Inflationary Brans-Dicke Quantum Universe

TL;DR

This paper develops a quantum-corrected model of the Brans-Dicke universe incorporating matter and dilaton fields, deriving inflationary solutions through anomaly-induced effective actions in both four and two dimensions.

Contribution

It introduces a novel quantum correction framework for Brans-Dicke gravity with matter, leading to inflationary solutions driven by quantum effects.

Findings

Derived one-loop anomaly-induced effective action for dilaton-coupled fermions.

Found an inflationary universe solution with exponential scale factor.

Constructed a purely quantum-driven 2D Brans-Dicke universe.

Abstract

The formulation of Brans-Dicke (BD) gravity with matter in the Einstein frame is realized as Einstein gravity with dilaton and dilaton coupled matter. We calculate the one-loop 4d anomaly-induced effective action due to N dilaton- coupled massless fermions on the time-dependent conformally flat background with non-trivial dilaton. Using that complete effective action the (fourth-order) quantum corrected equations of motion are derived. One special solution of these equations representing an inflationary Universe (with exponential scale factor) and (much slower) expanding BD dilaton is given. Similarly, the 2d quantum BD Universe with time-dependent dilaton is constructed. In the last case the dynamics is completely due to quantum effects.