CosmoFit.ADE

class CosmoFit.ADE(params)

Bases: Cosmology

New agegraphic dark energy: the holographic cutoff is the age of the universe, in conformal time.

The holographic family differs only in what length scale is put in rho_DE = 3 c^2 M_p^2 / L^2. HDE uses the future event horizon, RDE the Ricci scalar, and this uses the conformal age,

rho_DE = 3 n^2 M_p^2 / eta^2, eta = Int dt / a = Int da / (a^2 H),

which is causal, local in time, and needs no reference to the future – the objection HDE attracts.

Like HDE there is no closed form. Writing Omega_DE = n^2 / (eta H)^2 and differentiating the definition of eta gives

d Omega_DE / d ln a

= Omega_DE (1 - Omega_DE)

[3 - (2/n) sqrt(Omega_DE) / a],

solved and splined on every refresh(), with the expansion rate following from flatness as E^2 = Omega_m (1+z)^3 / (1 - Omega_DE).

The early-time behaviour is the model’s signature and its own consistency check: for Omega_DE << 1 the equation forces Omega_DE -> n^2 a^2 / 4 exactly, so dark energy dilutes as a^2 rather than the a of HDE, and the equation of state is

w = -1 + (2 / 3n) sqrt(Omega_DE) / a,

which tends to -2/3 at early times and to -1 in the far future for every n. So unlike HDE, this model cannot be phantom at any n: the crossing HDE predicts is simply not available here, which is the sharpest observational difference between them.

Caveats

Flat universes only, and refused by CAMBBackend, for the same reasons as HDE.

References

Wei & Cai (2008), Phys. Lett. B 660, 113, arXiv:0708.0884.

__init__(params)

Parameters:

params (CosmologyParameters)

Methods

E(z)
H(z)
Omega_de(z)	Dark-energy density in units of today's critical density -- the term inside E(z)^2, as every other model here returns.
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)	Analytic, from the ODE rather than by differencing E.
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).
omega_de_fraction(z)	The density parameter rho_DE(z) / rho_crit(z), which is what the ODE solves for -- not Omega_de(), which is in units of today's critical density.
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).
w_de(z)	w = -1 + (2 / 3n) sqrt(Omega_DE) / a.

Attributes

A_planck
A_s
DERIVED_PARAMS	Parameters this model derives rather than accepts.
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	Matter density, derived from n_ade rather than sampled.
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_ade
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.
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

Parameters:

params (CosmologyParameters)