Mass hierarchy, mass gap and corrections to Newton’s law on thick branes with Poincaré symmetry

Abstract

We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schrödinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with m 2 ≥ 0, in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza-Klein (KK) excitations and to analytically compute the corrections to Newton's law in the thin brane limit. In the first case we consider a novel solution with a mass gap in the spectrum of KK fluctuations with two bound states -the massless 4D graviton free of tachyonic instabilities and a massive KK excitation -as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the thin Randall-Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved with positive branes as in the Lykken-Randall (LR) model and the model is completely free of naked singularities. We also show that the scalar-tensor system is stable under scalar perturbations with no scalar modes localized on the braneworld configuration.

Effective monopoles within thick branes

“…[14] to our attention. R. da Rocha is grateful to Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) grants CNPq 476580/2010-2 and 304862/2009-6 for financial support.…”

Brane modeling in warped extra-dimension

“…There were many attempts to avoid the presence of thin (singular) branes. It has been shown [4][5][6][7][8][9][10][11][12][13][14], that the positive tension brane could be smoothed (or, in other words, regularized) by a background scalar field configuration which we term here as the smooth or thick brane. However there is no satisfactory simple strategy to model the negative tension brane at least for scalar field minimally coupled to gravity.…”

“…The corresponding bulk cosmological constant Λ B , in different regions along the extradimension, reads as, 13) and the values of bulk cosmological constant at the brane locations are Λ B (y 1 ) = 0 and…”

“…To calculate the 4D Plank mass it is important to note that eq. (6.4) only involves 2nd derivatives of the metric perturbationH µν (x, z) which is related to the fact that in the action these fluctuations have the following canonical kinetic term 13) where the indices are contracted with the 5D Minkowski metric η M N . Since we havẽ H µν (x, z) =Ĥ µν (x)H(z) therefore (6.13) could be rewritten as follows…”

Tensor perturbations off(T)branes

“…However, the stability of f (T ) brane system is still unknown. In this paper we will focus on this issue and analyse the localization of the graviton zero mode, which is an important issue in brane model since it will ensure the four-dimensional Newtonian potential on the brane [28,[53][54][55][56][57][58][59][60][61][62][63][64][65][66][67]. This paper is organised as follows.…”