Effective potential in SO(N) symmetric scalar field theories in curved spacetime

In this paper, we derive recurrence relations for leading logarithmic all-loop quantum corrections in the case of [Formula: see text] symmetric scalar theory with an arbitrary potential in curved spacetime. On this basis, a system of renormalization group (RG) equations in the general approach is obtained for the effective potential in the large N limit. As a simple illustration, we analyze the case of power-like potentials in the Jordan frame and discuss their application to inflationary cosmology.