Scalar field instability in de Sitter space-time

Starting from the equation of motion of the quantum operator of a real scalar field φ in de Sitter space-time, a simple differential equation is derived which describes the evolution of quantum fluctuations 〈φ2〉 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.