Scalar field instability in de Sitter space-time

TL;DR

This paper derives and solves an equation for quantum fluctuations of a scalar field in de Sitter space, revealing differences in massless cases that suggest possible spontaneous symmetry breaking.

Contribution

It provides a new explicit solution for quantum fluctuations in de Sitter space without infrared cutoff, highlighting potential symmetry breaking effects.

Findings

Agreement with standard results in the massive case

Different large-time behavior in the massless case

Potential indication of spontaneous de Sitter invariance breaking

Abstract

Starting from the equation of motion of the quantum operator of a real scalar field phi in de Sitter space-time, a simple differential equation is derived which describes the evolution of quantum fluctuations <phi^2> of this field. Full de Sitter invariance is assumed and no ad hoc infrared cutoff is introduced. This equation is solved explicitly and in massive case our result agrees with the standard one. In massless case the large time behavior of our solution differs by sign from the expression found in earlier papers. A possible cause of discrepancy may be a spontaneous breaking of de Sitter invariance.