Related papers: Tensor Minkowski Functionals: first application to…
We use the Cosmic Microwave Background (CMB) anisotropy data from Planck to constrain the spatial fluctuations of the fine-structure constant \alpha. Through Thompson scattering of CMB photons, spatial anisotropies of \alpha lead to…
The Minkowski tensors are the natural tensor-valued generalizations of the intrinsic volumes of convex bodies. We prove two complete sets of integral geometric formulae, so called kinematic and Crofton formulae, for these Minkowski tensors.…
We apply Minkowski functionals and various derived measures to decipher the morphological properties of large-scale structure seen in simulations of gravitational evolution. Minkowski functionals of isodensity contours serve as tools to…
We present an efficient method to compute CMB anisotropies in non-flat universes. First we derive the Boltzmann equation for cosmic microwave background temperature and polarization fluctuations produced by scalar perturbations in a general…
The Gaussian Kinematic Formula (GKF, see Adler and Taylor (2007,2011)) is an extremely powerful tool allowing for explicit analytic predictions of expected values of Minkowski functionals under realistic experimental conditions for…
Inflation gives rise to a nearly scale-invariant spectrum of tensor perturbations (gravitational waves), their contribution to the Cosmic Background Radiation (CBR) anisotropy depends upon the present cosmological parameters as well as…
In this paper, the Cartan tensors of the $(\alpha,\beta)$-norms are investigated in details. Then an equivalence theorem of $(\alpha,\beta)$-norms is proved. As a consequence in Finsler geometry, general $(\alpha,\beta)$-metrics on smooth…
We present a description of CMB anisotropies generated by tensor perturbations in f(R) theories of gravity. The temperature power spectrum in the special case of $f(R)=R^n$ is computed using a modified version of CAMB package.
Higher-rank Minkowski valuations are efficient means for describing the geometry and connectivity of spatial patterns. We show how to extend the framework of the scalar Minkowski valuations to vector- and tensor-valued measures. The…
The study of shapes of the images of objects is an important issue not only because it reveals its dynamical state but also it helps to understand the object's evolutionary history. We discuss a new technique in cosmological image analysis…
We study the cosmological information contained in the Minkowski Functionals (MFs) of weak gravitational lensing convergence maps. We show that the MFs provide strong constraints on the local type primordial non-Gaussianity parameter f_NL.…
We explore the potential of the B-mode anisotropies of the Cosmic Microwave Background radiation (CMB) to constrain the shape of the primordial tensor power spectrum in a model-independent way. We expand possible perturbations to the…
The recent BICEP2 detection of degree scale CMB B-mode polarization, coupled with a deficit of observed power in large angle temperature anisotropy, suggest that the slow-roll parameter $\epsilon_H$, the fractional variation in the Hubble…
In this paper, we introduce the topological persistence diagram as a statistic for Cosmic Microwave Background (CMB) temperature anisotropy maps. A central concept in `Topological Data Analysis' (TDA), the idea of persistence is to…
It has been shown that local algorithms based on grey-scale images sometimes lead to asymptotically unbiased estimators for surface area and integrated mean curvature. This paper extends the results to estimators for Minkowski tensors. In…
We introduce surface Minkowski tensors to characterize rotational symmetries of shapes embedded in curved surfaces. The definition is based on a modified vector transport of the shapes boundary co-normal into a reference point which…
We generate simulations of the CMB temperature field as observed by the WMAP satellite, taking into account the detailed shape of the asymmetric beams and scanning strategy of the experiment, and use these to re-estimate the WMAP beam…
Cosmic microwave background (CMB) anisotropies and density fluctuations are calculated for flat cold dark matter (CDM) models with a wide range of parameters, i.e., $\Omega_0, h$ and $\Omega_B$ for both standard recombination and various…
Angular power spectra of temperature anisotropies and polarization of the cosmic microwave background (CMB) as well as the linear matter power spectra are calculated for models with three light neutrinos with non-thermal phase-space…
A new method for the statistical analysis of 3D point processes, based on the family of Minkowski functionals, is explained and applied to modelled galaxy distributions generated by a toy-model and cosmological simulations of the…