Reheating a multi-throat universe by brane motion

We propose a mechanism of reheating after inflation in multi-throat scenarios of warped extra dimensions. Validity of an effective field theory on the standard model (SM) brane requires that the position of the SM brane during inflation be different from the position after inflation. The latter is supposed to be near the tip of the SM throat but the former is not. After inflation, when the Hubble expansion rate becomes sufficiently low, the SM brane starts moving towards the tip and eventually oscillates. The SM fields are excited by the brane motion and the universe is reheated. Since interaction between the brane position modulus and the SM fields is suppressed only by the local string scale, the modulus effectively decays into the SM fields.     

The Klein–Gordon equation in the Anti-de Sitter cosmology

This paper deals with the Klein–Gordon equation on the Poincaré chart of the 5-dimensional Anti-de Sitter universe. When the mass μ is larger than , the Cauchy problem is well-posed despite the loss of global hyperbolicity due to the time-like horizon. We express the finite energy solutions in the form of a continuous Kaluza–Klein tower and we deduce a uniform decay as . We investigate the case , ν∈N^?, which encompasses the gravitational fluctuations, ν=4, and the electromagnetic waves, ν=2. The propagation of the wave front set shows that the horizon acts like a perfect mirror. We establish that the smooth solutions decay as , and we get global Lp estimates of Strichartz type. When ν is even, there appears a lacuna and the equipartition of the energy occurs at finite time for the compactly supported initial data, although the Huygens principle fails. We address the cosmological model of the negative-tension Minkowski brane, on which a Robin boundary condition is imposed. We prove the hyperbolic mixed problem is well-posed and the normalizable solutions can be expanded into a discrete Kaluza–Klein tower. We establish some L²−L^∞ estimates in suitable weighted Sobolev spaces.     

Consistent ADD scenario with stabilized extra dimension

A model with one compact extra dimension and a scalar field of Brans–Dicke type in the bulk is discussed. It describes two branes with non-zero tension embedded into the space-time with flat background. This setup allows one to use a very simple method for stabilization of the size of extra dimension. It appears that the four-dimensional Planck mass is expressed only through parameters of the scalar field potentials on the branes.     

Dark matter in the framework of the shell-universe

We show that the shell-universe model (used to explain the observed expansion rate of the universe without a dark energy component) provides a natural mechanism for local increasing of the brane tension leading to the modified Newtons law alternative to galactic dark matter.     

Brane world cosmology in Jordan-Brans-Dicke theory

We consider the embedding of 3+1 dimensional cosmology in 4+1 dimensional Jordan-Brans-Dicke theory. We show that exponentially growing and power law scale factors are implied. Whereas the 4+1 dimensional scalar field is approximately constant for each, the effective 3+1 dimensional scalar field is constant for exponentially growing scale factor and time dependent for power law scale factor.     

Low-energy effects in brane worlds: Liennard–Wiechert potentials and Hydrogen Lamb shift

Testing extra dimensions at low-energies may lead to interesting effects. In this work a test point charge is taken to move uniformly in the 3D subspace of a (3 + n)-brane embedded in a (3 + n + 1)-space with n compact and one warped infinite spatial extra dimensions. We found that the electromagnetic potentials of the point charge match standard Liennard–Wiechert’s at large distances but differ from them close to it. These are finite at the position of the charge and produce finite self-energies. We also studied a localized Hydrogen atom and take the deviation from the standard Coulomb potential as a perturbation. This produces a Lamb shift that is compared with known experimental data to set bounds for the parameter of the model. This work provides details and extends results reported in a previous Letter. We are pleased to dedicate this work to Professor Octavio Obregón on occasion of his 60th birthday. H. A. Morales-Técotl is an associate member of the Abdus Salam ICTP, Trieste Italy.     

The 4D Klein-Gordon, Dirac and Quantization Equations from 5D Null Paths

Results from 5D induced-matter and membrane theory with null paths are extended to show that a particle obeys the 4D Klein-Gordon equation but with a variable mass. The Dirac equation also follows, but raises concerns about 4D quantization in the two natural 5D gauges, and reopens the question of a Regge-like trajectory for the spin angular momenta and squared masses of gravitationally-dominated systems.     

Casimir energy and brane stability

We investigate the role of Casimir energy as a mechanism for brane stability in five-dimensional models with the fifth dimension compactified on an S¹/_Z2$S^1/{\mathbb{Z}}_2$ orbifold, which includes the Randall–Sundrum two brane model (RS1). We employ a ζ$\zeta$-function regularization technique utilizing the Schwinger proper time method and the Jacobi theta function identity to calculate the one-loop effective potential. We show that the combination of the Casimir energies of a scalar Higgs field, the three generations of Standard Model fermions and one additional massive non-SM scalar in the bulk produces a non-trivial minimum of the potential. In particular, we consider a scalar field with a coupling in the bulk to a Lorentz violating vector particle localized to the compactified dimension. Such a scalar may provide a natural means of fine tuning needed for stabilization of the brane separation. Finally, we briefly review the possibility that Casimir energy plays a role in generating the currently observed epoch of cosmological inflation by examining a simple five-dimensional anisotropic metric.     

Transition from decelerated to accelerated cosmic expansion in braneworld universes

Braneworld theory provides a natural setting to treat, at a classical level, the cosmological effects of vacuum energy. Non-static extra dimensions can generally lead to a variable vacuum energy, which in turn may explain the present accelerated cosmic expansion. We concentrate our attention in models where the vacuum energy decreases as an inverse power law of the scale factor. These models agree with the observed accelerating universe, while fitting simultaneously the observational data for the density and deceleration parameter. The redshift at which the vacuum energy can start to dominate depends on the mass density of ordinary matter. For _m = 0.3, the transition from decelerated to accelerated cosmic expansion occurs at z _T ≈ 0.48 ± 0.20, which is compatible with SNe data. We set a lower bound on the deceleration parameter today, namely > − 1 + 3 _m /2, i.e., > − 0.55 for _m = 0.3. The future evolution of the universe crucially depends on the time when vacuum starts to dominate over ordinary matter. If it dominates only recently, at an epoch z < 0.64, then the universe is accelerating today and will continue that way forever. If vacuum dominates earlier, at z > 0.64, then the deceleration comes back and the universe recollapses at some point in the distant future. In the first case, quintessence and Cardassian expansion can be formally interpreted as the low energy limit of our model, although they are entirely different in philosophy. In the second case there is no correspondence between these models and ours.     

Black holes in brane worlds

A Kerr metric describing a rotating black hole is obtained on the three brane in a five-dimensional Randall-Sundrum brane world by considering a rotating five-dimensional black string in the bulk. We examine the causal structure of this space-time through the geodesic equations.