Type Ia supernovae (SNe) are excellent distance indicators. Observations of distant SNe Ia led to the discovery of the accelerating expansion of the Universe. The most recent analysis of SNe Ia indicates that considering a flat ΛCDM cosmology, the contribution of dark energy in the total density of the Universe is ∼ 70%. Cosmological parameters are estimated from the “luminosity distance-redshift” relation of SNe using the Hubble diagrams. Currently a lot of attention is paid to standardization of SNe, i.e. to increase of the accuracy of luminosity distance determination. The uncertainty on the redshift is quite often considered negligible. The redshift used in “luminosity distance-redshift” relation is a cosmological redshift, i.e. the redshift due to the expansion of the Universe. In fact the redshift observed on the Earth also includes the contribution from the unknown peculiar velocities. To minimize the influence of poorly constrained peculiar velocities, in cosmological analyses a standard value of 300-400 km/s peculiar velocity dispersion is added in quadrature to the redshift uncertainty. It has nonetheless been observed that velocity dispersion can exceed 1000 km/s in galaxy clusters and therefore, the dispersion inside the cluster can be greater than the one usually assumed in cosmological analyses and can affect the distance measurements. To take this effect into account we study SNe Ia that are exploded in the galaxy clusters. As a supernova sample we use ”Pantheon” — the largest combined sample of SN Ia (HST, SNLS, SDSS, low-z samples and Pan-STARRS1) consisting of a total of 1048 objects ranging from 0.01 < z < 2.3. For those SNe Ia that belong to the galaxy clusters we are going to use the galaxy cluster redshift instead of the host galaxy redshift and examine the effect of this correction on the Hubble diagram.
In the epoch of large transient surveys (such as LSST), a study of the second order effects and all possible sources of systematical uncertainties in the cosmological analysis is of high priority.