Related papers: Multidimensional Topological Foam
We consider a cosmological model with two scalar fields minimally coupled to gravity which have a mixed kinetic term. Hence, Chiral cosmology is included in our analysis. The coupling function and the potential function, which depend on one…
Within the scope of multidimensional Kaluza--Klein gravity with nonlinear curvature terms and two spherical extra spaces of dimensions $m$ and $n$, we study the properties of an effective action for the scale factors of the extra…
By compactifying a critical bosonic string theory on an internal non-flat space with a constant volume, we study the role played by the closed string tachyon in the cosmology of the effective four-dimensional space-time. The effective…
We consider scalar perturbations of energy-density for a class of cosmological models where an early phase of accelerated expansion evolves, without any fine-tuning for graceful exit, towards the standard Friedman eras of observed universe.…
A unified construction of canonical $H^m$-nonconforming finite elements is developed for $n$-dimensional simplices for any $m, n \geq 1$. Consistency with the Morley-Wang-Xu elements [Math. Comp. 82 (2013), pp. 25-43] is maintained when $m…
A two dimensional string effective action is obtained by dimensionally reducing the bosonic part of the ten dimensional heterotic string effective action. It is shown that this effective action, with a few restrictions on some backgrounds…
A Riemannian manifold is a called a good rational expander in dimension $i$ if every $i$-cycle bounds a rational $i+1$-chain of comparatively small volume. We construct 3-manifolds which are good expanders in all dimensions. On the other…
Multidimensional cosmological models with $n~(n > 1)$ Einstein spaces are discussed classically and with respect to canonical quantization. These models are integrable in the case of Ricci flat internal spaces. For negative curvature of the…
In this paper we will discuss how cosmic strings can be used to bridge the gap between the local geometry of our spacetime model and the global topology. The primary tool is the theory of foliations and surfaces, and together with…
In this note we discuss a toy model in which the value of the effective cosmological constant is associated with a symmetry properties of the vacuum background solution and defined by the model parameter associated with a scalar field…
In the saddle point approximation, the Euclidean path integral for quantum gravity closely resembles a thermodynamic partition function, with the cosmological constant $\Lambda$ playing the role of temperature and the ``density of…
An exactly solvable bounce model in loop quantum cosmology is identified which serves as a perturbative basis for realistic bounce scenarios. Its bouncing solutions are derived analytically, demonstrating why recent numerical simulations…
We show that cosmological observables can constrain the topology of the compact additional dimensions predicted by string theory. To do this, we develop a general strategy for relating cosmological observables to the microscopic parameters…
To support the validity of a factorizable metric ansatz used in string cosmology, we investigate a toy problem in RSI model. For this purpose, we revise the gradient expansion method to conform to the factorizable metric ansatz. By solving…
Theory of multi-dimensional representation of free energy surface of protein folding is developed by adopting structural order parameters of multiple regions in protein as multiple coordinates. Various scenarios of folding are classified in…
We consider definable topological spaces of dimension one in o-minimal structures, and state several equivalent conditions for when such a topological space $\left(X,\tau\right)$ is definably homeomorphic to an affine definable space…
Chemical space which encompasses all stable compounds is unfathomably large and its dimension scales linearly with the number of atoms considered. The success of machine learning methods suggests that many physical quantities exhibit…
Multidimensional cosmological models with factorizable geometry and their dimensional reduction to effective four-dimensional theories are analyzed on sensitivity to different scalings. It is shown that a non-correct gauging of the…
Multidimensional cosmological model describing the evolution of n+1 Einstein spaces in the theory with several scalar fields and forms is considered. When a (electro-magnetic composite) p-brane Ansatz is adopted the field equations are…
The continuous 1D defects of an isotropic homogeneous material in a flat 3D space are classified by the Volterra process construction method. We employ the same method to classify the continuous 2D defects of a vacuum in a 4D maximally…