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 ; "J.d.H. is supported by grant MTM2017-84214-C2-1-P, funded by MCIN/AEI/10.13039/501100011033, and by "ERDF A way of making Europe". E.E. is supported by MICINN (Spain), project PID2019-104397GB-I00, of the Spanish State Research Agency program AEI/10.13039/501100011033, and by the program Unidad de Excelencia María de Maeztu CEX2020-001058-M. Both authors are also supported in part by the Catalan Government, AGAUR project 2017-SGR-247" ; Peer Reviewed ; Postprint (published version)