CosmoFit.Cardassian

class CosmoFit.Cardassian(params)

Bases: Cosmology

Modified Polytropic Cardassian expansion (Freese & Lewis 2002; Wang et al. 2003),

E(z)^2 = Omega_k (1+z)^2

• Omega_m (1+z)^3 { 1 + [Omega_m*^{-q} - 1] (1+z)^{3q(n-1)} }^{1/q}

with Omega_m* = Omega_m / (1 - Omega_k).

The Cardassian idea is that the Friedmann equation itself gains an extra term, H^2 = A rho + B rho^n, from the universe being a 3-brane embedded in higher dimensions – so acceleration arises from matter alone, with no dark energy and no vacuum energy. The universe is matter-dominated at all times; it is the relation between H and rho that is modified.

Two extra parameters, n and q, and two reductions worth knowing:

• n = 0, q = 1 is exactly LCDM.

• q = 1 (any n) is the “original” Cardassian model, which is degenerate with wCDM at w = n - 1: the extra term scales as a power law, and a power-law density is what constant-w dark energy is. It is q != 1 that makes this a genuinely distinct expansion history rather than a reparametrization – which is precisely why the modified polytropic form is the one implemented here and the original one is not.

The bracket is normalized so that E(0) = 1 identically for any (n, q, Omega_k): at z = 0 it collapses to Omega_m*^{-1}, cancelling the Omega_m prefactor against the curvature term.

Notes

The original derivation assumes a flat universe. Curvature is admitted here through the Omega_m* rescaling above, which keeps the Friedmann constraint exact and reduces to the published flat form at Omega_k = 0; it is a consistent extension of the parametrization, not a result taken from the literature. Fit Omega_k with this model deliberately.

Numerically, Omega_m*^{-q} overflows for large q and small Omega_m, and the bracket can go negative for n > 1; both are outside the physically motivated region (0 <= n < 1, q > 0) that the default bounds cover.

References

Freese & Lewis (2002), “Cardassian Expansion: a Model in which the Universe is Flat, Matter Dominated, and Accelerating”, Phys. Lett. B 540, 1, arXiv:astro-ph/0201229.

Wang, Freese, Gondolo & Lewis (2003), ApJ 594, 25, arXiv:astro-ph/0302064 (the modified polytropic form).

Parameters:

params (CosmologyParameters)

__init__(params)

Parameters:

params (CosmologyParameters)

Methods

E(z)
H(z)
Omega_de(z)	The effective dark-energy density an observer assuming GR plus a fluid would reconstruct from this expansion history:
Omega_matter(z)	Matter density at redshift z, in units of today's critical density -- i.e. the Omega_m (1+z)^3 term as it appears inside E(z)^2, before dividing by E(z)^2.
__init__(params)
dEdz(z)
mu(a[, k])	Effective-to-Newtonian gravitational coupling ratio, G_eff(a,k)/G_N, entering the linear growth equation solved by GrowthCalculator (see that module's docstring for the equation itself).
plain_name()	This model's name as plain text: MODEL_NAME if it declares one, else the class name.
plot_label()	This model's name as it should appear in a figure legend or title -- MODEL_LABEL (LaTeX) if it declares one, else plain_name().
refresh()	Rebuild internal numerical tables after the underlying params object has been mutated in place (e.g. by params.update(theta) during an MCMC step).

Attributes

A_planck
A_s
EXTRA_PARAMS	Extra parameters this model adds beyond CosmologyParameters.
H0
MB
MODEL_LABEL	a LaTeX math string where the plain name is really a set of symbols (LCDM -> $\Lambda$CDM), None where the plain name is already what a reader should see (an acronym like CPL).
MODEL_NAME	Plain-text name for this model, for tables, JSON and log lines.
N_eff
Omega_b
Omega_de0
Omega_k
Omega_m
alpha
compute_rd	Whether rd is computed from the physical densities (rd_computed()) rather than read from the free rd parameter.
derive_sigma8	Whether sigma8 is derived from the Boltzmann code rather than read from the free sigma8 parameter.
h	Reduced Hubble constant, H0 / 100.
ln1e10As
m_nu
n_card
n_s
omega_b_h2	Physical baryon density, Omega_b h^2 -- the combination BBN and the CMB actually constrain.
omega_cdm_h2	Physical cold dark matter density, Omega_c h^2 -- matter less baryons.
omega_m_h2	Physical matter density, Omega_m h^2.
q_card
rd	The sound horizon at the drag epoch [Mpc] that the BAO likelihoods divide by.
sigma8	Present-day sigma_8, the normalization every growth prediction is built on.
tau_reio
w0
wa