CosmoFit.LsCDM¶

class CosmoFit.LsCDM(params)[source]¶

Bases: Cosmology

Lambda_s CDM (Akarsu et al. 2021): LCDM, except that the cosmological constant changes sign at a redshift z_dagger.

E(z)^2 = Omega_m (1+z)^3 + Omega_k (1+z)^2

Omega_Ls0 sgn(z_dagger - z)

Below z_dagger this is ordinary LCDM with a positive (de Sitter) Lambda. Above it, Lambda is negative – an anti-de Sitter vacuum – which suppresses the expansion rate in the pre-transition universe.

Why a discontinuous model is taken seriously¶

It looks like a hack, and the mechanism (a rapid AdS-to-dS vacuum transition, as in graduated dark energy or certain string-swampland constructions) is genuinely speculative. What earns it a place is that it addresses the H0 and S8 tensions and the BAO sound-horizon problem with a single parameter, by the one route that is otherwise hard to arrange: a lower expansion rate before z_dagger ~ 2 shrinks the sound horizon r_d, and a smaller r_d raises the H0 inferred from a fixed BAO angular scale. Parametrizations that only alter late-time dark energy cannot do this, because they leave r_d untouched.

The extra parameter is z_dagger, with fits typically preferring z_dagger ~ 1.7-2.3.

Numerical note¶

E(z) is genuinely discontinuous at z_dagger – that is the model, not an artifact. The comoving distance chi(z) = int dz/E remains continuous (it acquires a kink, not a jump), but the trapezoidal grid in DistanceIntegrator smears the step across one grid cell. Measured against a piecewise-exact integration that splits the integral at z_dagger, the resulting error in chi is below 1e-4 relative – an order of magnitude under the precision of any dataset in this library. It is quantified rather than assumed; see tests/test_models.py.

dEdz returns the derivative of the smooth part only. The distributional delta at the transition is not representable as a float and is not used by anything: chi integrates E rather than differentiating it, and the deceleration parameter q(z) is undefined exactly at a discontinuity anyway.

References

Akarsu, Kumar, Ozulker & Vazquez (2021), “Relaxing cosmological tensions with a sign switching cosmological constant”, Phys. Rev. D 104, 123512, arXiv:2108.09239.

Akarsu, Kumar, Ozulker, Vazquez & Yadav (2023), Phys. Rev. D 108, 023513, arXiv:2211.05742 (updated constraints).

__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).

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`
`z_dagger`

Parameters:: params (CosmologyParameters)