  One well known method of generating a large blue spectral index for axionic
isocurvature perturbations is through a flat direction not having a quartic
potential term for the radial partner of the axion field. In this work, we show
how one can obtain a large blue spectral index even with a quartic potential
term associated with the Peccei-Quinn symmetry breaking radial partner. We use
the fact that a large radial direction with a quartic term can naturally induce
a conformal limit which generates an isocurvature spectral index of 3. We point
out that this conformal representation is intrinsically different from both the
ordinary equilibrium axion scenario or massless fields in Minkowski spacetime.
Another way to view this limit is as a scenario where the angular momentum of
the initial conditions slows down the radial field or as a superfluid limit.
Quantization of the non-static system in which derivative of the radial field
and the derivative of the angular field do not commute is treated with great
care to compute the vacuum state. The parametric region consistent with axion
dark matter and isocurvature cosmology is discussed.
