f(R)gravity without a cosmological constant

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Cruz Dombriz, Álvaro de la
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In this work we consider the possibility of describing the current evolution of the universe, without the introduction of any cosmological constant or dark energy (DE), by modifying the Einstein-Hilbert (EH) action. In the context of the f(R) gravities within the metric formalism, we show that it is possible to find an action without cosmological constant which exactly reproduces the behavior of the EH action with cosmological constant. In addition the f(R) action is analytical at the origin having Minkowski and Schwarzschild solutions as vacuum solutions. The found f(R) action is highly nontrivial and must be written in terms of hypergeometric functions but, in spite of looking somewhat artificial, it shows that the cosmological constant, or more generally the DE, is not a logical necessity.
© 2006 The American Physical Society. We would like to thank J. A. R. Cembranos and very specially A. L. Maroto for useful comments and discussions. We also thank S. D. Odintsov for bringing to our attention [13], where special functions are also considered as f(R)candidates for cosmologically viable models. This work has been partially supported by the DGICYT (Spain) under the project No. FPA2005-02327.
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