Scalar graviton as dark matter
- PDF / 529,327 Bytes
- 5 Pages / 612 x 792 pts (letter) Page_size
- 98 Downloads / 184 Views
ELEMENTARY PARTICLES AND FIELDS Theory
Scalar Graviton as Dark Matter∗ Yu. F. Pirogov** Theory Division, Institute for High Energy Physics, Protvino, NRC “Kurchatov Institute”, Russia Received December 1, 2014
Abstract—The basics of the theory of unimodular bimode gravity built on the principles of unimodular gauge invariance/relativity and general covariance are exposed. Besides the massless tensor graviton of General Relativity, the theory includes an (almost) massless scalar graviton treated as the gravitational dark matter. A spherically symmetric vacuum solution describing the coherent scalar-graviton field for the soft-core dark halos, with the asymptotically flat rotation curves, is demonstrated as an example. DOI: 10.1134/S1063778815030084
INTRODUCTION An extension to General Relativity (GR)—the so-called Unimodular Bimode Gravity (UBG)— constructed on the principles of the general covariance and unimodular gauge invariance/relativity, with the (massless) tensor and (light) scalar gravity modes, is presented in the report. The latter is based, in part, on papers [1–5]. The basics of the theory are only indicated1) . For illustration, the dark halos built of a new particle—the (nearly) massless scalar graviton—are shown to naturally emulate the galaxy dark matter (DM) halos, with the asymptotically flat rotation curve profiles. 1. UNIMODULAR RELATIVITY
Gauge Invariance/Relativity To be consistent as the effective field theory, in particular, to allow for the quantum corrections, a gravity theory, describing the spin-two field, should be built on a gauge principle. The essence of the theory is determined by its gauge properties under the diffeomorphism transformations and the group of the gauge invariance/relativity. More particularly, the diffeomorphisms are given by the coordinate transformations: xμ → xμ = xμ (x) followed by the field substitutions ϕ(x) → ϕ (x ). At that, the local properties of the theory are determined by the infinitesimal diffeomorphims: xμ → xμ = xμ + δξ xμ , with δξ xμ ≡ −ξ μ being a vector field. These properties are expressed through the so-called Lie derivative given by the net infinitesimal variation of a field exclusively due to its ∗
The text was submitted by the author in English. E-mail: [email protected] 1) For more detail, see also [6].
**
tensor properties: δξ ϕ(x) = (ϕ (x ) − ϕ(x ))x →x . In particular, one has for metric δξ gμν = ∇μ ξν + ∇ν ξμ ,
(1)
where ξμ = gμν ξ ν and ∇μ is a covariant derivative. For a scalar field one has δξ φ = ξ μ ∂μ φ. The general gauge invariance/relativity corresponds to the group of the general diffeomorphisms (GDiff): GDiff: ξ μ unrestricted.
(2)
By means of GDiff, one can eliminate in metric all the excessive degrees of freedom, but two corresponding to the transverse-tensor graviton. As a result, this ensures the masslessness of the graviton, mg = 0. This takes place in GR, as well as in its generally invariant extensions. √ Of particular interest is the field −g, g ≡ det(gμν ), which may, under certain conditions, present an additional, scalar
Data Loading...
