Metric Tests for Curvature from Weak Lensing and Baryon Acoustic Oscillations

Details Metric Tests for Curvature from Weak Lensing and Baryon Acoustic Oscillations Metric Tests for Curvature from Weak Lensing and Baryon Acoustic Oscillations

2005-03-11

arxiv.org/abs/astro-ph/0503276v2

Astrophys.J. 637 (2006) 598-607

Astronomy and Astrophysics

Astrophysics

26 pages, accepted to ApJ. New notation and minor changes

Scientific paper

10.1086/498079

We describe a practical measurement of the curvature of the Universe which relies purely on the properties of the Robertson-Walker metric rather than any model for the dynamics or content of the Universe. The cross-correlation between foreground mass and gravitational shear of background galaxies depends upon the angular diameter distances d_A(z_l), d_A(z_s), and d_A(z_s,z_l) on the degenerate triangle formed by observer, source, and lens. In a flat Universe, d_A(z_l,z_s) = d_A(z_s)-d_A(z_l), but in curved Universes an additional term $\propto\Omega_k$ alters the lensing observables even if d_A(z) is fixed. Weak lensing data may be used to solve simultaneously for d_A and the curvature. This method is completely insensitive to: the equation of state; amendments to the General Relativity formulae for the deflection of light or the growth of structure; or biases in the photometric redshift scale. There is however a degeneracy among d_A, $\Omega_k$ and the galaxy bias factors, that can be broken by using measurements of baryon acoustic oscillations with the same imaging data. Ambitious weak-lensing + baryon-oscillation surveys would measure $\Omega_k$ to an accuracy $\approx0.04 f_{\rm sky}^{-1/2} (\sigma_{\ln z}/0.04)^{1/2}$, where $\sigma_{\ln z}$ is the photometric redshift error. We also predict bounds on curvature and other parameters in the context of specific dark-energy models, and compare to other analyses of the weak lensing cross-correlation method. We find both curvature and parametric constraints to be surprisingly insensitive to systematic shear calibration errors.

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