Related papers: Sharpened Dynamical Cobordism
By means of the present geometrical and dynamical observational data, it is very hard to establish, from a statistical perspective, a clear preference among the vast majority of the proposed models for the dynamical dark energy and/or…
The lift of K-theoretic D-brane charge to M-theory was recently hypothesized to land in Cohomotopy cohomology theory. To further check this "Hypothesis H", here we explicitly compute the constraints on fractional D-brane charges at…
I show here that if we construct D-branes not in the form of infinite superpositions of string modes, in order to satisfy the technical condition of coherence by means of eigenstates of annihilation operators, but instead insist on an…
Continuing the analysis in a unified scheme for treating generalized superselection sectors based upon the notion of selection criteria for states of relevance in quantum physics, we extend the Doplicher-Roberts superselection theory for…
Given an $n$-dimensional compact complex Hermitian manifold $X$, a $C^\infty$ complex line bundle $L$ equipped with a connection $D$ whose $(0,\,1)$-component $D''$ squares to zero and a real-valued function $\eta$ on $X$, we prove that the…
The aim of this Thesis is twofold. On the one hand, we find the necessary and sufficient conditions for a maximally supersymmetric supergravity theory in 3D to be a solution of 11D supergravity (but the result is general and also holds for…
Based on the idea that the components of a cosmological metric may be determined by the total gravitational potential of the universe, the scalar field $\phi=1/G$ in the Jordan-Brans-Dicke (JBD) theory is introduced as evolving with the…
We consider detection and localization of an abrupt break in the covariance structure of high-dimensional random data. The paper proposes a novel testing procedure for this problem. Due to its nature, the approach requires a properly chosen…
The hypothesis of a discrete fabric of the universe--the "Planck scale"--is always on stage, since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for…
The so called $f(X)$ hybrid metric-Palatini gravity presents a unique viable generalisation of the $f(R)$ theories within the metric-affine formalism. Here the cosmology of the $f(X)$ theories is studied using the dynamical system approach.…
We introduce a formalism based on a combinatorial notion of cell complex subject to an inclusion-reversing duality operation. Our main goal is to open the way for a functorial definition of field theories in a context where no manifold or…
One way to account for the acceleration of the universe is to modify general relativity, rather than introducing dark energy. Typically, such modifications introduce new degrees of freedom. It is interesting to consider models with no new…
This paper introduces a geometric mechanics framework for constrained systems on principal bundles through \emph{compatible pairs} $(\mathcal{D}, \lambda)$, addressing fundamental challenges in gauge-constrained physical systems. We…
Standard singularity theorems are proven in Lorentzian manifolds of arbitrary dimension n if they contain closed trapped submanifolds of arbitrary co-dimension. By using the mean curvature vector to characterize trapped submanifolds, a…
Alternatives to Einstein's theory of general relativity can be distinguished by measuring the parametrised post Newtonian parameters. Two such parameters $\beta$ and $\gamma$, equal to one in Einstein theory, can be obtained from static…
Regular black strings solutions associated to a dynamical Friedmann-Robertson-Walker braneworld are obtained as a particular case of a regular bulk metric, in the context of a variable brane tension. By analyzing the 5D Kretschmann…
We report on some advances made in the problem of singularities in general relativity. First is introduced the singular semi-Riemannian geometry for metrics which can change their signature (in particular be degenerate). The standard…
We argue that the space-time uncertainty relation of the form $\Delta X \Delta T \gtrsim \alpha'$ for the observability of the distances with respect to time, $\Delta T$, and space, $\Delta X$, is universally valid in string theory…
A physical interpretation of axioms of the differential structure of space-time is presented. Consequences of such interpretation for cosmic string's space-time with a scalar field are studied. It is shown that the assumption of smoothness…
The Eddington-inspired-Born-Infeld scenario (EiBI) can prevent the Big Bang singularity for a matter content whose equation of state is constant and positive. In a recent paper we showed that, on the contrary, it is impossible to smooth a…