General Relativity and Gravitation

, Volume 43, Issue 12, pp 3355–3366 | Cite as

On cosmological mass with positive Λ

Open Access
Research Article

Abstract

For asymptotically flat space-times, a very satisfactory expression for the total mass/energy of a system defined at future null infinity was provided by Bondi and Sachs, in the early 1960s. A generalization of this to space-times that are asymptotically de Sitter now has particular relevance in view of observational evidence, from 1998 onwards, indicating the presence of a positive cosmological constant Λ. In this article, some of the issues involved in such a definition are examined, showing that a somewhat different attitude to mass/energy must be taken, from that which was appropriate for asymptotically flat space-times. Two tentative suggestions are put forward for a retarded mass/energy definition with positive Λ, one based on a conformally invariant integral expression whose advanced time-derivative gives the Bondi–Sachs definition in the asymptotically flat case and the other, on the author’s 1982 approach to quasi-local energy. Such expressions could have some direct relevance to the proposal of Conformal Cyclic Cosmology, for which recent analysis of the CMB has provided some striking support.

Keywords

Cosmological constant Energy in cosmology Bondi–Sachs mass Conformal cyclic cosmology 

Notes

Acknowledgments

The author is grateful to Ben Jeffryes for a helpful suggestion.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Mathematical InstituteOxfordUK
  2. 2.Department of PhysicsUniversity of LeidenLeidenThe Netherlands

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