Constraints on f(R) cosmologies from strong gravitational lensing
  systems
  f(R) gravity is thought to be an alternative to dark energy which can explain
the acceleration of the universe. It has been tested by different observations
including type Ia supernovae (SNIa), the cosmic microwave background (CMB), the
baryon acoustic oscillations (BAO) and so on. In this Letter, we use the Hubble
constant independent ratio between two angular diameter distances
$D=D_{ls}/D_s$ to constrain f(R) model in Palatini approach $f(R)=R-\alpha
H^2_0(-\frac{R}{H^2_0})^\beta$. These data are from various large systematic
lensing surveys and lensing by galaxy clusters combined with X-ray
observations. We also combine the lensing data with CMB and BAO, which gives a
stringent constraint. The best-fit results are $(\alpha,\beta)=(-1.50,0.696)$
or $(\Omega_m,\beta)=(0.0734,0.696)$ using lensing data only. When combined
with CMB and BAO, the best-fit results are $(\alpha,\beta)=(-3.75,0.0651)$ or
$(\Omega_m,\beta)=(0.286,0.0651)$. If we further fix $\beta=0$ (corresponding
to $\Lambda$CDM), the best-fit value for $\alpha$ is
$\alpha$=$-4.84_{-0.68}^{+0.91}(1\sigma)_{-0.98}^{+1.63}(2\sigma)$ for the
lensing analysis and
$\alpha$=$-4.35_{-0.16}^{+0.18}(1\sigma)_{-0.25}^{+0.3}(2\sigma)$ for the
combined data, respectively. Our results show that $\Lambda$CDM model is within
1$\sigma$ range.
