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

TL;DR

The paper demonstrates that the de Sitter state remains invariant under Wick rotation, implying its formation in both imaginary and real time, and suggests this invariance underpins inflation and dark energy in the universe.

Contribution

It introduces the invariance of the de Sitter state under Wick rotation and links this property to the origins of inflation and dark energy in cosmology.

Findings

De Sitter state is invariant under Wick rotation.

Quantum and classical fluctuations form a self-consistent de Sitter state.

This invariance supports the idea that de Sitter expansion causes 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