Title: Non-canonical Conformal Attractors for Single Field Inflation,
Abstract: We extend the idea of conformal attractors in inflation to non-canonical
sectors by developing a non-canonical conformally invariant theory from two
different approaches. In the first approach, namely, ${\cal N}=1$ supergravity,
the construction is more or less phenomenological, where the non-canonical
kinetic sector is derived from a particular form of the K$\ddot{a}$hler
potential respecting shift symmetry. In the second approach i.e.,
superconformal theory, we derive the form of the Lagrangian from a
superconformal action and it turns out to be exactly of the same form as in the
first approach. Conformal breaking of these theories results in a new class of
non-canonical models which can govern inflation with modulated shape of the
T-models. We further employ this framework to explore inflationary
phenomenology with a representative example and show how the form of the
K$\ddot{a}$hler potential can possibly be constrained in non-canonical models
using the latest confidence contour in the $n_s-r$ plane given by Planck.