Introduction to Cosmology

Welcome to the Cosmology series. The "Introduction to Cosmology" is the first course in this series. In this one, we are going to set up important ideas in Cosmology which will be useful for advanced Cosmology I & II courses.In the first chapter, we start with a brief introduction to general relativity, then we go on to discuss the curvature of spacetime, derive the FLRW metric, comoving and physical distance, Hubble's law, scale factor, conformal time.In the second chapter, we learn more about our universe. We learn about the Isotropic and Homogenous nature of our universe, redshift caused by the expanding universe.Further, in the third chapter, we carry out a fantastic exercise. Starting from scratch, we analyse the Newtonian model of Cosmology. We apply Newton's law to an equation that governs the dynamics of scale factor, which is also known as the first Friedmann equation. And using the energy equation, we also derive the second Friedmann equation. We verify that the universe can not be static because if it was it would have been empty. We understand more about the behaviour of the scale factor, how it grows with time in a matter-dominated, radiation-dominated universe. We see how the scale factor grows when both the matter and radiation components are present in the Newtonian universe.In the fourth chapter, we consider a relativistic version of the Friedmann equations. The Newtonian analysis helps us a lot to understand the relativistic model. We consider the densities of various components, including radiation, baryonic matter, dark matter, dark energy.The fifth chapter is a surprise =)On the internet, we find many sources that claim there's 68% of dark energy in this universe, 27% of dark matter and 5% of observable matter. But nobody gives us any proof. We will consider modern observations and see why these numbers are true. Moreover, as the whole universe was in the hot dense state and nearly 14 billion years ago expansion started...wait...but WHY is the age of our universe is about 14 billion years? We will find out answers to such questions, not by claiming, but by using plain mathematics.So why wait for such an extraordinary journey. These 3 courses will take you from Earth to well beyond the horizon of our universe! Let's get started.And of course, I will see you in the next one!