General covariance violation and the gravitational dark matter: Scalar graviton
- PDF / 448,156 Bytes
- 7 Pages / 612 x 792 pts (letter) Page_size
- 21 Downloads / 200 Views
ELEMENTARY PARTICLES AND FIELDS Theory
General Covariance Violation and the Gravitational Dark Matter: Scalar Graviton* Yu. F. Pirogov Institute for High Energy Physics, Protvino, Moscow oblast, 142284 Russia Received May 19, 2005; in final form, October 28, 2005
Abstract—The violation of the general covariance is proposed as a resource of the gravitational dark matter. The minimal violation of the covariance to the unimodular one is associated with the massive scalar graviton as the simplest representative of such matter. The Lagrangian formalism for a continuous medium, a perfect fluid in particular, in the scalar graviton environment is developed. The implications for cosmology are briefly indicated. PACS numbers : 04.20.Cv, 95.35.+d, 98.80.-k DOI: 10.1134/S1063778806080102
1. INTRODUCTION General Relativity (GR) is the viable theory of gravity, perfectly consistent with observations. Nevertheless, it encounters a number of conceptual problems, among which one can mention that of the dark matter (DM). To solve the latter problem, one usually adjusts the conventional or new matter particles, remaining still in the realm of GR (for a recent review, see, e.g., [1]). The ultimate goal of the DM being in essence to participate only in gravitational interactions, one can try to attribute to this purpose the gravity itself, thus going beyond GR. Namely, GR is the field theory of the massless tensor graviton as a part of the metric. However, the metric also contains extra degrees of freedom, which could be associated with the scalar, vector, and tensor gravitons. Nevertheless, all the extra degrees of freedom lack the explicit physical manifestations. This is due to the fact that GR incorporates as the basic symmetry the general covariance (GC). The latter serves as the gauge symmetry to remove from the observables the degrees of freedom in excess of the massless tensor graviton. So, to associate the extra particles contained in the metric with (a part of) the DM, the violation of the GC is obligatory. Starting from GR, an arbitrary variety of GC violations is admissible. Contrary to this, a hierarchy of GC violations is expected in the framework of the affine Goldstone approach to gravity [2]. The latter approach, in contrast to GR, is based on two symmetries: the global affine symmetry (AS) plus the GC. As a result, there are two conceivable types of GC violations: those with and without explicit AS ∗
violation. The first type of violation is to be strongly suppressed. But the second one is a priori arbitrary. Under reasonable assumptions, the GC violation can be parametrized in the affine Goldstone approach through the background metric.1) Marginally, the latter description can depend only on the determinant of the background metric. In this case, there still resides the unimodular covariance (UC). In comparison with the GC, the UC lacks only the local scale transformations. Being next-ofkin to the GC, the UC suffices to incorporate both the massive scalar graviton and the massless tensor one, but nothing redundant.2) The viola
Data Loading...
