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YinZhe Ma
Joined: 09 Oct 2008 Posts: 11 Affiliation: University of KwaZuluNatal

Posted: April 13 2013 


Hi Guys,
I am confused about the bias and galaxy overdensity.
First, galaxy overdensity is related to matter density contrast through:
δ_{g} = b * δ_{m}, where b is the bias. δ_{m} cannot be less than −1, because it is defined as , since , .
However, b can take any value. It can be − 3, − 2 (void), or very positive number, such as 2 in Table 5 and 6 of 1303.4486. Therefore, δ_{g} can be any value. For example, If δ_{m} = − 0.8, b = 2, then δ_{g} = − 1.6. Then what is the definition of δ_{g} if it can take any value?
It certainly cannot be defined as the matter density contrast because it can be less than −1. Then how to understand its physical meaning?
Thanks. 

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Maciej Bilicki
Joined: 12 May 2010 Posts: 19 Affiliation: University of Cape Town

Posted: April 14 2013 


The bias as defined here is linear. Voids with δ=−0.8 are pretty nonlinear.
Galaxy underdensity, as any other underdensity, cannot – by definition – be smaller than −1.
You can find more basics on the bias in for instance the classic review by Strauss & Willick (1995).
I am quite sure that the bias can't be negative. 

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Wojciech Hellwing
Joined: 17 May 2006 Posts: 1 Affiliation: Institute for Computational Cosmology, Durham

Posted: April 14 2013 


A negative bias would be totally unphysical when one concerns density. However an antibias (0<b<1) is possible and in the fact is present for small galaxies/haloes.
As Maciej had noticed You have used a definition of the linear bias. In general we have:
δ_{g} = f(δ)
in particular we can express the nonlinear function f in Tylor series:
(see e.g. Fry&Gaztanaga 1994)
hence in regions where b_{1} > 1 and δ < 0.8 rest of the bias parameters will have values making the in the end. 

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YinZhe Ma
Joined: 09 Oct 2008 Posts: 11 Affiliation: University of KwaZuluNatal

Posted: April 17 2013 


However, what if b=3 (positive bias), but delta_m=−0.5? In this case, delta_g=b*delta_m=−1.5, still < − 1. 

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Boud Roukema
Joined: 24 Feb 2005 Posts: 84 Affiliation: Torun Centre for Astronomy, University of Nicolaus Copernicus

Posted: July 16 2013 


As Maciej and Wojciech said, the discussion concerns linear perturbation theory, meaning . Your value of δ_{m} = − 0.5 is highly nonlinear, so the linear theory is no longer valid. If you apply it anyway, then you get unphysical results.
Similarly, when the overall virialisation fraction at low redshifts f_{vir}(z) fails to satisfy , the underlying homogeneity assumption fails and an artefact  wouldbe "dark energy"  arises if the homogeneous (FLRW) metric is used to interpret the observations despite the invalidity of the homogeneity assumption (1303.4444). 

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