  It is well known that the renormalization group equations depend on the scale
where they are applied. This phenomenon is especially relevant for the massive
fields in curved space, because the decoupling effects may be responsible for
important cosmological applications like the graceful exit from the inflation
and low-energy quantum dynamics of the cosmological constant. We investigate,
using both covariant and non-covariant methods of calculations and
mass-dependent renormalization scheme, the vacuum quantum effects of a massive
scalar field in curved space-time. In the higher derivative sector we arrive at
the explicit form of decoupling and obtain the beta-functions in both UV and IR
regimes as the limits of general expressions. For the cosmological and Newton
constants the corresponding beta-functions are not accessible in the
perturbative regime and in particular the form of decoupling remains unclear.
