We investigate the relations between the physical quantities and the physical constants by the dimensional analysis. From normal form of uncertainty relations (URs), we propose an assumption which the physical quantities have the formal symmetry with the physical constants; and find three basic formulas. A physical quantity has a corresponding Planck scale and many physical quantities have the ...

We investigate constraints on cosmic reionization extracted from the Planck cosmic microwave background (CMB) data. We combine the Planck CMB anisotropy data in temperature with the low-multipole polarization data to fit ΛCDM models with various parameterizations of the reionization history. We obtain a Thomson optical depth τ = 0.058±0.012 for the commonly adopted instantaneous reionization mo...

We describe the all-sky Planck catalogue of clusters and cluster candidates derived from Sunyaev–Zeldovich (SZ) effect detections using the first 15.5 months of Planck satellite observations. The catalogue contains 1227 entries, making it over six times the size of the Planck Early SZ (ESZ) sample and the largest SZ-selected catalogue to date. It contains 861 confirmed clusters, of which 178 ha...

Abstract. We present a novel code which solves the Vlasov-Fokker-Planck (VFP) equation in three dimensional magnetic turbulence using finite difference methods. The approach is distinct from particle tracking codes. The angular component of velocity space distribution function is represented by a spherical harmonic expansion drawing on an approach pioneered by A.R. Bell et al. (PPCF 48, R37 (20...