This chapter describes how large-scale structure -- the distribution of galaxies on the sky -- can be used to probe the cosmological model. We start by defining the density perturbation and its most fundamental statistical property -- the correlation function. We briefly review the evolution of density perturbations in the standard cosmological model, emphasizing key results. We next discuss the growth of cosmic structure, and segue into talking about the power spectrum of density perturbations, its theoretical description, and its measurements. This leads us to discuss structure formation in the universe more generally, the role of numerical (N-body) simulations, and the mass function. We end by discussing how the statistical properties of dark-matter halos, which can easily be modeled in simulations, are related to those of galaxies that we typically observe.

This chapter reviews the Boltzmann equation, which is a starting point for some of the key results in cosmology. We introduce a general version of the Boltzmann equation, then study its implications in the simple scenario of a few interacting particles. We introduce the concept of a freezeout of particle species, and illustrate it using a simple example. We end the chapter by discussing baryogenesis (the process that generated the excess of baryons over antibaryons), and Sakharov conditions for successful baryogenesis to take place.

We study the evolution of particle species throughout the history of the universe. We introduce the phase-space distribution function, and review basic concepts in statistical mechanics as applied to early-universe cosmology, including thermal equilibrium, entropy, and chemical potential. We calculate the effective number of relativistic species, and show how it varies as a function of time.

We give a broad-brush overview of cosmology, including a timeline of events starting from the Big Bang until the present day. We introduce the three pillars of the Big Bang cosmological model, the concepts of homogeneity and isotropy, as well as parsec as a unit of distance. We also introduce natural units, and develop intuition on how to adopt and use them.

Here we review dark energy, the component that causes accelerated expansion of the universe. We start by reviewing the history of this fascinating discovery, describing in detail how type Ia supernovae were used to measure the expansion rate and find that the expansion is speeding up. We then outline modern evidence for the existence of dark energy, how dark energy is parametrically described, and what its phenomenological properties are. We review the cosmological-constant problem that encapsulates the tiny size of dark energy relative to expectations from particle physics. Next we introduce physical candidates for dark energy, including scalar fields and modified gravity. We end by explaining the controversial anthropic principle, and describe the possible future expansion histories of the universe dominated by dark energy.

Neutrinos have an important role in cosmology, and here we review them in some detail. We review the fascinating history of how neutrinos were first proposed then detected. We then mathematically describe neutrino oscillations. We describe decoupling of neutrinos from the thermal bath, point out the likely existence of the cosmic neutrino background, and discuss prospects for detecting it directly.

One of the problems with the concept of spacetime is that it is hard for us to actually appreciate the implications of living in a curved spacetime, and the origin of this difficulty is that our local spacetime is essentially flat! Hence, all of our understanding of physics – of 'how things work' – has been built on the basis of perceptions that take place in almost flat spacetime. This chapter will provide a pragmatic approach to the measurement of spacetime by illustrating how it is actually not too difficult to obtain an estimate of local curvature by using simple physical quantities, such as the mass and the size of the object. In this manner, we will be able to appreciate that the curvature on Earth is only a few parts in a billion, hence explaining why we perceive everything in the actual absence of curvature. we will learn how to actually bend spacetime reaching the extreme values that are encountered near a neutron star and a black hole, both of which will be discussed more in detail in the following chapters.

Two scientists more than anyone else have contributed in defining our understanding of gravity: Newton in 1679 and Einstein in 1915. The mathematical frameworks the two have developed and proposed, however, are very different. Newton’s gravity is the one we learn at school and is normally taught at university. It provides a very natural interpretation of what we experience - the apple falls from the tree because the Earth attracts it! Einstein’s gravity is studied only in the most advanced courses at the university and provides a very counterintuitive explanation, requiring the concepts of spacetime and curvature. This chapter will provide a first description of the Einstein equations and, although it will not enter into the mathematical aspects of the equations, it will explain the basic concepts behind them. Acquiring a first qualitative understanding of Einstein equations will be useful to comprehend better the concept of spacetime curvature discussed in Chapter 4.

Gravity attracts – this is such an obvious phenomenon that writing this book was not necessary to stress it. Less obvious is that, even before it appears in the form of physical interaction, gravity attracts our attention and our imagination. As soon as we are born, before developing a conscious relationship with the physical universe, we already know gravity at an instinctive level. For the rest of our lives, it will represent the only one of the four fundamental interactions of which we will have conscious awareness. And from which we will often try to escape.