ar X iv : g r - qc / 9 40 70 10 v 1 1 2 Ju l 1 99 4 FOUR DIMENSIONAL CONFORMAL GRAVITY , CONFINEMENT , AND GALACTIC ROTATION CURVES

We review the current status and prospects for the conformal invariant fourth order theory of gravity which has recently been advanced by Mannheim and Kazanas 1−9 as a candidate alternative to the standard second order Einstein theory. We examine how it is possible in principle to replace the Einstein theory at all while retaining its tested features, and we appeal to the wisdom gleaned from particle physics to suggest a covariant alternative. Specifically, motivated by the underlying scale invariance of the fundamental strong, electromagnetic and weak interactions, we propose that, just like their inertial counterparts in the other fundamental theories, gravitational mass and length scales should also be induced dynamically by spontaneous breakdown in a theory of gravity which itself possesses no fundamental scales at all. Indeed, in a sense this viewpoint is even mandated by the equivalence principle since once inertial masses are dynamical, it is natural to expect gravitational masses to be dynamical too. Given the connection of conformal gravity to particle theory, we explore the theory as a microscopic fundamental theory of elementary particles, to thus give curvature a more prominent role in elementary particle dynamics, and in particular in the generation both of elementary particle masses and the extended bag-like models which are thought to describe them. We discuss the degree to which conformal gravity can compete with string theory as a consistent candidate microscopic theory of gravity. Additionally, we explore the theory as a macroscopic theory of gravity where the exact, non-perturbative, classical potential is found to be of the confining V (r) = −β/r + γr/2 form, a form which enables us to provide an explanation for the general systematics of galactic rotational velocity curves without the need to assume the existence of copious amounts of dark matter; with this explanation of the curves apparently not being in conflict with the current round of microlensing observations. (1) The Case for Reconsidering the Standard Einstein Theory At the present time there is little doubt in the general community as to the correctness of the standard second order Einstein theory of gravity which is based on the action I EH = − d 4 x(−g) 1/2 R α α /16πG (1) and gravitational equations of motion of the form R µν − g µν R α α /2 = −8πGT µν (2) However given the fact that this theory when applied to currently available astrophysi-cal and …