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 la 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 = Dls/Ds to constrain f(R) model in Palatini approach f(R) = R - alpha H-0(2)(-R/H-0(2))(R). 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)(+0.63)(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 ACDM model is within la range. (C) 2012 Elsevier B.V. All rights reserved.