We introduce weak lensing due to foreground structures with the aim of treating lensing of CMB anisotropies and polarization. This second-order effect is especially important on small scales but has to be taken into account for ℓ ≳ 400 if we want to achieve an accuracy of better than 1%. We first derive the deflection angle and the lensing power spectrum. Then we discuss lensing of CMB fluctuations and polarization in the at sky approximation, which is sufficiently accurate for angular harmonics with ℓ ≳50 where lensing is relevant.

This chapter is devoted to the initial conditions. Here we explain how the unavoidable quantum fluctuations are amplified during an inflationary phase and lead to a nearly scale-invariant spectrum of scalar and tensor perturbations. We also calculate the small non-Gaussianities generated during single field in ation and discuss the initial conditions for mixed adiabatic and iso-curvature perturbations.

In this chapter we present the analysis of the large scale matter distribution within linear perturbation theory in a fully relativistic way. We take into account that only directions and redshifts are observable while lengths scales are always inferred from a cosmological model. We first introduce the traditional density and redshift space distortion contribution to the observed uctuations and then proceed to discuss the smaller lensing and large scale relativistic terms. We express the clustering properties of matter in terms of directly observable quantities and study their scale and redshift dependence. We also discuss ‘intensity mapping’ a new observational technique which will hopefully bear fruit in the near future. Also this chapter has been newly added in the second edition.

In a series of appendices we give a list of physical constants and conversion factors; we present some mathematical details and the special functions needed in the main text; we derive the Boltzmann equation for a curved universe and we compute the fluctuations of the luminosity distance. We also solve some of the exercises given in the main text.

In a series of appendices we give a list of physical constants and conversion factors; we present some mathematical details and the special functions needed in the main text; we derive the Boltzmann equation for a curved universe and we compute the fluctuations of the luminosity distance. We also solve some of the exercises given in the main text.

Here, we develop cosmological perturbation theory. This is the basics of CMB physics. The main reason why the CMB allows such an accurate determination of cosmological parameters lies in the fact that its anisotropies are small and can be determined mainly within first-order perturbation theory. We derive the perturbations of Einstein’s equations and the energy {momentum conservation equations and solve them for some simple but relevant cases. We also discuss the perturbation equation for light-like geodesics. This is sufficient to calculate the CMB anisotropies in the so-called instant recombination approximation. The main physical effects that are missed in such a treatment are Silk damping on small scales and polarization. We then introduce the matter and CMB power spectrum and draw our first conclusions for its dependence on cosmological and primordial parameters. For example, we derive an approximate formula for the position of the acoustic peaks. In the last section we discuss fluctuations not laid down at some initial time but continuously sourced by some inhomogeneous component, a source, such as, for topological defects example, / that / may form during a phase transition in the early universe.

The first chapter contains a räsumä of the cosmology treating the homogeneous and isotropic universe. The Friedmann equations are derived and the thermal history of the Universe is discussed in some detail. Special emphasis is laid on the process of recombination and the decoupling of photons from the cosmic uid. Nucleosynthesis and cosmic in ation are also discussed.

In a series of appendices we give a list of physical constants and conversion factors; we present some mathematical details and the special functions needed in the main text; we derive the Boltzmann equation for a curved universe and we compute the fluctuations of the luminosity distance. We also solve some of the exercises given in the main text.

In this preface I motivate this book and put it into context. I also explain how it can be read and give a brief abstract of each chapter. I end with acknowledgments to all the colleagues and students who have helped by commenting and by proofreading parts.

In a series of appendices we give a list of physical constants and conversion factors; we present some mathematical details and the special functions needed in the main text; we derive the Boltzmann equation for a curved universe and we compute the fluctuations of the luminosity distance. We also solve some of the exercises given in the main text.

Two models of galaxy formation were being investigated simultaneously on the 1970’s. The bottom-up model was championed by Peebles, and the top-down model by Zeldovich. At first, dark matter was not part of either model, but this effort to explain the origin of galaxies eventually stalled for both models the because the temperature fluctuations in the cosmic background radiation are too small to accommodate galaxy formation from baryons alone. At first massive neutrinos were introduced as dark matter, and when this failed to word, cold dark matter (CDM) was introduced. CDM forms early halos, and then baryons eventually fall into these halos. The first CDM computer models of galaxy formation were introduced by Melott and Shandarin and later developed by the “Gang of Four” (White, Davis, Efstathiou and Frenk). Eventually, the top-down and bottom-up models gracefully merged, and the concept of “biasing” became part of the final model.