Abstract
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 α-attractors in the context of quintessential inflation.
Highlights
A long time ago, humans raised their eyes to the sky and started to try to understand everything that was around: the whole universe
We 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
Modern cosmology is based on Einstein’s equations (EE) of general relativity (GR), which relates the geometry of spacetime—a four-dimensional manifold—with the matter/energy it contains in the following way: “matter tells spacetime how to curve and spacetime tells test particles how to move”
Summary
A long time ago, humans raised their eyes to the sky and started to try to understand everything that was around: the whole universe. This constant is at the heart of the famous Λ cold dark matter model, which is presently the standard cosmological model used by many scientists to depict our universe. The importance of dark matter on a cosmological level, e.g., for the formation of large-scale structures in the universe, cannot be underestimated It can provide a better picture of the current state of the art of the Big Bang cosmological model (for easy-to-follow references, see [47–49]). This is the reason why other forms of dark energy have been introduced, in order to deal with this issue One of these proposals is quintessence, which we review in the context of quintessential inflation: a theory that aims at unifying the early and the late-time accelerated phases of our universe. The temperature of the universe one second after the Big Bang is around 10−3 GeV or 10−21 Mpl, which, in IS units, is approximately 108 K
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