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Register a new user$f(R)$ gravity theories in the Palatini Formalism constrained from strong lensing
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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.
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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 show not only that this model of Vollick does not have a good Newtonian limit, but also that any f(R) theory with a pole of order n in R=0 and its second derivative respect to R evaluated at Ro is not zero, where Ro is the scalar curvature of background, does not have a good Newtonian limit.
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 cosmological models for chosen series of parameters to see if they distinguish from one another. The diagnostic involves the statefinder pair ${r,s}$, where $r$ is derived from the scale factor $a$ and its higher derivatives with respect to the cosmic time $t$, and $s$ is expressed by $r$ and the deceleration parameter $q$. In conclusion, we find that although two types of $f(R)$ theories: (i) $f(R) = R + alpha R^m - beta R^{-n}$ and (ii) $f(R) = R + alpha ln R - beta$ can lead to late-time acceleration, their evolutionary trajectories in the $r-s$ and $r-q$ planes reveal different evolutionary properties, which certainly justify the merits of statefinder diagnostic. Additionally, we utilize the observational Hubble parameter data (OHD) to constrain these models of $f(R)$ gravity. As a result, except for $m=n=1/2$ of (i) case, $alpha=0$ of (i) case and (ii) case allow $Lambda$CDM model to exist in 1$sigma$ confidence region. After adopting statefinder diagnostic to the best-fit models, we find that all the best-fit models are capable of going through deceleration/acceleration transition stage with late-time acceleration epoch, and all these models turn to de-Sitter point (${r,s}={1,0}$) in the future. Also, the evolutionary differences between these models are distinct, especially in $r-s$ plane, which makes the statefinder diagnostic more reliable in discriminating cosmological models.
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 supernova type Ia, large scale structure formation and cosmic microwave background observations. We find that best fit to the data is a non-null leading order correction to the Einstein gravity, but the current data exhibits no significant preference over the concordance LCDM model. Our results show that the often considered 1/R models are not compatible with the data. The results demonstrate that the background expansion alone can act as a good discriminator between modified gravity models when multiple data sets are used.
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 formalisms are not equivalent and that the set of solutions of the Palatini equations is a non-trivial subset of the solutions of the metric equations. However we also argue that for Lovelock gravities, the equivalence of the two formalism holds completely and give an explanation of why it holds precisely for these theories.
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. After reformulation of the model in the Einstein frame, it reduces to the FRW cosmological model with a homogeneous scalar field and vanishing kinetic energy term. This potential determines the running cosmological constant term as a function of the Ricci scalar. As a result we obtain the emergent dark energy parametrization from the covariant theory. We study also singularities of the model and demonstrate that in the Einstein frame some undesirable singularities disappear.
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