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. 
Ozgur Akarsu, Sibel Boran, Emre O. Kahya, Nese Ozdemir, Mehmet Ozkan
astro-ph.CO gr-qc hep-th