Cosmologie¶

Model
Can be 1, 2, 3, or 4. Default value is Model = 1.
1 for CPL model
2 for Cardassian model
3 for Interacting DE Model
4 for Holographic Ricci Scale with CPL

H0 float
float defines the value of {{latex(H_0)}} in Mpc/km/s. Default value is {{latex(H_0)}} = 50.

omega float
float defines the value of {{latex(\Omega_{0})}}. Default value is {{latex(\Omega_{0})}} = 1.

lambda (or omegaX) float
float defines the normalized value of {{latex(\lambda)}}. (for a flat universe {{latex(\Omega_{0})}} + {{latex(\lambda)}} = 1.)
Default value {{latex(\lambda)}} = 0.

omegaK float
float defines the normalized value of the curvature of the Universe {{latex(\Omega_k)}}

wX (q, or w0) float
If Model is equal to 1 , float defines the first parameter in the CPL model.
If Model is equal to 2, float defines the {{latex(q)}} parameter in the Cardassian model.
If Model is equal to 3, float defines the {{latex(w_x)}} parameter in the Interacting DE model.
If Model is equal to 4, float defines the {{latex(w_0)}} parameter in the Holographic Ricci scale with CPL.

wa (n, delta, or w1) float
If Model is equal to 1 , float defines the second parameter in the CPL model.
If Model is equal to 2, float defines the {{latex(n)}} parameter in the Cardassian model.
If Model is equal to 3, float defines the {{latex(\delta)}} parameter in the Interacting DE model.
If Model is equal to 4, float defines the {{latex(w_1)}} parameter in the Holographic Ricci scale with CPL.

Additional remarks on the Cosmologie identifier

Model 1
Using the so-called CPL parameterization

{{latex( w(z) = w_x + \frac{w_az}{1+z} )}},

proposed by Chevalier & Polarski (2001) and Linder (2003), the square of the Hubble parameter (normalized by {{latex(H_0)}}) can be written as

{{latex( \frac{H(z)^2}{H_0^2} )}} {{latex( = \Omega_k(1+z)^2 )}} {{latex( + \Omega_r(1+z)^4 )}} {{latex( +\Omega_0(1+z)^3)}} {{latex( + (1-\Omega_k-\Omega_r-\Omega_0)(1+z)^{3(1+w_x+w_a)} )}}{{latex(exp(\frac{-3w_az}{1+z}) )}}.

Certainly, in the code {{latex( \Omega_r \equiv 0 )}}, always.

Model 2
The modified polytropic Cardassian Universe (see Gondolo & Freese, 2003) is a generalization of the original Cardassian model of Freese & Lewis (2002). In such Universe the Hubble parameter is given by:

{{latex( \frac{H(z)^2}{H_0^2} )}} {{latex( = \Omega_k(1+z)^2 )}} {{latex( + \Omega_r(1+z)^4 )}} {{latex( +\Omega_0(1+z)^3)}}{{latex(\left[ 1 + ((\frac{1-\Omega_k-\Omega_r}{\Omega_0})^{q}-1)(1+z)^{3q(n-1)} \right]^{1/q} )}}

Model 3
In the interacting Dark Energy model (Citation needed!) we have

{{latex( \frac{H(z)^2}{H_0^2} )}} {{latex( = \Omega_k(1+z)^2 )}} {{latex( + \Omega_r(1+z)^4 )}} {{latex( + (1-\Omega_k-\Omega_r-\Omega_0)(1+z)^{3(1+w_x)} )}} {{latex( + \frac{\Omega_0}{\delta+3w_x} )}}{{latex(\left[ \delta(1+z)^{3(1+w_x)} + 3w_x(1+z)^{3-\delta} \right] )}}

Model 4
Holographic Ricci Scale with CPL (Citation needed!):

{{latex( \frac{H(z)}{H_0} )}} {{latex( = (1+z)^{\frac{3}{2}\frac{1+r_0+w_0+4w_1}{1+r_0+3w_1}} )}}{{latex(\left[ \frac{1+r_0+3w_1z/(1+z)}{1+r_0} \right]^{-\frac{1}{2}\frac{1+r_0-3w_0}{1+r_0+3w_1}} )}}

In this case,

{{latex( w(z) = w_0 + \frac{w_1z}{1+z} )}},

and

{{latex( r_0 = \frac{\Omega_0}{1-\Omega_0} )}}.