Nuclear Physics B248 (1984) 727-753 @ North-Holland Publishing Company A MODEL OF SPONTANEOUS SYMMETRY BREAKDOWN IN SPATIALLY FLAT COSMOLOGICAL SPACETIMES* Prasun KUNDU Departnlerrt of Plrwics, Uttiaersi<v of lhd7, Salt Luke City, UT 841 I?, USA Received 9 December 1983 This paper is an elaboration of a previous short exposition of a theory of spontaneous symmetry breaking in a conformally coupled, massless X+4 model in a spatially flat Robertson- Walker spacetime. Under the weakened global boundary condition allowing the physical spacetime to be conformal to only a portion of the Mnkowski spacetime, the model admits a pair of degenerate vacua in which the $J --t -$ symmetry is spontaneously broken. The model is formulated as a cuclidean field theory in a space with a positive-definite metric obtained by analytically continuing the conformal time coordinate. An appropriate time-dependent zero energy solution of the euclidean equation of motion representing the field configuration in the asymmetric vacuum is considered and the corresponding quantum trace anomaly (Tp”) is computed in the one-loop approximation. The nontrivial infrared behavior of the model due to the singular nature of the classical background field forces a modification of the boundary conditions on the propagator. A general form for an “improved” one-loop trace anomaly is found by a simple argument based on renormalization group invariance. Via the Einstein equation, the trace anomaly leads to a self-consistent dynamical equation for the cosmic expansion scale factor. Some physical aspects ol the back-reaction problem based on a simple power law model of the expansion scale factor are discussed. 1. Introduction In recent years there has been a great deal of interest in the phenomenon of spontaneous symmetry breaking in quantum field theories in a curved spacetime as well as its possible significance for cosmology, and an extensive literature already exists on the subject [l-lo]. In the Minkowski spacetime the familiar Higgs phenomenon [ll] provides a mechanism by which spontaneous breakdown of internal symmetries occurs at the classical level in field theories containing elemen- tary scalars through an imaginary mass term in the lagrangian. Although in a massless theory the symmetric vacuum ((+) = 0) is in general the only possibility at the tree level, it has been shown by Coleman and Weinberg [12], that it tends to be destabilized by the radiative corrections which move the minimum of the effective potential away from the classical minimum at the origin in the space of constant * Research supported in part by grants from the National Science Foundation. 727