Invariance of de Sitter State with Respect to Wick Rotation, Inflation and Dark Energy

Abstract: It is shown that the de Sitter state is invariant with respect to Wick rotation. In imaginary time, super- horizon quantum and classical metric fluctuations of the empty FLRW space (with no matter fields) form a self-consistent de Sitter state. The invariance with respect to Wick rotation suggests that this de Sitter state is formed also in the empty space of real time. At the start and by the end of its cosmological evolution the Universe is empty, so that the de Sitter expansion of the empty space can be the cause of inflation and dark energy. This scenario is consistent with the existing observational data