Spontaneous breaking of conformal invariance, solitons, and gravitational waves in theories of conformally invariant gravitation

Abstract

We study conformal gravity as an alternative theory of gravitation. For conformal gravity to be phenomenologically viable requires that the conformal symmetry is not manifest at the energy scales of the other known physical forces. Hence we are required to find a mechanism for the spontaneous breaking of conformal invariance. In this paper we study the possibility that conformal invariance is spontaneously broken due to interactions with conformally coupled matter fields. The vacuum of the theory admits conformally noninvariant solutions corresponding to maximally symmetric space-times and variants thereof. These are either de Sitter space-time or anti-de Sitter space-time in the full four space-time dimensions and we find new solutions corresponding to maximal symmetry restricted to a lower dimensional subspace. We also consider normalizable, linearized gravitational perturbations around the anti-de Sitter background. We show to second order, that these gravitational fluctuations carry zero energy momentum. Finally we also show the possibility of domain wall solitons interpolating between the ground states of spontaneously broken conformal symmetry that we have found. These solitons necessarily require the vanishing of the scalar field. This offers a way of eschewing the recent suggestion and its consequences [E. Flanagan, Phys. Rev. D 74, 023002 (2006).] that the conformal symmetry could be quarantined to a sterile sector of the theory by choosing an appropriate field redefinition.

Monochromatic plane-fronted waves in conformal gravity are pure gauge

“…We have shown that transverse, traceless, plane fronted monochromatic gravitational waves given by the ansatz (4) are actually conformally and coordinate equivalent to flat Minkowski space-time. This generalizes to all orders, the result found to second order in [11] that transverse, traceless, linearized plane waves carry no energy to second order in Weyl gravity and that found in [1]. However our general result here follows from the unexpected discovery that such deviations from Minkowski space-time are actually trivial, they are just conformal and coordinate artifacts.…”

“…Since our solution is valid for any strength of the fluctuation, the Weyl gravitational field equations must be valid order by order in the parameter corresponding to the strength of the fluctuation. The result in [11] was an explicit verification of this fact for the second order terms.…”

Gravitomagnetic effects in conformal gravity

“…[29] (see also Refs. [30,31]) considered spontaneous symmetry breaking in Weyl gravity and showed that this can provide a mechanism to generate a scale in the theory. Taking advantage of the independence of the Lagrangian on the t− and φ−coordinates, and using θ = π/2 as the plane of the circular orbits without loss of generality due to spherical symmetry, the Euler-Lagrange equations of motion are given by…”

Linear Weyl gravity in de Sitter universe

“…As a conclusion, if a highly probable linear quantum of gravitational field exist, it could not be represented by Weyl gravity, since linear Weyl gravitational field does not transform under UIR of the conformal and de Sitter groups. Other authors have concluded the same through different methods [5,10].…”