CosmoFit.IDE¶

class CosmoFit.IDE(params)[source]¶

Bases: Cosmology

Interacting Dark Energy: dark matter and dark energy exchange energy, with a coupling Q = 3 xi H rho_de.

The two dark components are only ever observed gravitationally, so nothing forbids them from interacting – and if they do, the “coincidence problem” (why are their densities comparable now?) softens, because the ratio rho_de/rho_c evolves more slowly than in LCDM.

The continuity equations,

rho_de' + 3(1+w0) rho_de = -3 xi rho_de
rho_c'  + 3 rho_c        = +3 xi rho_de      (' = d/dln a)

have a closed-form solution, so this model costs no numerical integration:

E(z)^2 = (Omega_m - C) (1+z)^3
         + (Omega_de0 + C) (1+z)^{3(1+w0+xi)}
         + Omega_k (1+z)^2,
C = -xi Omega_de0 / (w0 + xi)

xi > 0 transfers energy from dark energy to dark matter; xi < 0 the other way. xi = 0 recovers WCDM exactly (C = 0), and xi = 0, w0 = -1 recovers LCDM.

Why it is interesting beyond the coincidence problem: an interaction changes how matter dilutes, which no w(z) parametrization does. That gives it a distinct signature in growth-of-structure data, and it is one of the few extensions that can move H0 and S8 in opposite directions – which is what resolving both tensions at once requires.

Parameters:

xi – Coupling strength. Prior bounds default to (-0.5, 0.5); realistic constraints are |xi| < 0.1.
params (CosmologyParameters)

Notes

The interaction is applied to the whole of ``Omega_m``, not to cold dark matter alone. Strictly, only the dark sector should couple – baryons are tightly constrained not to. This library’s background parametrization carries a single Omega_m, and splitting it here would introduce a baryon component that no other model has and that no background probe could distinguish anyway. The resulting difference is Omega_b/Omega_m ~ 16% of the coupling’s effect, which matters for a precision claim about xi and does not for the shape of E(z). Stated rather than hidden.

w0 + xi = 0 is a genuine singularity of the closed form (a resonance where the particular solution degenerates); the C-term limit is taken analytically there instead of dividing by zero.

References

Amendola (2000), Phys. Rev. D 62, 043511, arXiv:astro-ph/9908023 (coupled dark energy).

Wang, Abdalla, Atrio-Barandela & Pavon (2016), Rept. Prog. Phys. 79, 096901, arXiv:1603.08299 (review).

__init__(params)¶

Parameters:: params (CosmologyParameters)

Methods

`E`(z)
`H`(z)
`Omega_de`(z)
`Omega_matter`(z)	`(Omega_m - C)(1+z)^3 + C (1+z)^{3(1+w0+xi)}` -- the matter density with the interaction's transfer term included.
`__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)	Dark-energy equation of state, constant at `w0`.

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`
`xi`