Topics in Cosmology Clearly Explained by Means of Simple Examples

This is a very comprehensible review of some key issues in modern cosmology. Simple mathematical examples and analogies are used, whenever available. The starting point is the well-known Big Bang cosmology (BBC). We deal with the mathematical singularities appearing in this theory and discuss some ways to remove them. Next, and before introducing the inflationary paradigm by means of clear examples, we review the horizon and flatness problems of the old BBC model. We then consider the current cosmic acceleration and, as a procedure to deal with both periods of cosmic acceleration in a unified way, we study quintessential inflation. Finally, the reheating stage of the universe via gravitational particle production, which took place after inflation ended, is discussed in clear mathematical terms, by involving the so-called a-attractors in the context of quintessential inflation.

Automated summary

This is a clear review of some key issues in modern cosmology, where the author uses simple mathematical examples and analogies to aid in understanding. The paper discusses the mathematical singularities in the Big Bang cosmology theory and proposes methods to address them. It also reviews the horizon and flatness problems of the old cosmology model and discusses the current cosmic acceleration. The paper concludes by discussing the reheating stage of the universe after inflation ends.