CosmoFit.DGP

class CosmoFit.DGP(params)

Bases: Cosmology

Dvali-Gabadadze-Porrati braneworld gravity, self-accelerating branch.

E(z) = sqrt(Omega_rc + Omega_m (1+z)^3) + sqrt(Omega_rc) E(z)^2 -> that, plus Omega_k (1+z)^2 for a curved brane

Gravity leaks into a fifth dimension above a crossover scale r_c, weakening it at large distances. The universe then accelerates with no dark energy at all – there is no Omega_de term in the Friedmann equation above, and none in the theory. That is what distinguishes DGP from every dark-energy parametrization in this library: those add a fluid, this changes gravity.

Omega_rc = 1/(4 r_c^2 H0^2) is not free. The Friedmann constraint E(0) = 1 fixes it:

Omega_rc = (1 - Omega_k - Omega_m)^2 / (4 (1 - Omega_k))

so DGP, like PEDE, has exactly LCDM’s parameter count and a completely different expansion history – a fair comparison with no free parameter absorbing the difference.

Growth of structure

This model overrides mu(a, k) with the standard sub-horizon DGP result (Lue, Scoccimarro & Starkman 2004; Koyama & Maartens 2006):

mu = 1 + 1 / (3 beta), beta(a) = 1 - 2 H r_c [1 + Hdot / (3 H^2)]

On the self-accelerating branch beta < 0, so mu < 1 – gravity is weaker than in GR and structure grows more slowly. Today, for Omega_m = 0.3, mu ~ 0.72. This is the model’s real observational signature and the reason it is strongly disfavoured by growth data even where it can be tuned to fit distances: no dark-energy parametrization can suppress growth this way while keeping the same background.

Hdot / H^2 = -(1+z) E'(z) / E(z), built from this model’s own E/dEdz rather than from an LCDM approximation.

Caveats

The self-accelerating branch is known to carry a ghost instability in its scalar sector. It is implemented here as the historically and observationally important benchmark it is – the reference case against which “modified gravity can mimic dark energy” is tested – not as a viable theory. Its perturbations are also outside what a standard Boltzmann code solves, so it is refused by CAMBBackend; use the compressed distance priors for its CMB constraint.

References

Dvali, Gabadadze & Porrati (2000), Phys. Lett. B 485, 208, arXiv:hep-th/0005016.

Deffayet (2001), Phys. Lett. B 502, 199, arXiv:hep-th/0010186 (the cosmological solution).

Koyama & Maartens (2006), JCAP 01 (2006) 016, arXiv:astro-ph/0511634 (the growth of structure).

__init__(params)

Parameters:

params (CosmologyParameters)

Methods

E(z)
H(z)
Omega_de(z)	The effective dark-energy density this model's expansion history would be attributed to, if one insisted on writing it as GR plus a fluid:
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 gravitational coupling G_eff/G_N on the self-accelerating branch,
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
Omega_rc	The crossover-scale density parameter, Omega_rc = 1/(4 r_c^2 H0^2), fixed by E(0) = 1.
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)