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We present an application to cosmological models in $f({cal R})$ theories within the Palatini formalism of a method that combines cosmography and the explicit form of the field equations in the calculation of the redshift drift. The method yields a sequence of constraint equations which lead to limits on the parameter space of a given $f({cal R})$-model. Two particular families of $f({cal R})$-cosmologies capable of describing the current dynamics of the universe are explored here: (i) power law theories of the type $f({cal R})={cal R}-beta /{cal R}^n$, and (ii) theories of the form $f({cal R})={cal R}+alpha ln{{cal R}} -beta$. The constraints on $(n,beta)$ and $(alpha,beta)$, respectively, limit the values to intervals that are narrower than the ones previously obtained. As a byproduct, we show that when applied to General Relativity, the method yields values of the kinematic parameters with much smaller errors that those obtained directly from observations.
We focus on a series of $f(R)$ gravity theories in Palatini formalism to investigate the probabilities of producing the late-time acceleration for the flat Friedmann-Robertson-Walker (FRW) universe. We apply statefinder diagnostic to these cosmologic
Currently, in order to explain the accelerated expansion phase of the universe, several alternative approaches have been proposed, among which the most common are dark energy models and alternative theories of gravity. Although these approaches rest
A method to set constraints on the parameters of extended theories of gravitation is presented. It is based on the comparison of two series expansions of any observable that depends on H(z). The first expansion is of the cosmographical type, while th
We investigate cosmological dynamics based on $f(R)$ gravity in the Palatini formulation. In this study we use the dynamical system methods. We show that the evolution of the Friedmann equation reduces to the form of the piece-wise smooth dynamical s
Recently D. Vollick [Phys. Rev. D68, 063510 (2003)] has shown that the inclusion of the 1/R curvature terms in the gravitational action and the use of the Palatini formalism offer an alternative explanation for cosmological acceleration. In this work