It  is  generally accepted that, at the very
early  stage  of its evolution, the Universe has
undergone  a period of rapid, almost exponential
growth,  christened  inflation.  The  details of
this  process are largely unknown, and there are
lots   of  diverse  theoretical  models  on  the
market,  with  some of them stemming from string
theory.  However, one common feature in all this
plentitude  is a special scalar field (inflaton)
which   slowly  rolls  down  its  potential  and
provides  a  dynamical  mechanism of accelerated
expansion.   Unfortunately,  there  are  serious
stumbling  blocks  in  the way of any attempt to
employ  non-zero  spin  fields for this purpose.
First  of  all,  one  faces  a break-down of the
slow-roll  conditions and also a strong unwanted
anisotropy  of  expansion.  In this talk we will
present  an  original  attempt  to  overcome the
problems  and  make  a model with massive vector
inflatons.  Approximate  isotropy is achieved by
use   of   multiple  vector  fields,  while  the
slow-roll  conditions  can  be  satisfied due to
non-minimal  interaction  with  gravity. Then we
will  also  reveal  the  fatal  stability issues
which,  contrary  to some other opinions, do not
allow us to deem this attempt a successful model
of non-scalar inflation.