Some like it triaxial: the universality of dark matter halo shapes and
  their evolution along the cosmic time
  We present a detailed analysis of dark matter halo shapes, studying how the
distributions of ellipticity, prolateness and axial ratios evolve as a function
of time and mass. With this purpose in mind, we analysed the results of three
cosmological simulations, running an ellipsoidal halo finder to measure
triaxial halo shapes. The simulations have different scales, mass limits and
cosmological parameters, which allows us to ensure a good resolution and
statistics in a wide mass range, and to investigate the dependence of halo
properties on the cosmological model. We confirm the tendency of haloes to be
prolate at all times, even if they become more triaxial going to higher
redshifts. Regarding the dependence on mass, more massive haloes are also less
spherical at all redshifts, since they are the most recent forming systems and
so still retain memory of their original shape at the moment of collapse. We
then propose a rescaling of the shape-mass relations, using the variable $\nu =
\delta_{c}/\sigma$ to represent the mass, which absorbs the dependence on both
cosmology and time, allowing to find universal relations between halo masses
and shape parameters (ellipticity, prolateness and the axial ratios) which hold
at any redshift. This may be very useful to determine prior distributions of
halo shapes for observational studies.
