Fig. 8.1. Motion of the scalar field in the theory with V(0) = 2m202. If the potential energy density of the field is greater than the Planck density, pp ~ Mp ~ 1094 g cm~3, quantum fluctuations of spacetime are so strong that one cannot describe it in the usual terms. Such a state is called spacetime foam. At a somewhat smaller energy density (region A: mMp^ < V(0) < Mp) quantum fluctuations of spacetime are small but quantum fluctuations of the scalar field 0 may be large. Jumps of the scalar field due to quantum fluctuations lead to eternal self-reproduction of the inflationary universe. At even smaller values of V(0) (region B: m2Mp < V(0) < mMp3) fluctuations of the field 0 are small; it moves down slowly like a ball in a viscous liquid. Inflation occurs in both regions A and B. Finally, near the minimum of V(0) (region C) the scalar field rapidly oscillates, creates pairs of elementary particles, and the Universe becomes hot.
down very slowly, like a ball in a viscous liquid, with the viscosity being proportional to the speed of expansion.
There are two equations which describe evolution of a homogeneous scalar field in our model: the field equation,
and the Einstein equation,
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