INTERACTION OF ANOMALY-INDUCED GRAVITY WITH QUANTIZED MATTER AND TEMPERATURE EFFECTS

Matter fields during the very early Universe are described by GUT mode ls in curved spacetime. At high energies these fields are asymptotical ly free and conformally coupled to the external metric. The only possi ble quantum effect is the appearance of the conformal anomaly, which l eads to the propagation of the new degree of freedom, the conformal fa ctor. Simultaneously with the expansion of the Universe, the scale of energies decreases and the propagating conformal factor starts to inte ract with the Higgs held due to the violation of conformal invariance in the matter fields sector. In a previous paper we have shown that th is interaction can lead to special physical effects like renormalizati on group dow, which ends at some fixed point. Furthermore, in the vici nity of this fixed point the first-order phase transition may occur. I n the present paper we consider the same theory of the conformal facto r coupled to the Higgs field and incorporate the temperature effects. We reduce the complicated higher-derivative operator to several of sta ndard second-derivative form and calculate an exact effective potentia l with temperature on the anti-de Sitter (AdS) background. The physica l analysis of the effective potential is performed within the framewor k of the high-temperature expansion.