  Scattering transforms are a new type of summary statistics recently developed
for the study of highly non-Gaussian processes, which have been shown to be
very promising for astrophysical studies. In particular, they allow one to
build generative models of complex non-linear fields from a limited amount of
data, and have also been used as the basis of new statistical component
separation algorithms. In the context of upcoming cosmological surveys, such as
LiteBIRD for the cosmic microwave background polarization or Rubin-LSST and
Euclid for study of the large scale structures of the Universe, the extension
of these tools to spherical data is necessary. We develop scattering transforms
on the sphere and focus on the construction of maximum-entropy generative
models of several astrophysical fields. We construct, from a single target
field, generative models of homogeneous astrophysical and cosmological fields,
whose samples are quantitatively compared to the target fields using common
statistics (power spectrum, pixel probability density function and Minkowski
functionals). Our sampled fields agree well with the target fields, both
statistically and visually. These generative models therefore open up a wide
range of new applications for future astrophysical and cosmological studies;
particularly those for which very little simulated data is available. We make
our code available to the community so that this work can be easily reproduced
and developed further.
