All-loop effective potential for arbitrary scalar models in curved space-time

In this paper we calculate the leading divergences of the effective potential for an arbitrary scalar theory on a curved spacetime background. Based on the recurrence relation between the leading poles following from the locality condition, we obtain a system of generalised renormalisation-group equations that can be studied numerically or analytically in some special cases. We study the simplest effective potentials for power-like models and give a comparison of them in the framework of cosmological phenomenology.