CosmoFit.GEDE

class CosmoFit.GEDE(params)

Bases: Cosmology

Generalized Emergent Dark Energy (Li & Shafieloo 2020).

Omega_de(z) = Omega_de0
              * [1 - tanh(Delta log10((1+z)/(1+z_t)))]
              / [1 + tanh(Delta log10(1 + z_t))]

The one-parameter family that contains both of the models it generalizes, which is what makes it useful:

• Delta -> 0 gives a constant Omega_de – LCDM.

• Delta = 1, z_t = 0 gives PEDE.

So a fit for Delta is a direct, continuous test of how far the data pushes away from a cosmological constant, with LCDM sitting at a specific value of a real parameter rather than at the boundary of a different model. Delta controls how sharply dark energy emerges; z_t sets when.

The denominator is not decoration – it is the normalization that enforces Omega_de(z=0) = Omega_de0 for any (Delta, z_t), and hence E(z=0) = 1. Dropping it (an easy transcription slip) leaves a model that silently violates the Friedmann constraint by tens of percent.

Notes

In Li & Shafieloo’s original presentation z_t is a derived quantity – the redshift at which the dark-energy and matter densities are equal – fixed by Delta and Omega_m rather than sampled. Here it is a free parameter, which is the form used in most follow-up work: it makes the model a genuine two-parameter extension that can be compared against CPL on equal footing, at the cost of the two being somewhat degenerate.

References

Li & Shafieloo (2020), “Evidence for Emergent Dark Energy”, ApJ 902, 58, arXiv:2001.05103.

Parameters:

params (CosmologyParameters)

__init__(params)

Parameters:

params (CosmologyParameters)

Methods

E(z)
H(z)
Omega_de(z)
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).
w(z)	Effective dark-energy equation of state,

Attributes

A_planck
A_s
Delta
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_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
z_t