Connecting early and late universe by $f(R)$ gravity
  Inflation and dark energy are two of the most relevant aspects of modern cosmology. These different epochs provide the universe is passing through accelerated phases soon after the Big-Bang and at present stage of its evolution. In this review paper, we discuss that both eras can be, in principle, described by a geometric picture, under the standard of $f(R)$ gravity. We give the fundamental physics motivations and outline the main ingredients of $f(R)$ inflation, quintessence and cosmography. This wants to be a quick summary of $f(R)$ paradigm without claiming of completeness. 
Salvatore Capozziello, Mariafelicia De Laurentis, Orlando Luongo
gr-qc astro-ph.CO hep-th