# Cosmology from conservation of global energy

## TL;DR

This paper proposes that conserving the quasi-local Misner-Sharp energy within the apparent horizon offers a new perspective on cosmology, resolving issues related to energy conservation and explaining spatial flatness without the problems of standard models.

## Contribution

It introduces a conservation-based approach using Misner-Sharp energy, leading to a relational, Machian cosmological model that aligns with observations and avoids standard paradigm issues.

## Key findings

- Misner-Sharp energy conservation yields de Sitter as the unique solution.
- Total matter energy scales as curvature energy, inducing gravitational time dilation.
- Open de Sitter appears empty but contains matter effects explaining spatial flatness.

## 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.