Transformation of the Angular Power Spectrum of the Cosmic Microwave Background(CMB)Radiation into Reciprocal Spaces and Consequences of This Approach

A formalism of solid state physics has been applied to provide an additional tool for the research of cosmological problems. It is demonstrated how this new approach could be useful in the analysis of the Cosmic Microwave Background (CMB) data. After a transformation of the anisotropy spectrum of relict radiation into a special two-fold reciprocal space it was possible to propose a simple and general description of the interaction of relict photons with the matter by a “relict radiation factor”. This factor enabled us to process the transformed CMB anisotropy spectrum by a Fourier transform and thus arrive to a radial electron density distribution function (RDF) in a reciprocal space. As a consequence it was possible to estimate distances between Objects of the order of ~102 [m] and the density of the ordinary matter ~10-22 [kg.m-3]. Another analysis based on a direct calculation of the CMB radiation spectrum after its transformation into a simple reciprocal space and combined with appropriate structure modelling confirmed the cluster structure. The internal structure of Objects may be formed by Clusters distant ~10 [cm], whereas the internal structure of a Cluster consisted of particles distant ~0.3 [nm]. The work points in favour of clustering processes and to a cluster-like structure of the matter and thus contributes to the understanding of the structure of density fluctuations. As a consequence it may shed more light on the structure of the universe in the moment when the universe became transparent for photons. On the basis of our quantitative considerations it was possible to derive the number of particles (protons, helium nuclei, electrons and other particles) in Objects and Clusters and the number of Clusters in an Object.

The Feasibility of Constraining Dark Energy Using LAMOST Redshift Survey

We consider using future redshift surveys with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope （LAMOST） to constrain the equation of state of dark energy w. We analyze the Alcock ＆ Paczynski （AP） effect imprinted on the two-point correlation function of galaxies in redshift space. The Fisher matrix analysis is applied to estimate the expected error bounds of w0 and wα from galaxy redshift surveys, w0 and wα being the two parameters in the equation of state parametrization w（z） = w0 ＋ wαz/（1 ＋ z）. Strong degeneracies between w0 and wα are found. The direction of the degeneracy in w0 - wα plane, however, rotates counter-clockwise as the redshift increases. LAMOST can potentially contribute in the redshift range up to 0.5. In combination with other high redshift surveys, such as the proposed Kilo-Aperture Optical Spectrograph project （KAOS）, the joint constraint derived from galaxy surveys at different redshift ranges is likely to efficiently break the degeneracy of w0 and wα. We do not anticipate that the nature of dark energy can be well constrained with LAMOST alone, but it may help to reduce the error bounds expected from other observations, such as the Supernova/Acceleration Probe （SNAP）.

Cluster automorphism groups of cluster algebras with coefficients

We study the cluster automorphism group of a skew-symmetric cluster algebra with geometric coefficients. We introduce the notion of gluing free cluster algebra, and show that under a weak condition the cluster automorphism group of a gluing free cluster algebra is a subgroup of the cluster automorphism group of its principal part cluster algebra(i.e., the corresponding cluster algebra without coefficients). We show that several classes of cluster algebras with coefficients are gluing free, for example, cluster algebras with principal coefficients,cluster algebras with universal geometric coefficients, and cluster algebras from surfaces(except a 4-gon) with coefficients from boundaries. Moreover, except four kinds of surfaces, the cluster automorphism group of a cluster algebra from a surface with coefficients from boundaries is isomorphic to the cluster automorphism group of its principal part cluster algebra; for a cluster algebra with principal coefficients, its cluster automorphism group is isomorphic to the automorphism group of its initial quiver.