Quantum Fluctuations during Inflation

Abstract

Quantum field theory teaches us that a classical motion of a system is disturbed by quantum fluctuations. In the Minkowski space their role is rather weak because quantum corrections are proportional to Planck constant h. In addition, according to Heisenberg’s uncertainty principle, the larger the fluctuation, the smaller time it exists. A much more interesting picture was discovered in the inflationary stage. As it was shown in Chapter 2, this stage may be approximated by de Sitter space. The most important property of inflation is that any inhomogencity grows in space, going far beyond the horizon size. The fluctuations are also the specific sort of inhomogeneities. It seems reasonable that their destiny differs from the destiny of the fluctuations in Minkowski space. In de Sitter space, quantum fluctuations do not die out. On the contrary, their size in space increases exponentially as compared with the size of horizon and they contribute to classical constituent of the field. This process reminds us of a pair creation in strong fields. The energy is conserved due to work produced by the field. In our case this field is evidently a gravitational one. In this chapter we consider shortly important results on quantum fluctuations during the inflationary stage that are supported by modern observations.