Broken scale invariance, $\alpha$-attractors and vector impurity
  We show that if the $\alpha$-attractor model is realized by the spontaneous
breaking of the scale symmetry, then the stability and the dynamics of the
vector field that gauges the scale symmetry can severely constrain the
$\alpha$-parameter as $5/6 < \alpha < 1$ restricting the inflationary
predictions in a very tiny region in the $n_s - r$ plane that are in great
agreement with the latest Planck data. Although the different values of
$\alpha$ do not make a tangible difference for $n_s$ and $r$, they provide
radically different scenarios for the post-inflationary dynamics which
determines the standard BBN processes and the large scale isotropy of the
universe.
