The relative energy of homogeneous and isotropic universes from variational principles

摘要: We calculate the relative conserved currents, superpotentials and quantities between two homogeneous isotropic universes. In particular, we prove that their "energy" (defined as quantity associated to cosmic time coordinate translations for a comoving observer) is vanishing so are other related Lie subalgebra of vector fields isomorphic Poincare algebra. These also in time. find such kind solution which though non-vanishing. This example provides at least insights theory General Relativity. First, contribution cosmological matter fluid carefully studied proved be vanishing. Second, explicitly show our superpotential (that happens coincide with so-called KBL potential although it generated differently) strong conservation laws under much weaker hypotheses than ones usually required. symmetry generator not needed Killing (nor background, nor asymptotically Killing), prescription quasi-local works fine finite region too no matching condition on boundary