Zero Cosmological Constant from Normalized General Relativity
A. Davidson and S. Rubin, Class. Quant. Grav. 26, 235019 (2009) pdf file

Abstract: Normalizing the Einstein-Hilbert action by the volume functional makes the theory invariant under constant shifts in the Lagrangian. The associated field equations then resemble unimodular gravity whose otherwise arbitrary cosmological constant is now determined as a Machian universal average. We prove that an empty space-time is necessarily Ricci tensor flat, and demonstrate the vanishing of the cosmological constant within the scalar field paradigm. The cosmological analysis, carried out at the mini-superspace level, reveals a vanishing cosmological constant for a Universe which cannot be closed as long as gravity is attractive. Finally, we give an example of a normalized theory of gravity which does give rise to a non-zero cosmological constant.

Brane Gravitational Extension of Dirac's "Extensible Model of the Electron"
A. Davidson and S. Rubin,  Class. Quant. Grav. 26, 235006 (2009) pdf file

Abstract: A gravitational extension of Dirac's "Extensible model of the electron" is presented. The Dirac bubble, treated as a 3-dimensional electrically charged brane, is dynamically embedded within a 4-dimensinal Z2-symmetric Reissner-Nordstrom bulk. Crucial to our analysis is the gravitational extension of Dirac's brane variation prescription; its major effect is to induce a novel geometrically originated contribution to the energy-momentum tensor on the brane. In turn, the effective potential which governs the evolution of the bubble exhibits a global minimum, such that the size of the bubble stays finite (Planck scale) even at the limit where the mass approaches zero. This way, without fine-tuning, one avoids the problem so-called 'classical radius of the electron'

On the Problem of Vacuum Energy in Brane Theories
I. Gurwich, S. Rubin and A. Davidson,  Phys. Lett. B679, 515 (2009) pdf file

Abstract: We point out that modern brane theories suffer from a severe vacuum energy problem. To be specific, the Casimir energy associated with the matter fields confined to the brane, is stemming from the one and the same localization mechanism which forms the brane itself, and is thus generically unavoidable.
Possible practical solutions are discussed, including in particular spontaneously broken supersymmetry, and quantum mechanically induced brane tension.

Unified Brane Gravity: Artifact Dark Matter from a Scale Dependent Newton Constant
I. Gurwich and A. Davidson,  Phys. Rev. D80, 024039 (2009) pdf file

Abstract: We analyze, within the framework of unified brane gravity, the weak field perturbations caused by the presence of matter on a 3-brane. Although deviating from the Randall-Sundrum approach, the masslessness of the graviton is still preserved. In particular, the 4-dimensional Newton force law is recovered, but serendipitously, the corresponding Newton constant is shown to be necessarily lower than the one which governs FRW cosmology. This has the potential to puzzle out cosmological dark matter. A subsequent conjecture concerning galactic dark matter follows.

Radiation Driven Inflation
A. Davidson and I. Gurwich,  Jour. Cosmol. Astropart. Phys. JCAP 06, 001 (2008) pdf file

Abstract: A novel, scalar field free approach to cosmic inflation is presented. The inflationary Universe and the radiation dominated Universe are shown, within the framework of unified brane cosmology, to be two different phases governed by one and the same energy density. The phase transition of second order (the Hubble constant exhibits a finite jump) appears naturally and serves as the exit mechanism. No re-heating is needed. The required number of e-folds is achieved without fine tuning.