Galilei covariance and (4,1) de Sitter space

A vector space G is introduced such that the Galilei transformations are considered linear mappings in this manifold. The covariant structure of the Galilei Group (Y. Takahashi, Fortschr. Phys. 36 (1988) 63; 36 (1988) 83) is derived and the tensor analysis is developed. It is shown that the Euclidean space is embedded the (4,1) de Sitter space through in G. This is an interesting and useful aspect, in particular, for the analysis carried out for the Lie algebra of the generators of linear transformations in G.Comment: Late

Big-bang nucleosynthesis and gamma-ray constraints on cosmic strings with a large Higgs condensate

We consider constraints on cosmic strings from their emission of Higgs particles, in the case that the strings have a Higgs condensate with amplitude of order the string mass scale, assuming that a fraction of the energy of the condensate can be turned into radiation near cusps. The injection of energy by the decaying Higgs particles affects the light element abundances predicted by standard big-bang nucleosynthesis (BBN) and also contributes to the diffuse gamma-ray background (DGRB) in the Universe today. We examine the two main string scenarios (Nambu-Goto and field theory) and find that the primordial helium and deuterium abundances strongly constrain the string tension and the efficiency of the emission process in the NG scenario, while the strongest BBN constraint in the FT scenario comes from the deuterium abundance. The Fermi-LAT measurement of the DGRB constrains the field theory scenario even more strongly than previously estimated from EGRET data, requiring that the product of the string tension μ and Newton’s constant G is bounded by Gμ≲2.7×10−11β−2ft, where β2ft is the fraction of the strings’ energy going into Higgs particles

Bounds for Invariance Pressure

This paper provides an upper for the invariance pressure of control sets with nonempty interior and a lower bound for sets with finite volume. In the special case of the control set of a hyperbolic linear control system in R^{d} this yields an explicit formula. Further applications to linear control systems on Lie groups and to inner control sets are discussed.Comment: 16 page