Conformal Transformations in Metric-Affine Gravity and Ghosts

TL;DR

This paper explores how conformal transformations affect ghost fields in metric-affine gravity, showing that independence of metric and connection can prevent ghost issues present in pure metric theories.

Contribution

It demonstrates that in metric-affine gravity, conformal transformations can yield ghost-free scalar fields, with the connection's transformation properties crucial for avoiding ghost problems.

Findings

If the connection is invariant, the scalar field is a non-ghost auxiliary.

Additive transformation of the connection makes the scalar field dynamical and ghost-free.

Metric-affine gravity maintains connection independence, preventing conformal ghosts.

Abstract

Conformal transformations play a widespread role in gravity theories in regard to their cosmological and other implications. In the pure metric theory of gravity, conformal transformations change the frame to a new one wherein one obtains a conformal-invariant scalar-tensor theory such that the scalar field, deriving from the conformal factor, is a ghost. In this work, conformal transformations and ghosts will be analyzed in the framework of the metric-affine theory of gravity. Within this framework, metric and connection are independent variables, and hence, transform independently under conformal transformations. It will be shown that, if affine connection is invariant under conformal transformations then the scalar field under concern is a non-ghost, non-dynamical field. It is an auxiliary field at the classical level, and might develop a kinetic term at the quantum level. Alternatively, if connection transforms additively with a structure similar to yet more general than that of the Levi-Civita connection, the resulting action describes the gravitational dynamics correctly, and more importantly, the scalar field becomes a dynamical non-ghost field. The equations of motion, for generic geometrical and matter-sector variables, do not reduce connection to the Levi-Civita connection, and hence, independence of connection from metric is maintained. Therefore, metric-affine gravity provides an arena in which ghosts arising from conformal factor are avoided thanks to the independence of connection from the metric.