Definition of [itex]\sigma_8[/itex]

[Einj]

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

 

[George Jones]

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!

See the last paragraph of

https://ned.ipac.caltech.edu/level5/March04/Primack/Primack2.html

 

[Einj]

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

 

[George Jones]

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).

 

[kimbyd]

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.

 

[Einj]

All clear now! Thank you so much everyone!