Basic properties of the Einstein equations with a Ricci-Scalar-Dependent cosmological term
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ARTICLES, FIELDS, GRAVITATION, AND ASTROPHYSICS
Basic Properties of the Einstein Equations with a Ricci-Scalar-Dependent Cosmological Term P. A. Nakaznoy* Taras Shevchenko Kiev National University, Kiev, 03022 Ukraine *e-mail: [email protected] Received February 26, 2008
Abstract—Basic properties of the Einstein equations modified by a cosmological Λ-term dependent on the Ricci scalar R are considered. We show that in addition to a nonzero divergence of the energy–momentum tensor of the matter and the consequent cold matter mass nonconservation as the Universe expands, this model suggests a significant modification of the equations for the gravitational potential and particle acceleration in the Newtonian approximation. These circumstances allow the necessary criteria for possible functional dependences Λ(R) to be formulated. Nevertheless, by introducing a variable Λ-term, we can look at the problems of dark matter and dark energy anew. In particular, we show that the model in which the cosmological term depends linearly on the Ricci scalar (this corresponds to the approximation of a more complex dependence in the case of low matter densities) makes it possible to satisfactorily describe the rotation curves of galaxies without invoking the dark matter hypothesis and to construct a cosmological model with a variable vacuum energy density, in qualitative agreement with the present views of the early Universe. PACS numbers: 04.20.Cv, 95.36.+x, 98.80.-k DOI: 10.1134/S1063776108090082
1. INTRODUCTION To satisfactorily describe the currently available data on the composition and dynamics of the Universe [1–5], the idea of the so-called dark matter and dark energy is introduced in cosmology and astrophysics [6– 8]. Dark matter is believed to be localized in the halos around the visible parts of galaxies and to manifest itself through its gravitational interaction with ordinary matter. In contrast, dark energy is uniformly distributed in the Universe with a constant (in time) density. This allows one to associate it with the physical vacuum— the fundamental state of quantized fields and its density with the cosmological constant (Λ-term) in the Einstein equations [9, 10]. As is well known, the problem is that although the observational data can be described satisfactorily by phenomenologically introducing dark energy and dark matter, what their microscopic nature and properties are remains an open question. In particular, the possibility of a weak spacetime dependence of the energy– momentum tensor for the physical vacuum that expresses the response of the vacuum to its curvature cannot be ruled out. In this case, the cosmological constant alone will be not enough to describe dark energy, because it will also be necessary to apply the corresponding corrections dependent on the spacetime curvature (metric). In other words, in this approach, we can talk about a cosmological term that depends on the spacetime coordinates via a metric tensor and about its role in modeling the current value of the cosmological
constant. In thi
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