Inflation and nonminimal scalar-curvature coupling in gravity and supergravity

Inflationary slow-roll dynamics in Einstein gravity with a nonminimal scalar-curvature coupling can be equivalent to that in the certain f(R) gravity theory. We review the correspondence and extend it to N=1 supergravity. The nonminimal coupling in supergravity is rewritten in terms of the standard ('minimal') N=1 matter-coupled supergravity by using curved superspace. The established equivalence between two different inflationary theories means the same inflaton scalar potential, and does not imply the same post-inflationary dynamics and reheating.