Interaction of Low - Energy Induced Gravity with Quantized Matter -- II. Temperature effects

TL;DR

This paper investigates how temperature influences the interaction between the conformal factor and Higgs field in the early Universe, revealing effects like phase transitions through an exact effective potential calculation in AdS space.

Contribution

It extends previous work by incorporating temperature effects into the conformal factor-Higgs interaction model and derives an exact effective potential in AdS background.

Findings

Temperature affects the conformal factor-Higgs interaction dynamics.

Phase transitions occur near fixed points influenced by temperature.

Exact effective potential calculated for the model in AdS space.

Abstract

At the very early Universe the matter fields are described by the GUT models in curved space-time. At high energies these fields are asymptotically free and conformally coupled to external metric. The only possible quantum effect is the appearance of the conformal anomaly, which leads to the propagation of the new degree of freedom - conformal factor. Simultaneously with the expansion of the Universe, the scale of energies decreases and the propagating conformal factor starts to interact with the Higgs field due to the violation of conformal invariance in the matter fields sector. In a previous paper \cite{foo} we have shown that this interaction can lead to special physical effects like the renormalization group flow, which ends in some fixed point. Furthermore in the vicinity of this fixed point there occur the first order phase transitions. In the present paper we consider the same theory of conformal factor coupled to Higgs field and incorporate the temperature effects. We reduce the complicated higher-derivative operator to several ones of the standard second-derivative form and calculate an exact effective potential with temperature on the anti de Sitter (AdS) background.