Implications of Symmetry and Pressure in Friedmann Cosmology. I. Formalism

TL;DR

This paper revisits the derivation of Friedmann equations, revealing that pressure should be interpreted as an average over all regions, including compact objects, with implications for understanding dark energy.

Contribution

It introduces a new interpretation of pressure in Friedmann cosmology based on perturbation series and averaging, affecting the understanding of energy shifts in relativistic matter.

Findings

Pressure is an average over all regions, including interiors of compact objects.

Energy shifts in relativistic matter can be significant, unlike in non-relativistic cases.

The approach has implications for the dark energy problem.

Abstract

We show that derivation of Friedmann's equations from the Einstein-Hilbert action, paying attention to the requirements of isotropy and homogeneity during the variation, leads to a different interpretation of pressure than what is typically adopted. Our derivation follows if we assume that the unapproximated metric and Einstein tensor have convergent perturbation series representations on a sufficiently large Robertson-Walker coordinate patch. We find the source necessarily averages all pressures, everywhere, including the interiors of compact objects. We demonstrate that our considerations apply (on appropriately restricted spacetime domains) to the Kerr solution, the Schwarzschild constant-density sphere, and the static de-Sitter sphere. From conservation of stress-energy, it follows that material contributing to the averaged pressure must shift locally in energy. We show that these cosmological energy shifts are entirely negligible for non-relativistic material. In relativistic material, however, the effect can be significant. We comment on the implications of this study for the dark energy problem.