Broken scale invariance, $α$-attractors and vector impurity

Abstract

We show that if the α-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 α-parameter as 5/6 < α < 1 restricting the inflationary predictions in a very tiny region in the ns −r plane that are in great agreement with the latest Planck data. Although the different values of α do not make a tangible difference for ns 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.

Superconformal generalizations of auxiliary vector modified polynomial f(R) theories

“…For example, in the superconformal construction of the α-attractors, the α parameter is a measure of the curvature of the inflaton Kähler manifold [22]. This parameter also appears in other contexts such as the string field theory approach [24], spacetime with vector distortion [25], and scale-invariant gravity [26,27]. A particular approach, called the auxiliary vector modification [28], refers the α parameter as the Brans-Dicke parameter ω BD by replacing the Ricci scalar R with an auxiliary vector modified Ricci scalar…”