Isolating Geometry in Weak-Lensing Measurements

Given a foreground galaxy-density field or shear field, its cross-correlation with the shear field from a background population of source galaxies scales with the source redshift in a way that is specific to lensing. Such a source scaling can be exploited to effectively measure geometrical distances as a function of redshift and thereby constrain dark energy properties, free of any assumptions about the galaxy-mass/mass power spectrum (its shape, amplitude, or growth). Such a geometrical method can yield a ~(0.03-0.07)f measurement on the dark energy abundance and equation of state for a photometric redshift accuracy of Δz ~ 0.01-0.05 and a survey with a median redshift of ~1. While these constraints are weaker than conventional weak-lensing methods, they provide an important consistency check, because the geometrical method carries less theoretical baggage: there is no need to assume any structure formation model (e.g., CDM). The geometrical method is at the most conservative end of a whole spectrum of methods that obtain smaller error bars by making more restrictive assumptions—we discuss some examples. Our geometrical approach differs from previous investigations along similar lines in three respects. First, the source scaling we propose to use is less demanding on the photometric redshift accuracy. Second, the scaling works for both galaxy-shear and shear-shear correlations. Third, we find that previous studies underestimate the statistical errors associated with similar geometrical methods, the origin of which is discussed.

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