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 H_0 in Mpc/km/s. Default value is H_0 = 50.

omega float

float defines the value of \Omega_{0}. Default value is \Omega_{0} = 1.

lambda (or omegaX) float

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

omegaK float

float defines the normalized value of the curvature of the Universe \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 q parameter in the Cardassian model. If Model is equal to 3, float defines the w_x parameter in the Interacting DE model. If Model is equal to 4, float defines the 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 n parameter in the Cardassian model. If Model is equal to 3, float defines the \delta parameter in the Interacting DE model. If Model is equal to 4, float defines the w_1 parameter in the Holographic Ricci scale with CPL.

Additional remarks on the Cosmologie identifier

Model 1

Using the so-called CPL parameterization

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

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

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

Certainly, in the code \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:

\frac{H(z)^2}{H_0^2}=\Omega_k(1+z)^2+\Omega_r(1+z)^4+\Omega_0(1+z)^3\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

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

Model 4

Holographic Ricci Scale with CPL (Citation needed!):

\frac{H(z)}{H_0}=(1+z)^{\frac{3}{2}\frac{1+r_0+w_0+4w_1}{1+r_0+3w_1}}\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,

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

and

r_0=\frac{\Omega_0}{1-\Omega_0}