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 isomorph 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 provide 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.

Galaxy rotation curve in hyperconical universes: a natural relativistic MOND

“…The present work aims to formulate MOND-like dynamics with the minimum possible number of Lagrangian terms using natural features of the hyperconical universes in agreement with our previous work [41][42][43][44]. To address this goal, a hyperconical model was built by concatenating two steps.…”

“…The modification of the Lagrangian density implies that metrics of the Universe are globally independent of the matter content. Consistently, applying Friedmann equations to hyperconical cosmology [43], it is displayed that linear expansion produces the same equation of state of w = − 1 3 that implies a globally 'zero active gravitational mass-energy'. Moreover, the solution of k = 1 predicts [44]: (1) a third-order ΛCDM-compatible (apparent) acceleration when the hyperconical Universe is projected to an intrinsic viewpoint; (2) consequently, an apparent dark energy about Ω Λ = 0.70 is found as a constant for any age of the Universe; (3) dark matter is another parameter whose value could be totally or partially consequence of the distortion projection; and (4) the Hubble tension observed between direct geometrical methods (e.g.…”

“…Assuming that GR and ADM are valid at least at a local scale, the consistency of the hypercone-based dynamics displayed three remarkable results in [43]: (1) total energy density of the Universe is inactive since the equation of state is w = − 1 3 ;…”

“…The present work assumes that GR needs to be adapted to our previous results [41][42][43][44], especially concerning the 'zero active mass' (w = − 1 3 ), also proposed by Melia [49], and the modified Lagrangian density (equation ( 8)). To reach the goal of deriving natural galaxy dynamics, this paper is structured in four main sections: section 2 describes the theoretical framework of the hyperconical model; section 3 details the derivation of rotation curves; section 4 analyzes observational constraints with galaxies collected from the SPARC database [50,51], and section 5 enumerates the main conclusions of the work.…”

“…The model used in this study is the hyperconical Universe, which we developed in [41][42][43]. The basic idea of the model is that the Universe is globally homogeneous under an extrinsic viewpoint, but not under its intrinsic metric at large scales.…”