Related papers: Analytic Minkowski Functionals of the Cosmic Micro…
The Minkowski functionals are useful statistics to quantify the morphology of various random fields. They have been applied to numerous analyses of geometrical patterns, including various types of cosmic fields, morphological image…
Minkowski functionals quantify the morphology of smooth random fields. They are widely used to probe statistical properties of cosmological fields. Analytic formulae for ensemble expectations of Minkowski functionals are well known for…
In this work we effectively calculated the two-dimensional Minkowski functionals for cosmic microwave background (CMB) temperature maps generated by single field models of inflation with a standard kinetic term. We started with calculation…
Minkowski Functionals (MFs) are topological statistics that have become one of many standard tools used for investigating the statistical properties of cosmological random fields. They have found regular use in studies of departures from…
A Gaussian distribution of cosmic microwave background temperature fluctuations is a generic prediction of inflation. Upcoming high-resolution maps of the microwave background will allow detailed tests of Gaussianity down to small angular…
We derive analytical formulae for the Minkowski Functions of the cosmic microwave background (CMB) and large-scale structure (LSS) from primordial non-Gaussianity. These formulae enable us to estimate a non-linear coupling parameter, f_NL,…
Minkowski functionals are summary statistics that capture the geometric and morphological properties of fields. They are sensitive to all higher order correlations of the fields and can be used to complement more conventional statistics,…
The second-order formula of Minkowski functionals in weakly non-Gaussian fields is compared with the numerical $N$-body simulations. Recently, weakly non-Gaussian formula of Minkowski functionals is extended to include the second-order…
Two of the most commonly used tools to constrain the primordial non-Gaussianity are the bispectrum and the Minkowski functionals of CMB temperature anisotropies. These two measures of non-Gaussianity in principle provide distinct (though…
We analyze non-Gaussianity (NG) due to the primordial bispectrum and trispectrum using CMB temperature maps of WMAP 7-year data. We first apply the perturbative formulae of Minkowski functionals up to second-order NG derived by Matsubara…
We study Minkowski Functionals as probes of primordial non-Gaussianity in the Cosmic Microwave Background, specifically for the estimate of the primordial `local' bi-spectrum parameter f_NL, with instrumental parameters which should be…
In the conference presentation we have reviewed the theory of non-Gaussian geometrical measures for the 3D Cosmic Web of the matter distribution in the Universe and 2D sky data, such as Cosmic Microwave Background (CMB) maps that was…
We investigate the non-Gaussian signatures in Cosmic Microwave Background (CMB) maps induced by the intervening large-scale structure through weak lensing. In order to measure the deviation from the Gaussian behavior of the intrinsic…
The most direct probe of non-Gaussian initial conditions has come from bispectrum measurements of temperature fluctuations in the Cosmic Microwave Background and of the matter and galaxy distribution at large scales. Such bispectrum…
Why is non-Gaussianity interesting? One of generic predictions from inflationary scenarios is that primordial fluctuations are exactly Gaussian in linear order; however, the non-linearity in the inflation will produce weak non-Gaussianity.…
Minkowski Functionals (MF) are excellent tools to investigate the statistical properties of the cosmic background radiation (CMB) maps. Between their notorious advantages is the possibility to use them efficiently in patches of the CMB…
The angular power spectrum of the Cosmic Microwave Background (CMB) anisotropies is a key tool to study the Universe. However, it is blind to the presence of non--Gaussianities and deviations from statistical isotropy, which instead can be…
We generalize the concept of the ordinary skew-spectrum to probe the effect of non-Gaussianity on the morphology of Cosmic Microwave Background (CMB) maps in several domains: in real-space (where they are commonly known as…
We consider a cosmological model with non-Gaussian initial perturbations, which in principle could be generated in non-standard inflationary scenarios with two or more scalar fields. In particular we focus our attention on the model…
We calculate the bispectrum of the gravitational field fluctuations generated during warm inflation, where dissipation of the vacuum potential during inflation is the mechanism for structure formation. The bispectrum is non--zero because of…