Speaker
Description
In this work, we study the effective potential for non-renormalizable general and SO(N) symmetric scalar theories in curved space-time. We discuss a method for finding all-loop corrections in the leading logarithmic approximation, which incorporates the non-minimal coupling with gravity within the linear curvature approximation.
Using the Bogoliubov-Parasyuk theorem, we derive recurrence relations connecting different orders of loop correction contributions. Based on these relations, we obtain generalized renormalization group equations for the effective potential describing contributions on both flat and curved backgrounds. The developed approach is applicable to an arbitrary classical interaction potential. As an example, we analyze the simplest power-law potentials. It is shown that the obtained effective potentials can be considered in the theory of cosmological inflation. Finally, we calculate the cosmological parameters for these models and compare them with the observational data.
