Cosmological fit of the LTB model with the JLA supernova dataset

Abstract

We consider the possibility of explaining supernova data with an LTB void of effective size of 3 Gpc without a cosmological constant. We consider a relatively free parametrization of the matter density profile as a linear interpolation of three points upto a radial coordinate of 3 Gpc after which the density distribution is assumed to be fixed at the value as obtained from observations assuming the ΛCDM model. In this thesis we consider the JLA dataset consisting of 740 near and distant redshift supernovae. We also borrow the covariance matrices available with the dataset and include them into the chi-square. The free parameters varied in the fitting procedure include the three points determining the shape of the density profile and α, β and MB which are free parameters in the empirical expression for the distance modulus. MB itself is considered to be a step function having two values of MB1 and MB1 + ∆M depending on the mass of the host galaxy. Thus in total, there are seven free parameters that are to be varied. We get α = 0.142 ± 0.007 and β = 3.086 ± 0.082 when the parameters are determined by a chi-square minimization procedure. An effective Hubble’s constant was also computed for the best fit model at the observer’s location at present time. This gave a value of 66.312 (km/s)/Mpc.