CosmoFit.RunningVacuum

class CosmoFit.RunningVacuum(params)

Bases: Cosmology

Running Vacuum Model: a cosmological “constant” that runs with the expansion rate,

Lambda(H) = c0 + 3 nu H^2

Solving the Friedmann and continuity equations together with this gives a closed form with no numerical integration:

E(z)^2 = 1 + Omega_k [(1+z)^2 - 1]

• (Omega_m / (1 - nu)) [(1+z)^{3(1-nu)} - 1]

and nu = 0 recovers curved LCDM exactly.

The idea comes from quantum field theory in curved spacetime, where the vacuum energy density is a running quantity obeying a renormalization-group equation, and nu is the beta-function coefficient – expected to be |nu| ~ 10^-3 from a one-loop estimate, which is why the default bounds here are tight compared to the wide-open priors on w0/wa. It is one of the few dark-energy models whose extra parameter has a predicted magnitude rather than an arbitrary one, so a fit that returns nu ~ 10^-3 means something quite different from one that returns nu ~ 0.1.

Mechanically the model works by making matter dilute slightly differently from (1+z)^3 – the exponent is 3(1 - nu) – because vacuum and matter exchange energy. That is a different lever from any w(z) parametrization, which leaves the matter scaling alone, and it means nu is constrained by anything sensitive to the matter density’s redshift evolution, growth data included.

Notes

nu = 1 is a coordinate singularity of the closed form above (the 1/(1 - nu) prefactor), far outside any physical prior; E() falls back to the nu -> 1 limit there rather than dividing by zero.

This is the simplest member of the RVM family. Fuller versions add an Hdot term (Lambda = c0 + 3 nu H^2 + alpha Hdot) or higher powers of H relevant to inflation; neither is implemented.

References

Sola (2013), J. Phys. Conf. Ser. 453, 012015, arXiv:1306.1527 (review).

Sola, Gomez-Valent & de Cruz Perez (2017), ApJ 836, 43, arXiv:1602.02103 (cosmological constraints).

Parameters:

params (CosmologyParameters)

__init__(params)

Parameters:

params (CosmologyParameters)

Methods

E(z)
H(z)
Omega_de(z)	The running vacuum density,
Omega_matter(z)	Omega_m (1+z)^{3(1-nu)} -- matter dilutes more slowly than in LCDM because the running vacuum is feeding it.
__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.
h	Reduced Hubble constant, H0 / 100.
ln1e10As
m_nu
n_s
nu
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