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110 lines
3.2 KiB
Python
110 lines
3.2 KiB
Python
"""
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Title : Calculating the Hubble Parameter
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Description : The Hubble parameter H is the Universe expansion rate
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in any time. In cosmology is customary to use the redshift redshift
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in place of time, becausethe redshift is directily mensure
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in the light of galaxies moving away from us.
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So, the general relation that we obtain is
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H = hubble_constant*(radiation_density*(redshift+1)**4
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+ matter_density*(redshift+1)**3
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+ curvature*(redshift+1)**2 + dark_energy)**(1/2)
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where radiation_density, matter_density, dark_energy are the relativity
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(the percentage) energy densities that exist
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in the Universe today. Here, matter_density is the
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sum of the barion density and the
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dark matter. Curvature is the curvature parameter and can be written in term
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of the densities by the completeness
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curvature = 1 - (matter_density + radiation_density + dark_energy)
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Source :
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https://www.sciencedirect.com/topics/mathematics/hubble-parameter
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"""
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def hubble_parameter(
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hubble_constant: float,
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radiation_density: float,
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matter_density: float,
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dark_energy: float,
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redshift: float,
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) -> float:
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"""
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Input Parameters
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----------------
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hubble_constant: Hubble constante is the expansion rate today usually
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given in km/(s*Mpc)
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radiation_density: relative radiation density today
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matter_density: relative mass density today
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dark_energy: relative dark energy density today
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redshift: the light redshift
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Returns
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-------
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result : Hubble parameter in and the unit km/s/Mpc (the unit can be
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changed if you want, just need to change the unit of the Hubble constant)
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>>> hubble_parameter(hubble_constant=68.3, radiation_density=1e-4,
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... matter_density=-0.3, dark_energy=0.7, redshift=1)
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Traceback (most recent call last):
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...
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ValueError: All input parameters must be positive
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>>> hubble_parameter(hubble_constant=68.3, radiation_density=1e-4,
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... matter_density= 1.2, dark_energy=0.7, redshift=1)
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Traceback (most recent call last):
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...
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ValueError: Relative densities cannot be greater than one
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>>> hubble_parameter(hubble_constant=68.3, radiation_density=1e-4,
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... matter_density= 0.3, dark_energy=0.7, redshift=0)
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68.3
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"""
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parameters = [redshift, radiation_density, matter_density, dark_energy]
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if any(p < 0 for p in parameters):
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raise ValueError("All input parameters must be positive")
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if any(p > 1 for p in parameters[1:4]):
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raise ValueError("Relative densities cannot be greater than one")
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else:
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curvature = 1 - (matter_density + radiation_density + dark_energy)
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e_2 = (
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radiation_density * (redshift + 1) ** 4
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+ matter_density * (redshift + 1) ** 3
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+ curvature * (redshift + 1) ** 2
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+ dark_energy
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)
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hubble = hubble_constant * e_2 ** (1 / 2)
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return hubble
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if __name__ == "__main__":
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import doctest
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# run doctest
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doctest.testmod()
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# demo LCDM approximation
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matter_density = 0.3
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print(
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hubble_parameter(
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hubble_constant=68.3,
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radiation_density=1e-4,
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matter_density=matter_density,
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dark_energy=1 - matter_density,
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redshift=0,
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)
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)
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