Help on Hubble Constant, H0, h100 & Critical Density Rhoc

[Badger01]

For the most part I've been using the Hubble constant of:
H₀ = 72 km/s/Mpc

but I've started seeing it expressed as:
H₀ = 100 h₁₀₀ km/s/Mpc.

what is h₁₀₀ and why is it coming up in this??

I've also seen the critical density for the shape of the universe (flat/open/closed ect) as:
Rho_c = 1.879 h₁₀₀² kg/m³

what does it mean in this context, and as the critical density is given by:
Rho_c = 3 H₀²/8 pi G

i don't see where you get the 1.879 from even if you do replace the Hubble constant with the above.
i'm really confused, so could some one please help?

 

[Sybren]

That does not look consistent:

From your first two equations, it seems that
[tex]h_{100}\equiv\frac{72}{100},[/tex]
but when using that in the bottom two equations, I find
[tex]\rho_c\equiv\frac{3H_0^2}{8\pi G}\sim9.74\times10^{-27}\ \text{kg}\cdot\text{m}^{-3},[/tex]
and
[tex]\rho_c\equiv1.879h_{100}^2\ \text{kg}\cdot\text{m}^{-3}\sim9.74\times10^{-1}\ \text{kg}\cdot\text{m}^{-3},[/tex]
which don't agree. This means that at least one of these equations is not correct.

 

[Badger01]

ok, thanks for the help, perhaps i miss understood the definition of h₁₀₀ or something..

 

[Sybren]

What I find on this link: http://scienceworld.wolfram.com/physics/CriticalDensity.html, is that the critical density can be written
[tex]\rho_c=\frac{3H^2}{8\pi G}=1.9\times10^{-26}h^2\ \text{kg}\cdot\text{m}^{-3}.[/tex]
When using this together with the value of [itex]h=72/100[/itex], it becomes
[tex]\rho_c\sim9.85\times10^{-27}\ \text{kg}\cdot\text{m}^{-3}.[/tex]
It shows that the prefactor [itex]1.879[/itex] in your equation should be [itex]1.879\times10^{-26}[/itex]

 

[rwisz]

The Hubble constant (H0) is a measure of the rate at which the universe is expanding. It is expressed as the velocity of recession of a distant object divided by its distance from us. The value of H0 has been a topic of debate for many years, with different methods and observations giving different values.

The value of H0 has been traditionally expressed in units of kilometers per second per megaparsec (km/s/Mpc). However, in recent years, it has become more common to see it expressed as a dimensionless number (h100) multiplied by 100 kilometers per second per megaparsec (km/s/Mpc). This is mainly due to the fact that different studies and observations have given different values for H0, and using a dimensionless number allows for easier comparison and combination of these results.

The value of h100 is simply a scaling factor that is used to convert the dimensionless Hubble constant to the traditional units of km/s/Mpc. It is typically around 0.7, which means that H0 = 100 h100 km/s/Mpc is approximately equivalent to H0 = 70 km/s/Mpc.

The critical density (Rhoc) is a concept in cosmology that refers to the density of matter and energy needed for the universe to be flat (i.e. have zero curvature). This is based on the idea that the geometry of the universe is determined by its density. If the universe has a density greater than the critical density, it is closed (positively curved); if it has a density less than the critical density, it is open (negatively curved); and if it has a density equal to the critical density, it is flat (zero curvature).

The value of the critical density is given by the formula Rhoc = 3 H02/8 pi G, where G is the gravitational constant. The factor of 1.879 that you have seen is simply a numerical value that results from using specific units for H0 and G. It is not a universal value and may vary depending on the units used.

In summary, h100 is a scaling factor used to convert the dimensionless Hubble constant to traditional units, and the critical density (Rhoc) is a concept that relates to the density needed for the universe to have a specific curvature. The value of 1.879 is a numerical factor that results from using specific units in the formula for the critical density.