CosmoFit.RDE

class CosmoFit.RDE(params)

Bases: Cosmology

Ricci dark energy: the holographic cutoff is the Ricci scalar.

HDE takes the future event horizon as its infrared cutoff, which makes today’s dark-energy density depend on the entire future expansion history – unusual as physics, and the thing most often objected to. Ricci dark energy takes a local curvature scale instead,

rho_DE = 3 gamma M_p^2 (Hdot + 2 H^2),

which is the Ricci scalar of a spatially flat universe up to a constant. Same holographic idea, no reference to the future.

Unlike HDE this has a closed form. Solving the Friedmann equation with that density gives

E(z)^2 = A (1+z)^3 + (1 - A) (1+z)^(4 - 2/gamma), A = 2 Omega_m / (2 - gamma),

so the dark sector behaves as a power law in (1+z) whose exponent the single parameter gamma_rde sets. Flatness fixes the normalization: E(0) = 1 identically, for every gamma.

Reading the exponent is the quickest way to see what the model does. gamma = 1/2 gives (1+z)^0, a constant dark-energy density – so the model is LCDM there, though with an effective matter density A = (4/3) Omega_m rather than Omega_m, because part of the Ricci density scales like matter. Below that the exponent is negative and the dark energy grows into the future; above it the density falls with redshift like a decaying component. Fits have consistently preferred gamma slightly above 1/2 – and, more awkwardly, a low matter density: this model wants Omega_m ~ 0.22 where everything else in this library wants 0.31, which is its main observational problem rather than a detail.

Caveats

Its perturbations are outside what a standard Boltzmann code solves, so it is refused by CAMBBackend; use the compressed distance priors for its CMB constraint.

Flat universes only, for the same reason as HDE: the closed form above is derived from the flat Friedmann equation, and curvature changes the Ricci scalar the cutoff is built from rather than adding a term.

References

Gao, Chen, Shen & Saridakis (2009), Phys. Rev. D 79, 043511, arXiv:0712.1394.

__init__(params)

Parameters:

params (CosmologyParameters)

Methods

E(z)
H(z)
Omega_de(z)	Dark-energy density in units of today's critical density -- E(z)^2 - Omega_m (1+z)^3, as every other model here returns, so that Omega_de(0) = 1 - Omega_m.
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.
gamma_rde
h	Reduced Hubble constant, H0 / 100.
ln1e10As
m_nu
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)