CosmoFit.PEDE

class CosmoFit.PEDE(params)

Bases: Cosmology

Phenomenologically Emergent Dark Energy (Li & Shafieloo 2019).

Omega_de(z) = Omega_de0 [1 - tanh(log10(1 + z))]

Dark energy that is absent at high redshift and “emerges” toward the present: the bracket goes to 0 as z grows and to 1 at z = 0, so the model has no dark-energy density during matter domination at all.

What makes it worth having in a library that already carries six dark-energy parametrizations is that it has no free parameter for dark energy whatsoever. CPL, JBP and BA each buy their extra flexibility with two parameters (w0, wa); PEDE has the same number of free parameters as LCDM – H0 and Omega_m – and a completely different expansion history. That makes the model comparison honest in a way a nested-model comparison is not: AIC/BIC penalties are identical, so a difference in chi2 is a difference in fit, full stop.

Its other claim is on the Hubble tension. The effective equation of state,

w(z) = -1 - (1 / (3 ln 10)) [1 + tanh(log10(1 + z))]

is phantom at every redshift and equals -1.145 today, which raises the inferred H0 for a CMB-anchored fit relative to LCDM. Whether that survives the full data set is exactly the kind of question this library exists to ask, not something to assert here.

Notes

Omega_de0 = 1 - Omega_m - Omega_k as usual, so E(z=0) = 1 holds identically, including for curved cases.

References

Li & Shafieloo (2019), “A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension”, ApJ 883, L3, arXiv:1906.08275.

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
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