The Effects of Weak Gravitational Lensing on Determinations of the Cosmology from Type Ia Supernovæ

Underlying cosmologies with deceleration parameter, q0 = −0.51 +0.03 −0.24, may be interpreted as having q0 = −0.55, on the basis of weak gravitational lensing effects. 1. Computing the Three-Dimensional Shear The algorithm used for determining the three-dimensional shear has been described fully by Couchman, Barber & Thomas (1998). Of particular interest is the variable softening feature in the algorithm, designed to distribute the mass of each particle within a radial profile, which depends on its specific environment. The algorithm has been applied to a number of different cosmological N -body simulations available from the Hydra consortium; see, for example, Barber, Thomas & Couchman (1999). 2. The Effects of Weak Lensing on Determinations of the Deceleration Parameter Both Riess et al. (1998) and Perlmutter et al. (1999), point to cosmologies which are close to the ΩM = 0.3, ΩΛ = 0.7 cosmological simulation (designated LCDM) I have analyzed in terms of weak lensing. I shall therefore discuss the dispersions in magnification and the impact on determinations of the deceleration parameter, q0, with regard to this assumed underlying cosmology. By considering Type Ia supernovæ sources at ten evenly spaced redshifts, z, between z = 0 and z = 1, the resulting distributions of the magnifications show the expected increasing dispersions with z, which could be interpreted as observational dispersions in the peak magnitudes. They are equivalent to differences in distance modulus, m, and these differences have been evaluated to correspond to the 2σ range in the magnification distribution, denoted by μlow and μhigh. Riess et al. (1998) have recognized that weak lensing of high-redshift Type Ia supernovæ can alter the observed magnitudes and quote the findings of Wambsganss et al. (1997), http://coho.astro.uwo.ca/pub/data.html