pyWMAP

A WMAP likelihood implementation for Cobaya. This code is a python adaptation of a subset of the publicly available WMAP v5 likelihood (Bennet et al., 2012) retaining only data in temperature and high-l polarization. This allows to use WMAP data in combination with low-l polarization data from Planck or e.g., using a tau prior as done in the ACT DR4 analysis (Aiola et al., 2020). The relevant terms of the original WMAP v5 likelihood needed for this -- and that have been implemented in this adaptation of the code -- are the high-ell TT/TE/EE master components and the low-ell TT. To fully remove the TE data at low-ell the minimum multipole in TE needs to be set to ell=24 (otherwise the code uses master TE data from ell=2) and this then requires to remove the beam term in TT (the original code gives a matrix inversion error if not). The beam/pointsource correction terms and the high-l TB likelihood are also implemented in this code but disabled by default. The low-ell polarization part of the likelihood has not been implemented since better Planck data are available at those scales. This adaptation can be cross-checked with the original code setting to False the "use_lowl_pol" and "use_TT_beam_ptsrc" flags and setting "temin=24". This code has been coupled to Cobaya and provides identical results in likelihood/cosmological parameters compared to what can be obtained with the original code coupled to Cosmomc.

Installation

Clone the git with

git clone https://github.com/HTJense/pyWMAP <path/to/download>

You can install the likelihood by running

pip install [-e] <path/to/download>

where the -e flag is an option you can use if you intend to modify the code yourself. This will install the package for you.

To download the WMAP v5 data that is used for the likelihood, you need to install the likelihood with cobaya, as:

cobaya-install wmaplike.WMAPLike

This will download the WMAP data into your packages path set by your cobaya environment (this will take a while).

You can test your installation afterwards with

pytest -v

If all went well, you should see a bunch of "passed" tests in your console log.

Usage

To use the likelihood, two sample .yaml file are included. The file eval_wmap.yaml will evaluate WMAP at the best-fitting cosmology as reported in table 2 of Hinshaw et al. 2012. It should give a chi-square value of 5625.25.

The file mcmc_wmap.yaml will run a simple MCMC chain with the likelihood. It included a prior on tau, since there is no low-l polarization component to constrain the tau/As degeneracy.

Settings

WMAP comes with the following settings. They are all copied, verbatim, from the original wmap_v5 likelihood. You can check the description given in the WMAPLike.yaml file for descriptions.

• use_lowl_TT and use_gibbs: whether or not to use the low-ell temperature data, and whether or not to evaluate it using Dunkley et al. 2008's gibbs sampling method. Note that disabling use_gibbs is, as of writing, not implemented. It should refer to using the pixel likelihood, but this is not included as the gibbs sampler is faster and does not noticably affect the results.

• use_lowl_pol: whether or not to include the low-ell polarisation data. This is commonly replaced by a prior on tau. Should you do this, it is advised to set temin: 24 as well, since this likelihood mimics the original WMAP's likelihood's behaviour of setting it to 2 by default.

• use_lowl_TBEB: whether or not to include the low-l TB and EB data. Note that this function is currently not implemented and will raise an exception if you enable it.

• use_highl_TT, use_highl_TE, and use_highl_TB: whether to enable the high-l MASTER TT/TE/TB likelihoods. By default, only TT and TE are included, but TB is implemented and can be enabled if you wish.

• use_highl_TT_beam_ptsrc: whether or not to include the beam and pointsource correction terms in the likelihoods. By default, these dare disabled, but they are implemented, but they do include a small mistake in the calculation.

• use_sz: whether or not to include the SZ template implemented in the CosmoMC implementation of the WMAP likelihood. If you do this, you can point the likelihood to a sz_filename (it will download the LAMBDA-provided template if it cannot find any), and you can sample over the SZ amplitude A_sz.

• The ttmin, ttmax, temin and temax parameters refer to the range of l-modes that should be considered by the likelihood. Note that the temin and temax parameters are also used by the B-modes.

The remainder of the settings mostly refer to names of files. You can modify these if you wish.

The best-fitting v5 Theory

Packaged with the likelihood is the WMAPBestFitv5 theory code that simply returns the best-fitting power spectrum that was included in the wmap_v5 likelihood. It has one parameter, cl_amp, that simply scales the entire power spectrum up or down. If you want to include it, simply replace your camb or classy theory code by WMAPBestFitv5.