Related papers: On the embedding of spacetime in five-dimensional …
We consider a mimetic type extension of the Weyl geometric gravity theory, by assuming that the metric of the space-time manifold can be parameterized in terms of a scalar field, called the mimetic field. The action of the model is obtained…
Cosmological consequences of the brane world scenario are reviewed in a pedagogical manner. According to the brane world idea, the standard model particles are confined on a hyper--surface (a so--called brane), which is embedded in a…
For the Laplacian of an $n$-Riemannian manifold $X$, the Weyl law states that the $k$-th eigenvalue is asymptotically proportional to $(k/V)^{2/n}$, where $V$ is the volume of $X$. We show that this result can be derived via physical…
Weyl famously argued that if space were discrete, then Euclidean geometry could not hold even approximately. Since then, many philosophers have responded to this argument by advancing alternative accounts of discrete geometry that recover…
The braneworlds models were inspired partly by Kaluza-Klein's theory, where both the gravitational and the gauge fields are obtained from the geometry of a higher dimensional space. The positive aspects of these models consist in…
H. Weyl in 1921 demonstrated that for a connected manifold of dimension greater than $1$, if two Riemannian metrics are conformal and have the same geodesics up to a reparametrization, then one metric is a constant scaling of the other one.…
We study the classical geodesic motions of nonzero rest mass test particles and photons in five-dimensional warped product spaces. We show that it is possible to obtain a general picture of these motions, using the natural decoupling that…
Quantum Hall physics has been theoretically predicted in 4-dimensions and higher. In hypothetical 2n-dimensions, the topological characters of both the bulk and the boundary are manifested as quantized non-linear transport coefficients that…
The cosmology of a brane-universe embedded in a higher dimensional bulk spacetime presents some peculiarities not seen in ordinary (3+1) dimensional gravity. I summarize the current understanding, with emphasis on the suggestion by Randall…
Weyl fermions are one of the simplest objects that link ideas in geometry and topology to highenergy physics and condensed matter physics. Although the existence of Weyl fermions as elementary particles remains dubious, there is mounting…
In this work we would like to address the problem of the effect of bulk matter on the brane cosmological evolution in a general way. We assume that the spatial part of the brane metric is not maximally symmetric, therefore spatially…
A little known theorem due to Campbell is employed to establish the local embedding of a wide class of 4-dimensional spacetimes in 5-dimensional Ricci-flat spaces. An embedding for the class of n-dimensional Einstein spaces is also found.…
We present a numerical method for solving Weyl's embedding problem which consists of finding a global isometric embedding of a positively curved and positive-definite spherical 2-metric into the Euclidean three space. The method is based on…
We study cosmological perturbations in a brane-world scenario where the matter fields live on a four-dimensional brane and gravity propagates in the five-dimensional bulk. We present the equations of motion in an arbitrary gauge for metric…
To capture important physical properties of a spacetime we construct a new diagram, the card diagram, which accurately draws generalized Weyl spacetimes in arbitrary dimensions by encoding their global spacetime structure, singularities,…
We investigate the possibility that the observed behavior of test particles outside galaxies, which is usually explained by assuming the existence of dark matter, is the result of the dynamical evolution of particles in a Weyl type…
The advanced state of cosmological observations constantly tests the alternative theories of gravity that originate from Einstein's theory. However, this is not restricted to modifications to general relativity. In this sense, we work in…
One of the key conceptual challenges in quantum gravity is to understand how quantum theory should modify the very notion of spacetime. One way to investigate this question is to study the alternatives to Schr\"odinger quantum mechanics.…
We study the particle spectrum and the unitarity of the generic n-dimensional Weyl-invariant quadratic curvature gravity theories around their (anti-)de Sitter [(A)dS] and flat vacua. Weyl symmetry is spontaneously broken in (A)dS and…
The Weyl geometric gravity theory, in which the gravitational action is constructed from the square of the Weyl curvature scalar and the strength of the Weyl vector, has been intensively investigated recently. The theory admits a…