Spontaneous Symmetry Breaking in 5D Conformally Invariant Gravity

Abstract

We explore the possibility of the spontaneous symmetry breaking in 5D conformally invariant gravity, whose action consists of a scalar field nonminimally coupled to the curvature with its potential. Performing dimensional reduction via ADM decomposition, we find that the model allows an exact solution giving rise to the 4D Minkowski vacuum. Exploiting the conformal invariance with Gaussian warp factor, we show that it also admits a solution which implement the spontaneous breaking of conformal symmetry. We investigate its stability by performing the tensor perturbation and find the resulting system is described by the conformal quantum mechanics. Possible applications to the spontaneous symmetry breaking of time-translational symmetry along the dynamical fifth direction and the brane-world scenario are discussed.

z-Weyl gravity in higher dimensions

“…The anisotropic conformal invariance puts no restriction a priori on the value of the conformal weight z, at least at the classical level and this may lead to some new aspects hidden in the anisotropic theory. For example, in 5D, the isotropic potential yields a fractional power V ∼ φ 10 3 [16]. Such a potential renders a perturbative approach inaccessible, and could be plagued with possible discontinuities of the potential.…”

“…where ζ, b, y 0 , N 0 , ϕ 0 are some constants. Both of these solutions describe warped spacetime with Gaussian warp factor which has been discussed in a number of papers [13][14][15][16]. But we will not go further along this direction.…”

Extended anisotropic models in noncompact Kaluza–Klein theory

“…Moreover, there are corresponding reduced cosmologies which can bear a reasonable agreement with specific cosmological observables [15][16][17][18]. Different cosmological models are present in the literature [1,9,10,[19][20][21][22], whose (effective) matter sources emerge from the geometry of higher dimensions. Such contribution not only can yield implications similar to ordinary matter sources but it can also play the role of dark energy or dark matter in the universe [9,10,23,24].…”