Lie Group of Spacetime

Abstract

A brief review is presented of de Sitter-Fantappiè relativity, and we propose some cosmological reflections suggested by this theory. Compared to the original works, some deductions have been very simplified, and only the physical meaning of the equations has been analyzed.

Cosmos and Particles: a Different View of Dark Matter

“…It follows from equation (6) that the dark matter inside a spherical molecule is uniformly distributed with a density: (7) We note that if in equation (7) the molecular radius were replaced with the De Sitter radius r one would obtain exactly the critical mean density (apart from the dilution factor R 3 caused by expansion), as discussed in reference [11]: (8) One can easily see that the spatial mean of the field a, extended to volumes comprising many molecules, produces the same dynamic effects as the uniform density (8). Indeed, let us imagine a frame of reference whose origin is placed in a certain pointevent of PGR spacetime, and consider the a(x) vector field seen in this reference (x is the spatial distance vector from the origin).…”

“…Projective Special Relativity (PSR), perhaps more commonly known as De Sitter relativity [4][5][6][7][8][9]13], was suggested *Address correspondence to this author at the AUSL Medical Physics Laboratory; Via Enrico Fermi 15, 01100 Viterbo (Italy) and Einstein-Galilei Institute for Theoretical Physics and Advanced Mathematics (I.F.M. ); Via Santa Gonda 14, 59100 Prato Italy; Tel: +39 761 1711055; Fax: +39 761 1711055; E-mail: fisica1.san@asl.vt.it by Fantappié in 1954 as the most general relativity that could be associated with a global covariance group of the physical laws in (3+1)-dimensional spacetime [14], having the Poincaré group as a local limit.…”

“…We shall assume that the reader is familiar with the language used in this approach, especially with the concept of the granular structure of "cosmic fluid" organized in "molecules". For a systematic description, please see references [4][5][6][7][8][9][10][11][12]. This paper is structured as follows.…”