January 29, 2007
We discuss the possibility of obtaining the present acceleration of the universe via f(R) gravity theories which recently attracted much attention. It is known that f(R) theories generally have room for this. In this work we stress that the requirement for the stabilization of extra dimensions is naturally incorporated in such a generalization of Einstein gravity under rather orthodox assumptions. We have restricted our study to pure f(R) gravity without additional matter sources partially in view of the fact that if the acceleration is to continue indefinitely any ordinary matter term is to redshift to irrelevancy and mostly for economy in understanding. The general conditions we find is that the manifold of the extra dimensional space is to have negative internal curvature and that the Ricci scalar of the full space-time manifold is also negative. The positive curvature case for extra dimensional manifold is actually the most generic case. However this necessitates a fine tuning between the Hubble constant and the size of extra dimensions in the absence of matter sources.
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October 15, 2008
We review the state of the art of f(R) theories of gravity (in their various formulations), which have been proposed as an explanation of the cosmic acceleration alternative to dark energy. The successes of f(R) gravity are discussed, together with the challenges imposed by minimal criteria for their viability.
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We survey the landscape of $f(R)$ theories of gravity in their various formulations, which have been used to model the cosmic acceleration as alternatives to dark energy and dark matter. Besides, we take into account the problem of gravitational waves in such theories. We discuss some successes of $f(R)$-gravity (where $f(R)$ is a generic function of Ricci scalar $R$), theoretical and experimental challenges that they face in order to satisfy minimal criteria for viability.
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In recent times, there has been an increasing interest with theories of modified gravity as a means to gain a deeper understanding of the universe's late-time acceleration phase. In this study we focused our attention on a specific cosmologically viable $f(R)$ model. We performed a dynamic stability analysis of this model, revealing that the model supports presence of just one asymptotically stable solution which can explain the present-day acceleration of the universe.
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The discovery of cosmic acceleration has raised the intriguing possibility that we are witnessing the first breakdown of General Relativity on cosmological scales. In this article I will briefly review current attempts to construct a theoretically consistent and observationally viable modification of gravity that is capable of describing the accelerating universe. I will discuss f(R) models, and their obvious extensions, and the DGP model as an example of extra-dimensional im...
December 23, 2007
Modifications to gravity that add additional functions of the Ricci curvature to the Einstein-Hilbert action -- collectively known as $f(R)$ theories -- have been studied in great detail. When considered as complete theories of gravity they can generate non-perturbative deviations from the general relativistic predictions in the solar system, and the simplest models show instabilites on cosmological scales. Here we show that it is possible to treat $f(R)=R\pm\mu^4/R$ gravity ...
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Modified gravity is one of the most promising candidates for explaining the current accelerating expansion of the Universe, and even its unification with the inflationary epoch. Nevertheless, the wide range of models capable to explain the phenomena of dark energy, imposes that current research focuses on a more precise study of the possible effects of modified gravity may have on both cosmological and local levels. In this paper, we focus on the analysis of a type of modifie...
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In the present manuscript the basic Einstein--Hilbert cosmological model is extended, by adding a new functional $F(G, T_{\mu\nu}T^{\mu\nu})$ in the fundamental action, encoding specific geometrical effects due to a nontrivial coupling with the Gauss-Bonnet invariant ($G$), and the energy--momentum squared term ($T_{\mu\nu}T^{\mu\nu}$). After obtaining the corresponding gravitational field equations for the specific decomposition where $F(G, T_{\mu\nu}T^{\mu\nu})=f(G)+g(T_{\m...
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A general formalism for the investigation of the late time dynamics of the universe for any analytic f(R) gravity model, along with a cold dark matter, has been discussed in the present work. The formalism is then elucidated with two examples. The values of the parameters of the models are chosen in such a way that they are consistent with the basic observational requirement.
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We discuss the idea that the accelerated Universe could be the result of the gravitational leakage into extra dimensions on Hubble distances rather than the consequence of non-zero cosmological constant.