The violent Universe: the Big Bang

Abstract

Four lectures on Big Bang cosmology, including microwave background radiation, Big Bang nucleosynthesis, dark matter, inflation, and baryogenesis. The Big Bang theory provides a detailed description of the history and evolution of the Universe. Direct experimental and observational evidence allows us to probe back to the first second after the initial state (bang) when the temperatures were of order 1 MeV and the light elements were created. Our understanding of the Standard Model of electroweak interactions allows us to push the description of the early universe back to about 10−10 s after the bang when we expect that the electroweak symmetry was restored. Indeed, it is possible to discuss events back to the Planck time (10−44 s after the bang) albeit in a very model dependent way. In these four lectures, I hope to give an overview of modern cosmology with an emphasis on particle interactions in cosmology. After a description of the standard FLRW model (including the microwave background radiation) in Lecture 1, I will cover both inflation and baryogenesis in Lecture 2. Lecture 3 will focus on Big Bang Nucleosynthesis (BBN) and Lecture 4 on dark matter. 1 Lecture 1: Standard Cosmology 1.1 The FLRW metric and its consequences The standard Big Bang model assumes homogeneity and isotropy. As a result, one can construct the space-time metric by embedding a maximally symmetric three dimensional space in a four dimensional space-time (see, e.g., Ref. [1]). The most general form for a metric of this type is the Friedmann– Lemaitre–Robertson–Walker metric which in co-moving coordinates is given by ds = dt −R(t) [ dr2 (1− kr2) + r 2 ( dθ + sin θdφ )] , (1) where R(t) is the cosmological scale factor and k the three-space curvature constant (k = 0,+1,−1 for a spatially flat, closed or open universe). k and R are the only two quantities in the metric which distinguish it from flat Minkowski space. It is also common to assume the perfect fluid form for the energy-momentum tensor T μν = pg + (p+ ρ)uu , (2) where gμν is the space-time metric described by Eq. (1), p is the isotropic pressure, ρ is the energy density and uμ = (1, 0, 0, 0) is the velocity vector for the isotropic fluid. The (00) component of Einstein’s equation Rμν − 1 2 gμνR− Λgμν = 8πGNTμν (3) yields the Friedmann equation