Introduction to Cosmology

The standard big bang cosmological model and the history of the early universe according to the grand unified theories of strong, weak and electromagnetic interactions are summarized. The shortcomings of big bang are discussed together with their resolution by inflationary cosmology. Inflation and the subsequent oscillation and decay of the inflaton field are studied. The density perturbations produced during inflation and their evolution during the matter dominated era are analyzed. The temperature fluctuations of the cosmic background radiation are summarized. Finally, the nonsupersymmetric as well as the supersymmetric hybrid inflationary model is described. 1. The Big Bang Model The discovery of the cosmic background radiation (CBR) in 1964 together with the observed Hubble expansion of the universe had established hot big bang cosmology as a viable model of the universe. The success of the theory of nucleosynthesis in reproducing the observed abundance pattern of light elements together with the proof of the black body character of the CBR then established hot big bang as the standard cosmological model. This model combined with grand unified theories (GUTs) of strong, weak and electromagnetic interactions provides an appropriate framework for discussing the very early stages of the universe evolution. A brief introduction to hot big bang follows. 1.1 Hubble Expansion For cosmic times t > ∼ tP ≡ M P ∼ 10 sec (MP = 1.22× 10 GeV is the Planck scale) after the big bang, quantum fluctuations of gravity cease to exist. Gravitation can then be adequately described by classical relativity. Strong, weak and electromagnetic interactions, however, require relativistic quantum field theoretic treatment and are described by gauge theories. An important principle, on which the standard big bang (SBB) cosmological model [1] is based, is that the universe is homogeneous and isotropic. The strongest evidence so far for this cosmological principle is the observed [2] isotropy of the CBR. Under this assumption, the four dimensional spacetime in the universe is described by the Robertson-Walker metric