Abstract
A new gravity model with the function F(R) = (1/β) arctan (βR – β2R2) instead of the Ricci scalar in the Einstein–Hilbert action, describing inflation of the Universe, is suggested and analyzed. We obtain constant curvature solutions of the model in the Jordan frame. Performing the conformal transformation of the metric, the potential and the mass of a scalar degree of freedom in the Einstein frame are found. The slow-roll and cosmological parameters of the model are evaluated. It was demonstrated that the index of the scalar spectrum power law, ns, is in agreement with the PLANCK data.
Highlights
In modern cosmology, the inflationary scenario may solve the initial conditions problem and explain the formation of galaxies and irregularities in the microwave background
In this paper we suggest and analyze the particular model of modified gravity which is the modification of arctan-gravity model introduced in [15]
It should be noted that the model considered, as well as any F (R) gravity models, are effective models that are not renormalizable
Summary
The inflationary scenario may solve the initial conditions problem and explain the formation of galaxies and irregularities in the microwave background. At the same time F (R) gravity theories modifying general relativity (GR), without introduction of the fundamental scalar field, may be an alternative to the ΛCDM model. In such models the Ricci scalar, R, in the Einstein–Hilbert action, is replaced by the function F (R) [3,4]. Universe 2015, 1 and can be represented in a scalar-tensor form by using the conformal transformation and can describe the inflation and late time acceleration. The problem is to derive the F (R) function from first principles (probably from string or M theories) to describe the present and primordial DE and the evolution of our Universe Such derivation is absent and, different F (R) gravity models describing early time inflation and late time.
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