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Measurements of γ and ΩΛ from Lensing
Astrophysics
Schwab, Josiah
For a spacetime which gives Newtonian gravity, the metric in the weak field limit can be parameterized as
dτ2 = dt2 (1 − [2m/r]) − dr2 (1 + [(2γm)/r]) − r2 dφ2
where γ is referred to as the post-Newtonian parameter. In general relativity (GR), this parameter takes a value of unity. Measurement of the Shapiro delay for signals sent within the solar system by the Cassini mission have constrained the local value to be 1 within a few parts in 105 (Bertotti et al. 2003).
Bolton et al. (2006) used measurements of 15 elliptical galaxies which are gravitationally lensing background emission line galaxies to determine that γ = 0.98 ±0.07 on kiloparsec scales. By measuring the mass via lensing (which depends on γ) and via the surface brightness profile and dispersion velocity of luminous tracers (which is independent of γ), they determine a likelihood distribution for γ from each system.
This work updates this measurement using a larger sample of galaxies obtained by the SLACS (Sloan Lens ACS) Survey (Bolton et al. 2008) and more sophisticated galaxy models. Additionally, a measurement of the cosmological parameter ΩΛ is made using the lensed galaxy images as a standard ruler.