We briefly discuss cosmic inflation, which is the dominant paradigm for the generation of the large scale structure in the Universe and also for arranging for the initial conditions of the hot Big Bang. We then present quintessential inflation, which also accounts of the observed dark energy. We discuss how quintessential inflation can be successfully modelled in modified gravity in the Palatini formalism. Finally, we focus on the generation of primordial gravitational waves by inflation and how their spectrum can be enhanced when the early Universe goes through periods of stiff equation of state. This results in gravitational waves with a characteristic spectrum, which may well be observed in the near future, providing insights for the background theory.