Post-Newtonian Limit of Hybrid Metric-Palatini f ( R )-Gravity
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, PARTICLES, FIELDS, GRAVITATION, AND ASTROPHYSICS
Post-Newtonian Limit of Hybrid Metric-Palatini f(R)-Gravity P. I. Dyadinaa,*, S. P. Labazovab,**, and S. O. Alexeyeva,c,*** a
Sternberg Astronomical Institute, Moscow State University, Moscow, 119234 Russia of Astrophysics and Stellar Astronomy, Moscow State University, Moscow, 119234 Russia c Department of Quantum Theory and High Energy Physics, Moscow State University, Moscow, 119234 Russia * e-mail: [email protected] ** e-mail: [email protected] *** e-mail: [email protected] b Department
Received June 19, 2019; revised July 1, 2019; accepted July 3, 2019
Abstract—Using the latest most accurate values of post-Newtonian parameters γ and β obtained by MESSENGER we impose restrictions on the recently proposed hybrid f(R)-gravity model in its scalar–tensor representation. We show that the presence of a light scalar field in this theory does not contradict the experimental data based not only on the γ parameter (as was shown earlier), but also on all other PPN parameters. The application of parameterized post-Newtonian formalism to gravitational theories with massive fields is also discussed. DOI: 10.1134/S1063776119110025
1. INTRODUCTION Currently, General Relativity (GR) is a worldwide accepted theory of gravity. During more than one century a lot of problems were solved within such approach. However, as the quality of observations increased, new phenomena appeared that could not be explained within the framework of GR. For example, in the late XXth century, the problem of accelerating expansion of the Universe was discovered but the nature of this phenomenon has still not clear [1–3]. Another puzzle of modern physics is manifestations of dark matter (DM) on scales of galaxies and galaxyclusters [4, 5]. These issues can be studied in two ways: by introduction of new particles or by changing the geometry of space-time. The second way leads to the appearance of modified gravitational models, which are based on changing of GR. Among different ways of GR expansion f(R)-gravity should be identified especially [6–9]. The f(R)gravity is the simplest extension of the Einstein–Hilbert action. This theory is based on generalization of the gravitational part of the action as an arbitrary function of the Ricci scalar R. Such models have become widespread after f(R)-gravity was successfully applied in inflation theories [10]. The f(R)-gravity is attractive because the accelerated expansion of the Universe is natural consequence of the gravitational theory. In addition, f(R)-gravity is interesting as an alternative to the ΛCDM model, since it allows to simultaneously describe early-time inflation and late-time cosmic
acceleration [11–18]. Moreover, f(R)-models can provide good agreement with observational data, being almost indistinguishable from ΛCDM [19]. There are two possible approaches to obtain field equations from those modified actions: the metric one and the Palatini one. In the metric approach gμν is the only dynamical variable and the action is varie
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