Universe Models with Vacuum Energy

Soon after Einstein had introduced the cosmological constant he withdrew it and called it “the biggest blunder” of his life. However, there has been developments in the last decades that have given new life to the cosmological constant. Firstly, the idea of inflation gave cosmology a whole new view upon the first split second of our universe. A key ingredient in the inflationary model is the behaviour of models that have a cosmological constant-like behaviour. Secondly, recent observations may indicate that we live in an accelerated universe. The inclusion of a cosmological constant can give rise to such behaviour as we will show in this chapter. We will first start with the static solution that Einstein found and was the reason that Einstein introduced the cosmological constant in the first place.