Constraining the growth of perturbations with lensing of supernovae

A recently proposed technique allows one to constrain both the background and perturbation cosmological parameters through the distribution function of supernova Ia apparent magnitudes. Here we extend this technique to alternative cosmological scenarios, in which the growth of structure does not follow the $Lambda$CDM prescription. We apply the method first to the supernova data provided by the JLA catalog combined with all the current independent redshift distortion data and with low-redshift cluster data from Chandra and show that although the supernovae alone are not very constraining, they help in reducing the confidence regions. Then we apply our method to future data from LSST and from a survey that approximates the Euclid satellite mission. In this case we show that the combined data are nicely complementary and can constrain the normalization $sigma_8$ and the growth rate index $gamma$ to within $0.6%$ and $7%$, respectively. In particular, the LSST supernova catalog is forecast to give the constraint $gamma (sigma_8/0.83)^{6.7} = 0.55 pm 0.1$. We also report on constraints relative to a step-wise parametrization of the growth rate of structures. These results show that supernova lensing serves as a good cross-check on the measurement of perturbation parameters from more standard techniques.

Cosmic variance and the measurement of the local Hubble parameter

There is an approximately 9% discrepancy, corresponding to 2.4sigma, between two independent constraints on the expansion rate of the universe: one indirectly arising from the cosmic microwave background and baryon acoustic oscillations, and one more directly obtained from local measurements of the relation between redshifts and distances to sources. We argue that by taking into account the local gravitational potential at the position of the observer this tension - strengthened by the recent Planck results - is partially relieved and the concordance of the standard model of cosmology increased. We estimate that measurements of the local Hubble constant are subject to a cosmic variance of about 2.4% (limiting the local sample to redshifts z>0.010) or 1.3% (limiting it to z>0.023), a more significant correction than that taken into account already. Nonetheless, we show that one would need a very rare fluctuation to fully explain the offset in the Hubble rates. If this tension is further strengthened, a cosmology beyond the standard model may prove necessary.