WarmAndFuzzy: the halo model beyond CDM
  Cold dark matter (CDM) is a well established paradigm to describe
cosmological structure formation, and works extraordinarily well on large,
linear, scales. Progressing further in dark matter physics requires being able
to understand structure formation in the non-linear regime, both for CDM and
its alternatives. This short note describes a calculation, and accompanying
code, WarmAndFuzzy, incorporating the popular models of warm and fuzzy dark
matter (WDM and FDM) into the standard halo model to compute the non-linear
matter power spectrum. The FDM halo model power spectrum has not been computed
before. The FDM implementation models ultralight axions and other scalar fields
with $m_a\approx 10^{-22}\text{ eV}$. The WDM implementation models thermal WDM
with mass $m_X\approx 1\text{ keV}$. The halo model shows that differences
between WDM, FDM, and CDM survive at low redshifts in the quasi-linear and
fully non-linear regimes. The code uses analytic transfer functions for the
linear power spectrum, modified collapse barriers in the halo mass function,
and a modified concentration-mass relationship for the halo density profiles.
Modified halo density profiles (for example, cores) are not included, but are
under development. Cores are expected to have very minor effects on the power
spectrum on observable scales. Applications of this code to the Lyman-$\alpha$
forest flux power spectrum and the cosmic microwave background lensing power
spectrum will be discussed in companion papers. \textsc{WarmAndFuzzy} is
available online at \url{https://github.com/DoddyPhysics/HMcode}, where
collaboration in development is welcomed.
