Some topics in Cosmology -- Clearly explained by means of simple examples --

TL;DR

This paper provides a clear, example-based review of key cosmological concepts, including Big Bang singularities, inflation, cosmic acceleration, and reheating, making complex ideas accessible through simple mathematics and analogies.

Contribution

It offers an accessible, example-driven overview of modern cosmology topics, including singularities, inflation, and reheating, with simplified mathematical explanations and analogies.

Findings

Discussion of methods to remove Big Bang singularities

Explanation of inflationary problems with simple examples

Analysis of reheating via gravitational particle production

Abstract

This is a very comprehensible review of some key issues in Modern Cosmology. Simple mathematical examples and analogies are always used, whenever available. The starting point is the well know 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 some 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 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 simple mathematical terms, by involving the so-called $\alpha$-attractors in the context of quintessential inflation.