Planck PR4 TTTEEE+lowE+lensing Early ΛCDM Parameter Chains

This repository contains the early ΛCDM cosmological parameter chains derived from the Planck from the paper "CMB Constraints on the Early Universe Independent of Late-Time Cosmology" by Pablo Lemos and Antony Lewis (arXiv:2302.12911).

Overview

The early ΛCDM parameter chains allow for robust constraints on the early universe's physics while being minimally influenced by assumptions about late-time cosmology. By leveraging empirical constraints on CMB lensing and weak priors on integrated effects such as the Sachs-Wolfe effect and foreground contributions, these chains provide insights into the early universe that are independent of the complexities of late-time structure growth.

Data

The chains were generated using Cobaya and use:

• Planck PR4 CamSpec likelihood
• Temperature and polarization data (TTTEEE) at ℓ ≥ 30
• Low-ℓ EE polarization data
• Planck PR4 lensing likelihood

Methodology

Parameters are constrained using an approach that:

• Models CMB lensing empirically using a spline fit to the lensing power spectrum
• Excludes low-ℓ temperature data (ℓ < 30) to avoid ISW sensitivity
• Models residual ISW at ℓ ≥ 30 with a template
• Uses empirical foreground templates
• Treats reionization through a single τ parameter

Usage

Chains can be analysed or visualized using GetDist.

The .covmat file has the parameter covariance for Gaussian approximations.

To use a simple Gaussian approximation to the likelihood in Cobaya you can use gaussian_mixture, e.g. for 3-parameters

likelihood:
   gaussian_mixture:
     means: [[1.04103e-2, 0.02223, 0.1192]]
     covs: [[ 6.62099420e-12,  1.24442058e-10, -1.31731741e-09],
            [ 1.24442058e-10,  2.13441666e-08, -1.15345007e-07],
            [-1.31731741e-09, -1.15345007e-07,  1.69776300e-06]]
     input_params: ['thetastar', 'ombh2', 'omch2']
     output_params: []

You can calculate means and covariances from the the chains using getdist, e.g.

from getdist import loadMCSamples
samples = loadMCSamples('./spline_planck_PR4_TTTEEE_lowE_lensing_ISW',
                        settings={'ignore_rows': 0.3})
samples.addDerived(samples['thetastar']/100, 'thetaunscaled')

print(samples.mean(['thetaunscaled','ombh2','omch2']))
print(samples.cov(['thetaunscaled','ombh2','omch2']))

Note that theta values stored in the chain are scaled by 100.

Citation

If you use these chains or the associated analyses in your work, please cite:

@article{Lemos:2023xhs,
    author = "Lemos, Pablo and Lewis, Antony",
    title = "{CMB constraints on the early Universe independent of late-time cosmology}",
    eprint = "2302.12911",
    archivePrefix = "arXiv",
    primaryClass = "astro-ph.CO",
    doi = "10.1103/PhysRevD.107.103505",
    journal = "Phys. Rev. D",
    volume = "107",
    number = "10",
    pages = "103505",
    year = "2023"
}
}