Cosmology from conservation of global energy

Abstract: It is argued that many of the problems and ambiguities of standard cosmology derive from a single one: violation of conservation of energy in the standard paradigm. Standard cosmology satisfies conservation of local energy, however disregards the inherent global aspect of energy. We therefore explore conservation of the quasi-local Misner-Sharp energy within the causal horizon, which, as we argue, is necessarily an apparent horizon. Misner-Sharp energy assumes the presence of arbitrary mass-energy. Its conservation, however, yields "empty" de Sitter (open, flat, closed) as single cosmological solution, where Misner-Sharp total energy acts as cosmological constant and where the source of curvature energy is unidentified. It is argued that de Sitter is only apparently empty of matter. That is, total matter energy scales as curvature energy in open de Sitter, which causes evolution of the cosmic potential and induces gravitational time dilation. Curvature of time accounts completely for the extrinsic curvature, i.e., renders open de Sitter spatially flat. This explains the well known, surprising, spatial flatness of Misner-Sharp energy, even if extrinsic curvature is non-zero. The general relativistic derivation from Misner-Sharp energy is confirmed by a Machian equation of recessional and peculiar energy, which explicitly assumes the presence of matter. This relational model enhances interpretation. Time-dilated open de Sitter is spatially flat, dynamically close to $\Lambda$CDM, and is shown to be without the conceptual problems of concordance cosmology.