Magnetic-induced vacuum instability in de Sitter spacetime

We study the behavior of the vacuum expectation value of chemical bondphichemical bond2 under an external magnetic field in de Sitter spacetime, where phi is a charged scalar field. It is found that if a strong magnetic field is generated at early time in the inflationary Universe, the vacuum expectation value becomes negative and an instability of the vacuum arises. However, as time passes, this instability disappears and the vacuum becomes stable, except for massless and minimally coupled fields. Thus the magnetic field produced in the early Universe provides an important effect to the symmetry behavior of the inflationary-Universe model