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      Deceleration versus Acceleration Universe in Different Frames of \(F(R)\) Gravity

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          Abstract

          In this paper we study the occurrence of accelerating universe versus decelerating universe between the F(R) gravity frame (Jordan frame) and non-minimally coupled scalar field theory frame, and the minimally coupled scalar field theory frame (Einstein frame) for various models. As we show, if acceleration is imposed in one frame, it will not necessarily correspond to an accelerating metric when transformed in another frame. As we will demonstrate, this issue is model and frame-dependent but it seems there is no general scheme which permits to classify such cases.

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          Reconstructing the universe history, from inflation to acceleration, with phantom and canonical scalar fields

          Valerio Faraoni, Sergei D. Odintsov, Shin'ichi Nojiri … (2008)
          We consider the reconstruction technique in theories with a single or multiple (phantom and/or canonical) scalar fields. With the help of several examples, it is demonstrated explicitly that the universe expansion history, unifying early-time inflation and late-time acceleration, can be realized in scalar-tensor gravity. This is generalized to the theory of a scalar field coupled non-minimally to the curvature and to a Brans-Dicke-like theory. Different examples of unification of inflation with cosmic acceleration, in which de Sitter, phantom, and quintessence type fields play the fundamental role--in different combinations--are worked out. Specifically, the frame dependence and stability properties of de Sitter space scalar field theory are studied. Finally, for two-scalar theories, the late-time acceleration and early-time inflation epochs are successfully reconstructed, in realistic situations in which the more and more stringent observational bounds are satisfied, using the freedom of choice of the scalar field potential, and of the kinetic factor.
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            Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase

            S. Capozziello, A Troisi, S. Odintsov … (2006)
            We show that f(R)-gravity can, in general, give rise to cosmological viable models compatible with a matter-dominated epoch evolving into a late accelerated phase. We discuss the various representations of f(R)-gravity as an ideal fluid or a scalar-tensor gravity theory, taking into account conformal transformations. We point out that mathematical equivalence does not correspond, in several cases, to the physical equivalence of Jordan frame and Einstein frame. Finally, we show that wide classes of f(R)-gravity models, including matter and accelerated phases, can be phenomenologically reconstructed by means of observational data. In principle, any popular quintessence models could be "reframed" as an f(R)-gravity model.
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              Singular Inflationary Universe from \(F(R)\) Gravity

              , (2015)
              Unlike crushing singularities, the so-called Type IV finite-time singularity offers the possibility that the Universe passes smoothly through it, without any catastrophic effects. Then the question is if the effects of a Type IV singularity can be detected in the process of cosmic evolution. In this paper we address this question in the context of \(F(R)\) gravity. As we demonstrate, the effects of a Type IV singularity appear in the Hubble flow parameters, which determine the dynamical evolution of the cosmological system. So we study various inflation models incorporating a Type IV singularity, with the singularity occurring at the end of inflation. Particularly we study a toy model and a singular version of the \(R^2\) gravity Hubble rate. As we evince, some of the Hubble flow parameters become singular at the singularity, an effect which indicates that at that point a dynamical instability occurs. This dynamical instability eventually indicates the graceful exit from inflation. We demonstrate that the toy model has an unstable de Sitter point at the singularity, so indeed graceful exit could be triggered. In the case of the singular inflation model, graceful exit proceeds in the standard way. In the case of the singular inflation model, we found various scenarios for singular evolution, most of which are compatible with observations, and only one leads to severe instabilities. We also compare the ordinary Starobinsky with the singular inflation model, and we point out the qualitative and quantitative differences. Finally, we study the late-time dynamics of the toy model and of the singular inflation model and we demonstrate that the unification of early and late-time acceleration can be achieved. We also show that it is possible to achieve late-time acceleration similar to the \(\Lambda\)-Cold Dark Matter model.
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                Author and article information

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                Publication date Created: 2017-01-09
                Article
                ArXiV ID: 1701.02381
                SO-VID: a4b88374-8fa1-4d1e-8b61-e2fce207687e
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                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Comments To appear in Physics Letters B
                Categories gr-qc astro-ph.CO hep-th

                ScienceOpen disciplines: Cosmology & Extragalactic astrophysics,General relativity & Quantum cosmology,High energy & Particle physics
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                ScienceOpen disciplines: Cosmology & Extragalactic astrophysics, General relativity & Quantum cosmology, High energy & Particle physics

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