On Adiabatic Renormalization with a Physically Motivated Infrared
  Cut-Off
  We introduce a new approach to renormalize physical quantities in curved
space-time by adiabatic subtraction. We use a comoving infrared cut-off in
defining the adiabatic counterpart of the physical quantity under
consideration, building on the fact that the adiabatic approximation is
ill-defined in the infrared tail of the spectrum. We show how this infrared
cut-off should be used to obtain a completely well-defined renormalization
scheme and how it is fundamental to avoid unphysical divergences that can be
generated by a pathological behavior of the adiabatic subtraction extended to
the infrared tail. The infrared cut-off appears as a new degree of freedom
introduced in the theory and its actual value has to be consistently fixed by a
physical prescription. As an example, we show how such degree of freedom can be
set to obtain the correct value of the conformal anomaly in the symptomatic
case of an inflationary model with gauge fields coupled to a pseudo-scalar
inflaton.
