Uniqueness of Lagrangian Self-Expanders

We show that zero-Maslov class Lagrangian self-expanders in C^n which are asymptotic to a pair of planes intersecting transversely are locally unique if n>2 and unique if n=2.Comment: 32 page

On the Stability of Randall-Sundrum Braneworlds with Conformal Bulk Fields

In the Randall-Sundrum scenario we consider exact 5-dimensional solutions with localized gravity which are associated with a well defined class of conformal bulk fields. We analyze their behaviour under radion field perturbations. We show that if the Randall-Sundrum exponential warp is the localizing metric function and the equation of state of the conformal fields is not changed by the radion perturbation then the 5-dimensional solutions are unstable. We present new stable solutions which describe on the brane the dynamics of inhomogeneous dust, generalized dark radiation and homogeneous polytopic matter.Comment: 10 pages, latex, no figures. Contribution to the special issue of Vestnik of Tomsk State Pedagogical University in the field QFT/Cosmology/Gravity/Strings, edited by Sergei D. Odintso

Braneworlds, Conformal Fields and Dark Energy

In the Randall-Sundrum scenario we analize the dynamics of a spherically symmetric 3-brane when matter fields propagate in the bulk. For a well defined class of conformal fields of weight -4 we determine a new set of exact 5-dimensional solutions which localize gravity in the vicinity of the brane and are stable under radion field perturbations. Geometries which describe the dynamics of inhomogeneous dust, generalized dark radiation and homogeneous polytropic dark energy are shown to belong to this set.Comment: 7 pages, latex, no figures. Talk given at the Fifth International Workshop on New Worlds in Astroparticle Physics, University of Algarve, Faro, 8-10 January 2005. To be published in the workshop proceeding

Braneworlds, Conformal Fields and the Gravitons

We investigate the dynamics of Randall-Sundrum AdS5 braneworlds with 5-dimensional conformal matter fields. In the scenario with a compact fifth dimension the class of conformal fields with weight -4 is associated with exact 5-dimensional warped geometries which are stable under radion field perturbations and describe on the brane the dynamics of inhomogeneous dust, generalized dark radiation and homogeneous polytropic dark energy. We analyse the graviton mode flutuations around this class of background solutions and determine their mass eigenvalues and wavefunctions from a Sturm-Liouville problem. We show that the localization of gravity is not sharp enough for large mass hierarchies to be generated. We also discuss the physical bounds imposed by experiments in particle physics, in astrophysics and in precise measurements of the low energy gravitational interaction.Comment: LaTeX, 9 pages, 2 figures. Based on talk given in the Second International Conference on Quantum Theories and the Renormalization Group in Gravity and Cosmology, CSIC and University of Barcelona, Barcelona, Spain, 11-15 July 2006. Submitted to be published in the Conference Proceedings, J. Phys. A: Math. Ge