Strong lensing is an effective way to probing the properties of dark energy.In this paper,we use the strong lensing data to constrain the f(T)theory,which is a new modified gravity to explain the present accelerating cosmic expansion without the need of dark energy.In our discussion,the CMB and BAO data are also added to constrain model parameters tightly and three different f(T)models are studied.We find that strong lensing has an important role on constraining f(T)models,and once the CMB+BAO data is added,a tighter constraint is obtained.However,the consistency of our result with what is obtained from SNIa+CMB+BAO is actually model-dependent.
We test the distance-duality （DD） relation by combining the angular diameter distance DA provided by two galaxy cluster samples compiled by De Filippis et al. （the elliptical β model） and Bonamente et al. （the spherical β model）, and the luminosity distance DL from Constitution and Union2 type Ia supernova （SNe Ia） datasets. To obtain DL associated with the observed DA at the same redshift, we smooth the noise of the SNe Ia in a model-independent way, obtain the evolutionary curve of DL and, finally, test the DD relation. We find that the elliptical β model, when compared with the SNe Ia from the Constitution compilation, is only consistent with the DD relation at the 3σ confidence level （CL）, while the spherical β model is incompatible with the DD relation at the 3σ CL. For the Union2 compilation, the De Filippis and Bonamente samples are marginally compatible with the validity of the DD relation at the 1σ and 2σ CLs, respectively.
Observations show that Type Ia supernovae （SNe Ia） are dimmer than ex- pected from a matter dominated Universe. It has been suggested that this observed phenomenon can also be explained using light absorption instead of dark energy. However, there is a serious degeneracy between the cosmic absorption parameter and the present matter density parameter Ωm when one tries to place constraints on the cosmic opacity using SNe Ia data. We combine the latest baryon acoustic oscillation （BAO） and Union2 SNe Ia data in order to break this degeneracy. Assuming a fiat ACDM model, we find that, although an opaque Universe is favored by SNe Ia＋BAO since the best fit value of the cosmic absorption parameter is larger than zero, fire = 1 is ruled out at the 99.7% confidence level. Thus, cosmic opacity is not sufficient to account for the present observations and dark energy or modified gravity is still re- quired.
We analyze the attractor behaviour of the inflation field in braneworld scenarios using the Hamilton-Jacobi formalism, where the Friedmann equation has the form ofH2 = p ＋ εx/2poporH2 = p ＋εp2/2σ, with ε = ±1. We find that in all models the linear homogeneous perturbation can decay exponentially as the scalar field rolls down its potential. However, in the case of a -p2 correction to the standard cosmology with p 〈 or, the existence of an attractor solution requires （σ- p）/φ2 〉 1. Our results show that the perturbation decays more quickly in models with positive-energy correction than in the standard cosmology, which is opposite to the case of negative-energy correction. Thus, the positive-energy modification rather than the negative one can assist the inflation and widen the range of initial conditions.
There is an apparent tension between cosmological parameters obtained from Planck cosmic microwave background radiation observations and that derived from the observed magnitude-redshift relation for the type Ia supernova （SNe Ia）. Here, we show that the tension can be alleviated, if we first calibrate, with the help of the distance-duality relation, the light-curve fitting parameters in the distance estimation in SNe Ia observations with the angular diameter distance data of the galaxy clusters and then re-estimate the distances for the SNe Ia with the corrected fitting parameters. This was used to explore their cosmological implications in the context of the spatially fiat cosmology. We find a higher value for the matter density parameter, Ωm, as compared to that from the original SNLS3, which is in agreement with Planck observations at 68.3% confidence. Therefore, the tension between Planck measurements and SNe Ia observations regarding Ωm can be effectively alleviated without invoking new physics or resorting to extensions for the standard concordance model. Moreover, with the absolute magnitude of a fiducial SNe Ia, M, determined first, we obtained a constraint on the Hubble constant with SNLS3 alone, which is also consistent with Planck.
