#### An ebook in cosmology

According to the modern cosmology, our universe has begun with a Big Bang and it has gone into different phases through its expansion over time. Just after the Big Bang, when it was at the planck scale, the universe expanded exponentially to the astronomical scale, that is called inflation. Inflation happened in a very brief period of time and when it ended the age of our universe was about 10^{-33} to $ 10^{-32} seconds.

Inflation of the early universe is proposed in order to solve the issues with the Big Bang theory, for instance flatness problem, and isotropy and homogeneity of the universe in large scale. After inflation, radiation, and then dark and ordinary matters dominated our universe; these fluids with their positive pressure slowed down the expansion of the universe. But the expansion of our today’s universe is speeding up. Accelerated expansion of today’s universe is proved by observational data gathered from ground-based and space telescopes, from type Ia supernovas. So the existence of dark energy in the universe is hypothesized to explain the accelerated expansion of today’s universe and the inflationary expansion of the very early universe.

There are different models of dark energy; the first and simplest one is cosmological constant (or vacuum energy), that is constant all the time and space. The others are quintessential models which are dynamics, evolving and they can be inhomogeneous. In this book, scalar field that is one of the quintessential models of dark energy is studied.

Chapter one of this book is a brief review of general theory of relativity and chapter two covers topics of cosmology; in this chapter the need for a field which provides negative pressure and accelerates the expansion of our universe is discussed. Chapter three is the study of the equations of motion of scalar field with exponential potential.

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