physics.hubble_parameter

Title : Calculating the Hubble Parameter

Description : The Hubble parameter H is the Universe expansion rate in any time. In cosmology is customary to use the redshift redshift in place of time, becausethe redshift is directily mensure in the light of galaxies moving away from us.

So, the general relation that we obtain is

H = hubble_constant*(radiation_density*(redshift+1)**4

  • matter_density*(redshift+1)**3

  • curvature*(redshift+1)**2 + dark_energy)**(1/2)

where radiation_density, matter_density, dark_energy are the relativity (the percentage) energy densities that exist in the Universe today. Here, matter_density is the sum of the barion density and the dark matter. Curvature is the curvature parameter and can be written in term of the densities by the completeness

curvature = 1 - (matter_density + radiation_density + dark_energy)

Source : https://www.sciencedirect.com/topics/mathematics/hubble-parameter

Attributes

matter_density

Functions

hubble_parameter(→ float)

Input Parameters

Module Contents

physics.hubble_parameter.hubble_parameter(hubble_constant: float, radiation_density: float, matter_density: float, dark_energy: float, redshift: float) → float

Input Parameters

hubble_constant: Hubble constante is the expansion rate today usually given in km/(s*Mpc)

radiation_density: relative radiation density today

matter_density: relative mass density today

dark_energy: relative dark energy density today

redshift: the light redshift

Returns

result : Hubble parameter in and the unit km/s/Mpc (the unit can be changed if you want, just need to change the unit of the Hubble constant)

>>> hubble_parameter(hubble_constant=68.3, radiation_density=1e-4,
... matter_density=-0.3, dark_energy=0.7, redshift=1)
Traceback (most recent call last):
...
ValueError: All input parameters must be positive

>>> hubble_parameter(hubble_constant=68.3, radiation_density=1e-4,
... matter_density= 1.2, dark_energy=0.7, redshift=1)
Traceback (most recent call last):
...
ValueError: Relative densities cannot be greater than one

>>> hubble_parameter(hubble_constant=68.3, radiation_density=1e-4,
... matter_density= 0.3, dark_energy=0.7, redshift=0)
68.3
physics.hubble_parameter.matter_density = 0.3