Definition of [itex]\sigma_8[/itex]

  • Context: Graduate 
  • Thread starter Thread starter Einj
  • Start date Start date
  • Tags Tags
    Definition
Click For Summary

Discussion Overview

The discussion revolves around the definition of \(\sigma_8\) in the context of the power spectrum, specifically within cosmology. Participants seek clarification on its formulation and references for further reading.

Discussion Character

  • Exploratory, Technical explanation

Main Points Raised

  • One participant requests the definition of \(\sigma_8\) in terms of the power spectrum and asks for references.
  • Another participant suggests a reference link that may contain the definition.
  • Multiple participants propose that \(\sigma_8\) can be expressed as \(\sigma_8=\mathcal{P}(k=1/8 \,h/\text{Mpc})\), where \(\mathcal{P}\) represents the power spectrum.
  • It is noted that the context of \(\sigma_8\) pertains specifically to the matter power spectrum, distinguishing it from other power spectra used in cosmology.
  • One participant shares a page from "Fundamentals of Cosmology" to support their point regarding the definition.
  • Another participant expresses gratitude for the clarifications received during the discussion.

Areas of Agreement / Disagreement

Participants appear to agree on the formulation of \(\sigma_8\) in relation to the power spectrum, but there is no consensus on the definitive reference or the nuances of its application.

Contextual Notes

The discussion does not resolve the potential variations in definitions or applications of \(\sigma_8\) across different contexts in cosmology.

Einj
Messages
464
Reaction score
59
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
 
Space news on Phys.org
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).
 

Attachments

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!
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 23 ·
Replies
23
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K