# Convention of units for densities in cosmology

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• fab13
fab13
TL;DR Summary
I would like to know the Convention of units for densities in cosmology : I wonder if consistent units are used by multiplying or dividing with Delta_z
I have a table of densities of galaxies :

Expected number density of galaxies for photometric survey per unit area and redshift intervals, ##\mathrm{d} N / \mathrm{d} \Omega \mathrm{d} z\left[\mathrm{sr}^{-1}\right]## and the corresponding density of galaxies per ##\operatorname{arcmin}^2## for each redshift

I wonder if the second row values are correct : indeed, I hesitate between both calculus, for example for the bin :

- case 1

3 / 11818102.860 * 0.119 = 4219062.72 (rounded to 4219063) in units ##\text{d}N/\text{d}\Omega\text{d}z##

OR should I set rather :

- case 2

3 / 11818102.860 / 0.119 = 297935366.218 (rounded to 297935366) in units ##\text{d}N/\text{d}\Omega\text{d}z##

One of both is wrong since I don't know if the units are ##\text{d}N/\text{d}\Omega\text{d}z## or ##\text{d}N/\text{d}\Omega/\text{d}z##.

Could anyone help me what is the convention for the units of the writing ##\text{d}N/\text{d}\Omega\text{d}z## that causes some confusions ( we don't know if we have to multiply or divide by ##\Delta z## ?

## What are the common units used for density in cosmology?

In cosmology, the most common units for density are kilograms per cubic meter (kg/m³) and solar masses per cubic megaparsec (M☉/Mpc³). The former is part of the International System of Units (SI), while the latter is more convenient for astronomical scales.

## Why are different units used for density in cosmology?

Different units are used because cosmology deals with vastly different scales compared to terrestrial physics. SI units are often impractical for such large scales, so astronomers use units like solar masses and megaparsecs to make calculations and comparisons more manageable.

## How do you convert between different units of density in cosmology?

To convert between units, you need to know the conversion factors. For example, 1 solar mass (M☉) is approximately 1.989 x 10³⁰ kg, and 1 megaparsec (Mpc) is about 3.086 x 10²² meters. Using these, you can convert densities from kg/m³ to M☉/Mpc³ and vice versa.

## What is the critical density of the universe and its units?

The critical density is the density at which the universe is flat. It is approximately 8.6 x 10⁻²⁷ kg/m³ or equivalently about 1.26 x 10¹¹ M☉/Mpc³. This value is crucial for understanding the geometry and fate of the universe.

## Why is the concept of density important in cosmology?

Density is fundamental in cosmology because it helps determine the overall dynamics of the universe, including its expansion rate, geometry, and eventual fate. Different densities lead to different cosmological models, such as open, closed, or flat universes.

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