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I was reading a paper talking about the KBC Void, a local underdensity in the Universe which we are also part of.

The authors calculated: "[...] the observed relative density contrast δ ≡ 1 − ρ/ρ0 = 0.46 ± 0.06".

What does that mean? Does the value simply refer to a density 46 ± 6 % lower than the Universe average?

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  • $\begingroup$ It looks like $\rho/\rho_0$ is how much lower the void density is compared to the universal average. That would be $0.54$. $\endgroup$
    – mmesser314
    Commented Jul 23 at 13:56

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See equation 2 in the paper:

Suppose that we are living near the centre of a void whose true density relative to the cosmic mean is $\rho/\rho_0 = \alpha = 1-\delta$

Note that $\delta$ can also be written as $$\delta = \frac{\rho_0 - \rho}{\rho_0} = \frac{\Delta \rho}{\rho_0}$$ where $\Delta\rho$ is the density difference between the void and the cosmic mean. Dividing this by $\rho_0$ gives you the relative difference, a quantity commonly used when looking at deviations from a mean.

So the density of the void is actually $(\delta -1)\cdot \rho_0$, i.e. 54.4% of the cosmic mean density.

It's a little unintiutive, but again, very commonly used.

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