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$f(R)$ gravity, capable of driving the late-time acceleration of the universe, is emerging as a promising alternative to dark energy. Various $f(R)$ gravity models have been intensively tested against probes of the expansion history, including type Ia supernovae (SNIa), the cosmic microwave background (CMB) and baryon acoustic oscillations (BAO). In this paper we propose to use the statistical lens sample from Sloan Digital Sky Survey Quasar Lens Search Data Release 3 (SQLS DR3) to constrain $f(R)$ gravity models. This sample can probe the expansion history up to $zsim2.2$, higher than what probed by current SNIa and BAO data. We adopt a typical parameterization of the form $f(R)=R-alpha H^2_0(-frac{R}{H^2_0})^beta$ with $alpha$ and $beta$ constants. For $beta=0$ ($Lambda$CDM), we obtain the best-fit value of the parameter $alpha=-4.193$, for which the 95% confidence interval that is [-4.633, -3.754]. This best-fit value of $alpha$ corresponds to the matter density parameter $Omega_{m0}=0.301$, consistent with constraints from other probes. Allowing $beta$ to be free, the best-fit parameters are $(alpha, beta)=(-3.777, 0.06195)$. Consequently, we give $Omega_{m0}=0.285$ and the deceleration parameter $q_0=-0.544$. At the 95% confidence level, $alpha$ and $beta$ are constrained to [-4.67, -2.89] and [-0.078, 0.202] respectively. Clearly, given the currently limited sample size, we can only constrain $beta$ within the accuracy of $Deltabetasim 0.1$ and thus can not distinguish between $Lambda$CDM and $f(R)$ gravity with high significance, and actually, the former lies in the 68% confidence contour. We expect that the extension of the SQLS DR3 lens sample to the SDSS DR5 and SDSS-II will make constraints on the model more stringent.
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
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
We investigate f(R) theories of gravity within the Palatini approach and show how one can determine the expansion history, H(a), for an arbitrary choice of f(R). As an example, we consider cosmological constraints on such theories arising from the su
We compare the metric and the Palatini formalism to obtain the Einstein equations in the presence of higher-order curvature corrections that consist of contractions of the Riemann tensor, but not of its derivatives. We find that in general the two fo
We consider FRW cosmology in $f(R)= R+ gamma R^2+delta R^3$ modified framework. The Palatini approach reduces its dynamics to the simple generalization of Friedmann equation. Thus we study the dynamics in two-dimensional phase space with some details