PolyBin

PolyBin is a Python code that estimates the binned power spectrum, bispectrum, and trispectrum for full-sky HEALPix maps such as the CMB, using the algorithms of Philcox 2023a and Philcox 2023c. This can include both spin-0 and spin-2 fields, such as the CMB temperature and polarization, or galaxy positions and galaxy shear. Alternatively, one can use only scalar maps. For each statistic, two estimators are available: the standard (ideal) estimators, which do not take into account the mask, and window-deconvolved estimators. In the second case, we require computation of a Fisher matrix; this depends on binning and the mask, but does not need to be recomputed for each new simulation. For the bispectrum and trispectrum, we can compute both the parity-even and parity-odd components, accounting for any leakage between the two.

PolyBin contains the following modules:

• pspec: Binned power spectra
• bspec: Binned bispectra
• tspec: Binned trispectra

For usage details, see the Tutorial.

In the planck directory, we include measurements and analysis of the Planck parity-odd temperature trispectrum, as in Philcox 2023b. The scalar branch contains legacy scalar-only code from the Philcox 2023a paper (without a number of optimizations).

Authors

• Oliver Philcox (Columbia / Simons Foundation)

Dependencies

• Python 3
• healpy, pywigxjpf, fitsio, tqdm (pip installable)
• pixell [optional, for faster SHTs with libsharp]

References

Code references:

1. Philcox, O. H. E., "Optimal Estimation of the Binned Mask-Free Power Spectrum, Bispectrum, and Trispectrum on the Full Sky: Scalar Edition", (2023) (arXiv)
2. Philcox, O. H. E., "Optimal Estimation of the Binned Mask-Free Power Spectrum, Bispectrum, and Trispectrum on the Full Sky: Tensor Edition", (2023) (arXiv)

List of papers using Polybin:

1. Philcox, O. H. E., "Do the CMB Temperature Fluctuations Conserve Parity?", (2023) (arXiv)
2. Philcox, O. H. E., Shiraishi, M., "Testing Parity Symmetry with the Polarized Cosmic Microwave Background", (2023) (arXiv)
3. Philcox, O. H. E., Shiraishi, M., "Testing Graviton Parity and Gaussianity with Planck T -, E- and B-mode Bispectra", (2023) (arXiv)