CosmoFit.LogarithmicDE

class CosmoFit.LogarithmicDE(params)

Bases: Cosmology

Logarithmic (Efstathiou) dark-energy parametrization,

w(z) = w0 + wa ln(1 + z)

with the resulting density evolution obtained by integrating the continuity equation exactly:

rho_de(z)/rho_de0 = (1+z)^{3(1+w0)}

exp[(3/2) wa ln^2(1+z)]

The fourth w0-wa parametrization in the library, alongside CPL, JBP and BA – and it is here because it fails differently from all three. CPL, JBP and BA all saturate: each has a finite w(z -> infinity), so none can express a dark energy whose equation of state keeps drifting. The logarithmic form does not saturate, which makes it the natural control case for asking whether a detected wa is telling you about the data or about the shape you assumed.

Efstathiou proposed it specifically as a better fit to quintessence models’ actual w(z) over 0 < z < 4 than a linear-in-z form, and it reuses the existing w0/wa parameters, so it drops into any w0-wa comparison – including the w0-wa plane figure – without new machinery.

Caveat

The ln^2(1+z) in the exponent grows without bound, so for wa > 0 the dark-energy density diverges faster than any power law at high redshift, and for wa < 0 it is driven to zero. Neither is pathological over the redshift range this library’s datasets cover (z < 2.5 for BAO/SNe), but it does mean the model should not be extrapolated to recombination – which is exactly why fitting it against the compressed "planck" distance priors (which integrate E(z) out to z ~ 1090) needs a sanity check on the resulting Omega_de(z*), not blind trust.

References

Efstathiou (1999), “Constraining the equation of state of the Universe from distant Type Ia supernovae and cosmic microwave background anisotropies”, MNRAS 310, 842, arXiv:astro-ph/9904356.

__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)

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

Parameters:

params (CosmologyParameters)