On cosmological mass with positive Λ
 Roger Penrose
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Abstract
For asymptotically flat spacetimes, 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 spacetimes 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 spacetimes. 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 timederivative gives the Bondi–Sachs definition in the asymptotically flat case and the other, on the author’s 1982 approach to quasilocal 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.
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 Title
 On cosmological mass with positive Λ
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

General Relativity and Gravitation
Volume 43, Issue 12 , pp 33553366
 Cover Date
 20111201
 DOI
 10.1007/s107140111255x
 Print ISSN
 00017701
 Online ISSN
 15729532
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Cosmological constant
 Energy in cosmology
 Bondi–Sachs mass
 Conformal cyclic cosmology
 Industry Sectors
 Authors

 Roger Penrose ^{(1)} ^{(2)}
 Author Affiliations

 1. Mathematical Institute, 2429 St Giles’, Oxford, OX1 3LB, UK
 2. Department of Physics, University of Leiden, 2 Niels Bohrweg, Leiden, The Netherlands