mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-25 20:50:16 +00:00
64543faa98
* Make some ruff fixes * Undo manual fix * Undo manual fix * Updates from ruff=0.0.251
110 lines
3.2 KiB
Python
110 lines
3.2 KiB
Python
"""
|
|
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(p < 0 for p in parameters):
|
|
raise ValueError("All input parameters must be positive")
|
|
|
|
if any(p > 1 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,
|
|
)
|
|
)
|