  Using the renormalization group (RG) approach and the equivalency between the
class of gauge-Higgs-Yukawa models and the gauged Nambu-Jona-Lasinio (NJL)
model, we study the gauged NJL model in curved space-time. The behaviour of the
scalar-gravitational coupling constant $\xi(t)$ in both theories is discussed.
The RG improved effective potential of gauged NJL model in curved spacetime is
found. The curvature at which chiral symmetry in the gauged NJL model is broken
is obtained explicitly in a remarkably simple form. The powerful RG improved
effective potential formalizm leads to the same results as ladder
Schwinger-Dyson equations which have not been formulated yet in curved
spacetime what opens new possibilities in the study of GUTs and NJL-like models
in curved spacetime.
