Added a Hubble Parameter calculator file (#7921)

physics/hubble_parameter.py

@@ -0,0 +1,110 @@
+"""
+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,
+        )
+    )