Average Effective Potential for the Conformal Factor

TL;DR

This paper calculates the one-loop quantum effects on the effective potential for the conformal factor in a four-dimensional quadratic gravity theory with torsion, revealing a nontrivial potential and its scale dependence.

Contribution

It introduces a novel regularization approach in quantum gravity and applies the average effective potential method to analyze the conformal factor.

Findings

One-loop effects generate a nontrivial effective potential for the conformal factor.

The regularization method used differs from standard quantum gravity procedures.

The scale dependence of the conformal factor's vacuum expectation value is computed.

Abstract

In a four dimensional theory of gravity with lagrangian quadratic in curvature and torsion, we compute the effective action for metrics of the form $g_{\mu\nu}=\rho^2\delta_{\mu\nu}$, with $\rho$ constant. Using standard field-theoretic methods we find that one loop quantum effects produce a nontrivial effective potential for $\rho$. We explain this unexpected result by showing how our regularization procedure differs from the one that is usually adopted in Quantum Gravity. Using the method of the average effective potential, we compute the scale dependence of the v.e.v. of the conformal factor.