Lagrangian density and local symmetries of inhomogeneous hyperconical universes

Abstract

Hyperconical universes can be represented by means of an inhomogeneous metric with positive curvature and linear expansion, that is isomorphic to flat universes with acceleration thanks to an appropriate transformation. Various symmetry properties of this metric are analysed, primarily at the local scale. In particular, the Lagrangian formalism and the Arnowitt–Deser–Misner (ADM) equations are applied. To this extent, a modified gravity Lagrangian density is derived, from which the comoving paths as solutions of the Euler–Lagrange equations leading to a stationary linear expansion are deduced. It is shown that the evolution of this alternate metric is compatible with the ADM formalism when applied to the modified Lagrangian density, thanks to a redefinition of the energy density baseline (according to the global curvature). Finally, results on symmetry properties imply that only the angular momenta are global symmetries. The radial inhomogeneity of the metric is interpreted as an apparent radial acceleration, which breaks all the non-rotational local symmetries at large distances.