The universe during epochs of accelerating expansion

Cosmic inflation, the accelerated expansion of the early Universe, is an accepted pillar in the foundations of modern cosmology. This is due mainly to its success at explaining several anomalies between observations and the existing Hot Big Bang model of the Universe, but a specific model is not agreed upon in the literature. The Universe has also recently been observed to enter another phase of accelerating expansion, driven by an unexplained mechanism called ‘dark energy’. The research presented in this thesis grows organically; starting with an investigation into novel inflationary models and developing into quintessential inflation models. The latter explain both the primordial inflation and dark energy observations using one minimal framework. A new family of inflation models is presented, which excellently match observations for natural parameter values, and a derivation from supergravity is demonstrated. A period of thermal inflation allows the supergravity realisation of hybrid inflation to be realigned with observations. A new approach to inflection-point inflation is developed, which is considerably less fine-tuned and exotic than previous models. Two novel quintessential inflation models are introduced, the first embedded in α-attractors - a compelling framework of inflationary model building and the second in Gauss-Bonnet gravity - an extension to General Relativity. Detailed investigations of reheating after inflation are undertaken, focusing on gravitational reheating and instant preheating, analysing the necessary constraints including those from supergravity. Along the way, there is a brief diversion into primordial black holes, investigating how a slow reheating period affects their formation rates.