Implications of Symmetry and Pressure in Friedmann Cosmology. I. Formalism
Abstract
We show that derivation of Friedmann’s equations from the EinsteinHilbert 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 RobertsonWalker 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 constantdensity sphere, and the static deSitter sphere. From conservation of stressenergy, 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 nonrelativistic material. In relativistic material, however, the effect can be significant. We comment on the implications of this study for the dark energy problem.
 Publication:

The Astrophysical Journal
 Pub Date:
 September 2019
 DOI:
 10.3847/15384357/ab32da
 arXiv:
 arXiv:2107.06643
 Bibcode:
 2019ApJ...882...19C
 Keywords:

 cosmology: theory;
 dark energy;
 gravitation;
 methods: analytical;
 stars: black holes;
 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 ApJ 882 19 (2019)