Real-Space vs Redshift-Space Correlation Functions

[srivatsan]

I would like to know what is the difference between real-space correlation and redshift-space correlation functions?

 

[Drakkith]

I've never heard of "redshift-space". What is that exactly?

 

[srivatsan]

our “third dimension” in cosmology
is not radial distance but redshift. The two are related
by the Hubble expansion but also affected by peculiar velocities. This is called as redshift-space. Due to the peculiar velocities of galaxies, there are objects that appear stretched towards us..

 

[Drakkith]

Ah ok. So it's pretty much where the effects of cosmological expansion start to become noticeable then?

 

[sardar]

The real-space correlation function measures the distribution of galaxies in three-dimensional space, taking into account their actual physical positions. This can provide information about the clustering and large-scale structure of the universe.

On the other hand, the redshift-space correlation function takes into account the effects of the cosmological expansion on the observed positions of galaxies. This is because the light from distant galaxies is stretched as it travels through the expanding universe, causing their observed positions to be shifted towards longer wavelengths (i.e. redshifted). This effect is known as the cosmological redshift.

The main difference between the two correlation functions is that while the real-space correlation function reflects the underlying physical distribution of galaxies, the redshift-space correlation function is affected by the peculiar velocities of galaxies, which can distort their observed positions. These peculiar velocities are caused by the gravitational pull of nearby galaxies and can cause galaxies to appear to be moving away from us faster or slower than they actually are.

In summary, the real-space correlation function provides a more accurate representation of the true distribution of galaxies in the universe, while the redshift-space correlation function takes into account the effects of the expanding universe and peculiar velocities of galaxies. Both correlation functions are important tools for understanding the large-scale structure and evolution of the universe.