Cosmic Forms

Abstract

The continuous 1D defects of an isotropic homogeneous material in a flat 3D space are classified by the Volterra process construction method. We employ the same method to classify the continuous 2D defects of a vacuum in a 4D maximally symmetric spacetime. These so-called \textit{cosmic forms} fall into three classes: i)- $m$-forms, akin to 3D space disclinations, related to ordinary rotations, analogous to Kibble's global cosmic strings (except that being continuous any deficit angle is allowed); ii)- $t$-forms, related to Lorentz boosts (hyperbolic rotations); iii)- $r$-forms, never considered so far, related to null rotations. A detailed account of their metrics is presented. In each class, one distinguishes between wedge forms, whose singularities occupy a 2D world sheet, and twist or mixed forms, whose inner structure appears as a non-singular \textit{core} separated from the outer part by a 3D world shell with distributional curvature and/or torsion. Relaxation processes of the world shell involve new types of topological interactions between cosmic dislocations and cosmic disclinations. The resulting structures of the core region itself are not explored in this article. Whereas $m$-forms are \textit{compatible} with the usual cosmological principle (CP) of space homogeneity and isotropy, $t$- and $r$-forms demand spacetime homogeneity. Thus we advance that $t$- and $r$-forms are typical of a primeval false vacuum obeying the perfect CP in a de Sitter spacetime. Cosmic forms may assemble into networks with conservation laws at their nodes, such that all the segments are made of \textit{positive} forms, say, thus generating some characteristic curvature field. To this network may be adjunct a conjugated network made of \textit{negative} forms, in order to tune the final spatial curvature to a given value.