Is there vacuum when there is mass? Vacuum and nonvacuum solutions for massive gravity
Abstract
Massive gravity is a theory which has a tremendous amount of freedom to describe different cosmologies, but at the same time, the various solutions one encounters must fulfil some rather nontrivial constraints. Most of the freedom comes not from the Lagrangian, which contains only a small number of free parameters (typically three depending on counting conventions), but from the fact that one is in principle free to choose the reference metric almost arbitrarily—which effectively introduces a nondenumerable infinity of free parameters. In the current paper, we stress that although changing the reference metric would lead to a different cosmological model, this does not mean that the dynamics of the universe can be entirely divorced from its matter content. That is, while the choice of reference metric certainly influences the evolution of the physically observable foreground metric, the effect of matter cannot be neglected. Indeed the interplay between matter and geometry can be significantly changed in some specific models; effectively since the graviton would be able to curve the spacetime by itself, without the need of matter. Thus, even the set of vacuum solutions for massive gravity can have significant structure. In some cases, the effect of the reference metric could be so strong that no conceivable material content would be able to drastically affect the cosmological evolution.
Dedicated to the memory of Professor Pedro F GonzálezDíaz
 Publication:

Classical and Quantum Gravity
 Pub Date:
 August 2013
 DOI:
 10.1088/02649381/30/15/155021
 arXiv:
 arXiv:1301.2334
 Bibcode:
 2013CQGra..30o5021M
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Extragalactic Astrophysics;
 High Energy Physics  Theory
 EPrint:
 V1: 9 pages. V2: 10 pages, 5 references added. V3: 11 pages, some discussion added. This version accepted for publication in Classical and Quantum Gravity