Casimir effect with one large extra dimension

In this work, I study the Casimir effect of a massive complex scalar field in the presence of one large compactified extra dimension. I investigate the case of a scalar field confined between two parallel plates in the macroscopic three dimensions, and examine the cases of Dirichlet and mixed (Dirichlet–Neumann) boundary conditions on the plates. The case of Neumann boundary conditions is uninteresting, since it yields the same result as the case of Dirichlet boundary conditions. The scalar field also permeates a fourth compactified dimension of a size that could be comparable to the distance between the plates. This investigation is carried out using the [Formula: see text]-function regularization technique that allows me to obtain exact expressions for the Casimir energy and pressure. I discover that when the compactified length of the extra dimension is similar to the plate distance, or slightly larger, the Casimir energy and pressure become significantly different than their standard three-dimensional values, for either Dirichlet or mixed boundary conditions. Therefore, the Casimir effect of a quantum field that permeates a compactified fourth dimension could be used as an effective tool to explore the existence of large compactified extra dimensions.

De Sitter braneworld and gravitational waves

We study the braneworld theory constructed by multi scalar fields. The model contains a smooth and infinitely large extra dimension, allowing the background fields propagating in it. We give a de Sitter solution for the four-dimensional cosmology as a good approximation to the early universe inflation. We show that the graviton has a localizable massless mode, and a series of continuous massive modes, separated by a mass gap. There could be a normalizable massive mode, depending on the background solution. The gravitational waves of massless mode evolve the same as the four dimensional theory, while that of the massive modes evolve greatly different from the massless mode.

Large star/rose extra dimension with small leaves/petals

In this paper, we propose to compactify a single Large Extra Dimension (LED) on a star/rose graph with a large number of identical leaves/petals. The 5D Planck scale can be chosen to be [Formula: see text] TeV which can provide a path to solve the gauge hierarchy problem. The leaf/petal length scale is of [Formula: see text], where [Formula: see text] GeV is the weak scale, without the large geometrical hierarchy of the traditional LED models to stabilize. The 4D fields of the SM are localized on a 3-brane at the central vertex of the star/rose graph. We predict a tower of feebly coupled weak scale Kaluza–Klein (KK) gravitons below a regime of strongly coupled gravitational phenomena above the TeV scale. Moreover, we reformulate in our setup the LED mechanism to generate light Dirac neutrinos, where the right-handed neutrinos are KK-modes of gauge singlet fermions propagating in the bulk. A large number of KK-gravitons and KK-neutrinos interact only gravitationally and thus constitute a hidden sector.

The status of modern five-dimensional gravity (A short review: Why physics needs the fifth dimension)

Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification in regard to string theory, but is misguided as applied to five-dimensional (5D) theories with a large extra dimension. Such theories smoothly embed general relativity, ensuring recovery of the latter's observational support. When the embedding of spacetime is carried out in accordance with Campbell's theorem, the resulting 5D theory naturally explains the origin of classical matter and vacuum energy. Also, constraints on the equations of motion near a high-energy surface or membrane in the 5D manifold lead to quantization and quantum uncertainty. These are major returns on the modest investment of one extra dimension. Instead of fruitless bickering about whether it is possible to "see" the fifth dimension, it is suggested that it be treated on par with other concepts of physics, such as time. The main criterion for the acceptance of a fifth dimension (or not) should be its usefulness.

NEUTRINO SHORTCUTS IN SPACETIME

Theories with large extra dimensions may be tested using sterile neutrinos living in the bulk. A bulk neutrino can mix with a flavor neutrino localized in the brane leading to unconventional patterns of neutrino oscillations. A resonance phenomenon, strong mixing between the flavor and the sterile neutrino, allows one to determine the radius of the large extra dimension. If our brane is curved, then the sterile neutrino can take a shortcut through the bulk, leading to an apparent superluminal neutrino speed. The amount of "superluminality" is directly connected to parameters determining the shape of the brane. On the experimental side, we suggest that a long baseline neutrino beam from CERN to NESTOR neutrino telescope will help to clarify these important issues.