Related papers: Expected Lipschitz-Killing curvatures for spin ran…
We make use of O(2r+1) spinning particle models to construct linearized higher-spin curvatures in (A)dS spaces for fields of arbitrary half-integer spin propagating in a space of arbitrary (even) dimension: the field potentials, whose…
Geometrical and statistical properties of polarization of CMB are analyzed. Singular points of the vector field which describes CMB polarization are found and classified. Statistical distribution of the singularities is studied. A possible…
We study the a.s. convergence of a sequence of random embeddings of a fixed manifold into Euclidean spaces of increasing dimensions. We show that the limit is deterministic. As a consequence, we show that many intrinsic functionals of the…
Fractal Lipschitz-Killing curvature measures C^f_k(F,.), k = 0, ..., d, are determined for a large class of self-similar sets F in R^d. They arise as weak limits of the appropriately rescaled classical Lipschitz-Killing curvature measures…
A nonsingular emergent universe cosmology can be realized by a nonconventional spinor field as first developed in \cite{Cai:2012yf}. We study the mechanisms of generating scale-invariant primordial power spectrum of curvature perturbation…
The genus statistics of isodensity contours has become a well-established tool in cosmology. In this Letter we place the genus in the wider framework of a complete family of morphological descriptors. These are known as the Minkowski…
Both WMAP and PLANCK missions reported the extremely Cold Spot (CS) centered at Galactic coordinate ($l=209^{\circ}$, $b=-57^{\circ}$) in CMB map. In this paper, we study the local non-Gaussianity of CS by defining the local Minkowski…
We present exact non-Gaussian joint likelihoods for auto- and cross-correlation functions on arbitrarily masked spherical Gaussian random fields. Our considerations apply to spin-0 as well as spin-2 fields but are demonstrated here for the…
The periodic standing wave approach to binary inspiral assumes rigid rotation of gravitational fields and hence helically symmetric solutions. To exploit the symmetry, numerical computations must solve for ``helical scalars,'' fields that…
In free completely symmetric tensor gauge field theories on Minkowski space-time, all gauge invariant functions and Killing tensor fields are computed, both on-shell and off-shell. These problems are addressed in the metric-like formalisms.
We test the statistical isotropy (SI) of the $E$-mode polarization of the Cosmic Microwave Background (CMB) radiation observed by the Planck satellite using two statistics, namely, the $\alpha$ estimator that is derived from the contour…
In this paper, we continue the study of the Killing symmetries of a N-dimensional generalized Minkowski space, i.e. a space endowed with a (in general non-diagonal) metric tensor, whose coefficients do depend on a set of non-metrical…
Motivated by the classical Euler elastic curves, David A. Singer posed in 1999 the problem of determining a plane curve whose curvature is given in terms of its position. We propound the same question in Lorentz-Minkowski plane, focusing on…
We consider the possibility of extra spinning particles during inflation, focussing on the spin-2 case. Our analysis relies on the well-known fully non-linear formulation of interacting spin-2 theories. We explore the parameter space of the…
The asymptotic structure of three-dimensional higher-spin anti-de Sitter gravity is analyzed in the metric approach, in which the fields are described by completely symmetric tensors and the dynamics is determined by the standard…
We analyse the implications of the presence of spatial curvature in modified gravity models. As it is well known, the current standard cosmological model, the $\Lambda$CDM, is assumed to be spatially flat based on the results of many…
In this work, the effects of a nonminimally coupled model of gravity on a perturbed Minkowski metric are presented. The action functional of the model involves two functions $f^1(R)$ and $f^2(R)$ of the Ricci scalar curvature $R$. Based…
The aim of the paper is to extend the notion of $\alpha$-geometry in the classical and in the noncommutative case by introducing a more general class of pull-back metrics and to give concrete formulas for the scalar curvature of these…
The motion of particles on spherical $1 + 3$ dimensional spacetimes can, under some assumptions, be described by the curves on a 2-dimensional manifold, the optical and Jacobi manifolds for null and timelike curves, respectively. In this…
Using the complete orthonormal basis sets of nonrelativistic and quasirelativistic orbitals introduced by the author in previous papers for particles with arbitrary spin the new analytical relations for the -component relativistic tensor…