Editing Redshift-space distortions (section)

{{Cosmology}}
'''Redshift-space distortions''' are an effect in [[observational cosmology]] where the spatial distribution of galaxies appears squashed and distorted when their positions are plotted as a function of their [[redshift]] rather than as a function of their distance. The effect is due to the [[Peculiar velocity|peculiar velocities]] of the galaxies causing a [[Doppler shift]] in addition to the redshift caused by the [[Expansion of space|cosmological expansion]].

Redshift-space distortions (RSDs) manifest in two particular ways. The '''Fingers of God''' effect is where the galaxy distribution is elongated in redshift space, with an axis of elongation pointed toward the observer.<ref name="Jackson 1972">{{cite journal|doi=10.1093/mnras/156.1.1p|title=A Critique of Rees's Theory of Primordial Gravitational Radiation|journal=Monthly Notices of the Royal Astronomical Society|volume=156|pages=1P–5P|year=1972|last1=Jackson|first1=J. C.|doi-access=free |bibcode=1972MNRAS.156P...1J|arxiv=0810.3908}}</ref> It is caused by a Doppler shift associated with the random peculiar velocities of galaxies bound in structures such as clusters. The large velocities that lead to this effect are associated with the [[gravity]] of the cluster by means of the [[virial theorem]]; they change the observed redshifts of the galaxies in the cluster. The deviation from the [[Hubble's law]] relationship between distance and redshift is altered, and this leads to inaccurate distance measurements.

A closely related effect is the Kaiser effect, in which the distortion is caused by the coherent motions of galaxies as they fall inwards towards the cluster center as the cluster assembles.<ref name="Kaiser 1987">{{cite journal|doi=10.1093/mnras/227.1.1|title=Clustering in real space and in redshift space|journal=Monthly Notices of the Royal Astronomical Society|volume=227|pages=1–21|year=1987|last1=Kaiser|first1=Nick|bibcode=1987MNRAS.227....1K|doi-access=free}}</ref> Depending on the particular dynamics of the situation, the Kaiser effect usually leads not to an elongation, but an apparent flattening ("pancakes of God"), of the structure. It is a much smaller effect than the fingers of God, and can be distinguished by the fact that it occurs on larger scales.

The previous effects are a consequence of special relativity, and have been observed in real data. There are additional effects that arise from general relativity. One is gravitational redshift distortion, which arises from the net [[gravitational redshift]], or blueshift, that is acquired when the photon climbs out of the gravitational potential well of the distant galaxy and then falls into the potential well of the Milky Way galaxy.<ref name="McDonald 2009">{{cite journal|doi=10.1088/1475-7516/2009/11/026|title=Gravitational redshift and other redshift-space distortions of the imaginary part of the power spectrum|journal=Journal of Cosmology and Astroparticle Physics|volume=2009|issue=11|pages=026|year=2009|last1=McDonald|first1=Patrick|bibcode=2009JCAP...11..026M|arxiv=0907.5220|s2cid=119188837}}</ref> This effect will make galaxies at a higher gravitational potential than Earth appear slightly closer, and galaxies at lower potential will appear farther away.

The other effects of general relativity on clustering statistics are observed when the light from a background galaxy passes near, or through, a closer galaxy or cluster. These two effects are the integrated [[Sachs-Wolfe effect]] (ISW) and [[gravitational lens]]ing.<ref name="Yoo 2009">{{cite journal|doi=10.1103/physrevd.79.023517|title=Complete treatment of galaxy two-point statistics: Gravitational lensing effects and redshift-space distortions|journal=Physical Review D|volume=79|issue=2|pages=023517|year=2009|last1=Yoo|first1=Jaiyul|bibcode=2009PhRvD..79b3517Y|arxiv=0808.3138|s2cid=73543566}}</ref> ISW arises because large-scale gravitational potentials are decaying in time (due to [[dark energy]]), so that a photon passing through a low area of gravitational potential gains more energy on entry than it loses on exit, making the background galaxy appear closer. Gravitational lensing, unlike all of the previous effects, distorts the apparent position, and number, of background galaxies.

The RSDs measured in [[Redshift survey|galaxy redshift surveys]] can be used as a cosmological probe in their own right, providing information on how structure formed in the Universe,<ref>{{cite journal|last1=Percival|first1=Will J.|last2=White|first2=Martin|title=Testing cosmological structure formation using redshift-space distortions|journal=Monthly Notices of the Royal Astronomical Society|date=11 February 2009|volume=393|issue=1|pages=297–308|doi=10.1111/j.1365-2966.2008.14211.x|doi-access=free |arxiv = 0808.0003 |bibcode = 2009MNRAS.393..297P |s2cid=15066577}}</ref> and how gravity behaves on large scales.<ref>{{cite journal|last1=Raccanelli|first1=A.|last2=Bertacca|first2=D.|last3=Pietrobon|first3=D.|last4=Schmidt|first4=F.|last5=Samushia|first5=L.|last6=Bartolo|first6=N.|last7=Dore|first7=O.|last8=Matarrese|first8=S.|last9=Percival|first9=W. J.|title=Testing gravity using large-scale redshift-space distortions|journal=Monthly Notices of the Royal Astronomical Society|date=25 September 2013|volume=436|issue=1|pages=89–100|doi=10.1093/mnras/stt1517|doi-access=free |arxiv = 1207.0500 |bibcode = 2013MNRAS.436...89R |s2cid=9570774}}</ref>