguishing it from other types of power spectra used in cosmology.

PREREQUISITES
  • Understanding of cosmological parameters, specifically \(\sigma_8\)
  • Familiarity with the concept of power spectra in cosmology
  • Knowledge of the mathematical notation used in cosmology
  • Access to "Fundamentals of Cosmology" by James Rich for reference
NEXT STEPS
  • Research the implications of \(\sigma_8\) on cosmic structure formation
  • Study the matter power spectrum and its significance in cosmology
  • Learn about different types of power spectra used in cosmological studies
  • Examine equation (7.32) in "Fundamentals of Cosmology" for deeper insights
USEFUL FOR

Astronomers, cosmologists, and students studying the large-scale structure of the universe will benefit from this discussion, particularly those interested in the mathematical foundations of cosmological parameters.

Einj
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Hi everyone,
apologies if this question has been asked already. My search didn't give any results.

Can anyone tell me the definition of \sigma_8 in terms of the power spectrum? A reference where I could find it is perfect too!

Thanks a lot
 
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Thanks a lot! Does that simply mean \sigma_8=\mathcal{P}(k=1/8 \,h/Mpc)? Where \mathcal{P} is the power spectrum.
 
Einj said:
Thanks a lot! Does that simply mean \sigma_8=\mathcal{P}(k=1/8 \,h/Mpc)? Where \mathcal{P} is the power spectrum.

I have attached one page from the second edition of "Fundamentals of Cosmology" by James Rich. Take ##r=8## in equation (7.32).
 

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Einj said:
Thanks a lot! Does that simply mean \sigma_8=\mathcal{P}(k=1/8 \,h/Mpc)? Where \mathcal{P} is the power spectrum.
And just to clarify, this is the matter power spectrum. There are other power spectrums that are used in cosmology.
 
All clear now! Thank you so much everyone!
 

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