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Abstract
A modified theory of gravity with the function F(R) = R exp (αR) instead of Ricci scalar R in the Einstein–Hilbert action is considered and analyzed. The action of the model is converted into Einstein–Hilbert action at small value of the parameter α. From local tests we obtain a bound on the parameter α ≤ 10-6 cm 2. The Jordan and Einstein frames are investigated and the potential of the scalar field in Einstein's frame is found. The mass of a scalar degree of freedom as a function of curvature is obtained. The static solutions of the model are found corresponding to the Schwarzschild–de Sitter space. We show that the de Sitter space is unstable but a solution with zero curvature is stable. The cosmological parameters of the model are calculated. It was demonstrated that the model passes the matter stability test.
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