The early universe cosmology can be successfully described in the theoretical framework
of modified gravity and quintessence. I review the Starobinsky inflationary scenario in this
modern framework, in light of the recent (March 2013) observations by the PLANCK satellite
mission. I also briefly consider preheating and reheating after inflation, as well as their relation 
to the observational cosmology. Finally, some new recent theoretical results combining inflation,
lepto-genesis, dark matter and dark energy with supersymmetry are briefly outlined.