Model‐independent Constraints on Dark Energy Density from Flux‐averaging Analysis of Type Ia Supernova Data

We reconstruct the dark energy density ρ X ( z ) as a free function from current Type Ia supernova (SN Ia) data, together with the cosmic microwave background (CMB) shift parameter from CMB data from the Wilkinson Microwave Anisotropy Probe ( WMAP ), Cosmic Background Imager (CBI), and Arcminute Cosmology Bolometer Array Receiver (ACBAR), and the large-scale structure (LSS) growth factor from the Two-Degree Field (2dF) galaxy survey data. We parameterize ρ X ( z ) as a continuous function, given by interpolating its amplitudes at equally spaced z -values in the redshift range covered by SN Ia data, and a constant at larger z [where ρ X ( z ) is only weakly constrained by CMB data]. We assume a flat universe and use the Markov Chain Monte Carlo (MCMC) technique in our analysis. We find that the dark energy density ρ X ( z ) is constant for 0 ≲ z ≲ 0.5 and increases with redshift z for 0.5 ≲ z ≲ 1 at a 68.3% confidence level, but is consistent with a constant at a 95% confidence level. For comparison, we also give constraints on a constant equation of state for the dark energy. Flux averaging of SN Ia data is required to yield cosmological parameter constraints that are free of the bias induced by weak gravitational lensing. We set up a consistent framework for flux-averaging analysis of SN Ia data, based on the work of Wang. We find that flux averaging of SN Ia data leads to slightly lower Ω m and smaller time variation in ρ X ( z ). This suggests that a significant increase in the number of SNe Ia from deep SN surveys on a dedicated telescope is needed to place a robust constraint on the time dependence of the dark energy density.