In a theory where a global breaking of supersymmetry (F-type) occurs at a scale f, I discuss dynamical breaking of local supersymmetry (supergravity) without invoking other matter fields except condensates of gravitinos, formed dynamically. The goldstino associated with the global SUSY breaking is absorbed by the gravitino, the SUSY partner of graviton, which thus becomes massive via the formation of condensates at the non-trivial minima of the (one-loop) effective potential. The condensates are a result of four-gravitino (torsion) interaction terms in the supergravity action. The gravitons remain exactly massless, and thus local supersymmetry breaks dynamically. Such processes in the early Universe may lead to inflation, which for Jordan-frame supergravity models (with broken conformal symmetry) may fit the Planck data excellently. The inflaton in this minimal scenario is associated with the massive gravitino-condensate field. Under some circumstances, a Starobinsky-type inflation may also appear in the massive gravitino phase, that succeeds the above-described first inflation. This can also fit the Planck data very well. The importance of the above scenarios lies on the fact that the inflaton is a composite field and all the relevant scales arise dynamically, that is appear consistently in the solution of the pertinent Dyson-Schwinger equations that underlie the dynamical supergravity breaking.