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"""

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

"""

def 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

"""

parameters = [redshift, radiation_density, matter_density, dark_energy]

if any(0 > p for p in parameters):

raise ValueError("All input parameters must be positive")

if any(1 < p for p in parameters[1:4]):

raise ValueError("Relative densities cannot be greater than one")

else:

curvature = 1 - (matter_density + radiation_density + dark_energy)

e_2 = (

radiation_density * (redshift + 1) ** 4

+ matter_density * (redshift + 1) ** 3

+ curvature * (redshift + 1) ** 2

+ dark_energy

)

hubble = hubble_constant * e_2 ** (1 / 2)

return hubble

if __name__ == "__main__":

import doctest

# run doctest

doctest.testmod()

# demo LCDM approximation

matter_density = 0.3

print(

hubble_parameter(

hubble_constant=68.3,

radiation_density=1e-4,

matter_density=matter_density,

dark_energy=1 - matter_density,

redshift=0,

)

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