The quantum dynamics of the flat Friedmann-Lemaitre-Robertson-Walker and
Bianchi I models defined by loop quantum cosmology have recently been
translated into a spinfoam-like formalism. The construction is facilitated by
the presence of a massless scalar field which is used as an internal clock. The
implicit integration over the matter variable leads to a nonlocal spinfoam
amplitude. In this paper we consider a vacuum Bianchi I universe and show that
by choosing an appropriate regulator a spinfoam expansion can be obtained
without selecting a clock variable and that the resulting spinfoam amplitude is
local.Comment: 12 page
