Anomaly Induced Effective Action Combined with Generalized Brans-Dicke Theory

TL;DR

This paper explores the effects of anomaly-induced effective actions within a generalized Brans-Dicke framework, deriving scalar field equations and analyzing cosmological implications in a novel theoretical context.

Contribution

It extends the Brans-Dicke theory to include energy exchange with matter and incorporates anomaly-induced effects, providing new equations for scalar fields and cosmological dynamics.

Findings

Derived scalar field equations for dilaton and BD fields.

Discussed the generalized Friedmann equation in this context.

Extended previous work on conformal anomaly and classical gravity.

Abstract

We consider the anomaly induced effective action in N=4 super Yang-Mills theory in interaction with the Brans-Dicke (BD) field. The generalization of the BD theory so as to permit an energy exchange between the scalar field and ordinary matter fields, was recently worked out by T. Clifton and J. D. Barrow [Phys. Rev. D 73, 104022 (2006)]. We derive the scalar field equations for the dilaton field, and the BD field, and discuss the Friedmann equation in the general case. The present paper is a continuation of an investigation some years ago dealing with the case of conformal anomaly plus ordinary classical gravity [I. Brevik and S. D. Odintsov, Phys. Lett. B 455, 104 (1999)].