  The Boltzmann-Nordheim equation is a modification of the Boltzmann equation,
based on physical considerations, that describes the dynamics of the
distribution of particles in a quantum gas composed of bosons or fermions. In
this work we investigate the Cauchy theory of the spatially homogeneous
Boltzmann-Nordheim equation for bosons, in dimension $d\geq 3$. We show
existence and uniqueness locally in time for any initial data in
$L^\infty\left(1+|v|^s\right)$ with finite mass and energy, for a suitable $s$,
as well as the instantaneous creation of moments of all order.
