Spontaneous symmetry breaking in the present and early universe

Spontaneous symmetry breaking in λφ⁴ theory is formulated in terms of the operator φ², and in a manner which requires no specific expectation value to be assigned to φ. At the one-loop order of perturbation theory, a renormalized effective action for a field ζ, linearly related to φ², is obtained as a gradient expansion. Potential advantages of this formulation in applications to phase transitions in the early universe are discussed. They include the possibilities (i) of obtaining a well-defined semiclassical equation of motion, and (ii) of following the evolution of a field theory from an initial symmetrical high temperature state without the introduction, ad hoc, of regions in which 〈φ〉 ≠ 0.