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Published May 1, 2003 | Published + Submitted
Journal Article Open

Constraining dark energy from the abundance of weak gravitational lenses


We examine the prospect of using the observed abundance of weak gravitational lenses to constrain the equation-of-state parameter w = p/ρ of dark energy. Dark energy modifies the distance-redshift relation, the amplitude of the matter power spectrum, and the rate of structure growth. As a result, it affects the efficiency with which dark-matter concentrations produce detectable weak-lensing signals. Here we solve the spherical-collapse model with dark energy, clarifying some ambiguities found in the literature. We also provide fitting formulae for the non-linear overdensity at virialization and the linear-theory overdensity at collapse. We then compute the variation in the predicted weak-lens abundance with w. We find that the predicted redshift distribution and number count of weak lenses are highly degenerate in w and the present matter density Ω₀. If we fix Ω₀ the number count of weak lenses for w = −2/3 is a factor of ∼2 smaller than for the Λ cold dark matter (CDM) model w = −1. However, if we allow Ω₀ to vary with w such that the amplitude of the matter power spectrum as measured by the Cosmic Background Explorer (COBE) matches that obtained from the X-ray cluster abundance, the decrease in the predicted lens abundance is less than 25 per cent for −1 ⩽ w < −0.4. We show that a more promising method for constraining dark energy - one that is largely unaffected by the Ω₀−w degeneracy as well as uncertainties in observational noise - is to compare the relative abundance of virialized X-ray lensing clusters with the abundance of non-virialized, X-ray underluminous, lensing haloes. For aperture sizes of ∼15 arcmin, the predicted ratio of the non-virialized to virialized lenses is greater than 40 per cent and varies by ∼20 per cent between w = −1 and −0.6. Overall, we find that, if all other weak-lensing parameters are fixed, a survey must cover at least ∼40 deg² in order for the weak-lens number count to differentiate a ΛCDM cosmology from a dark-energy model with w = −0.9 at the 3σ level. If, on the other hand, we take into account uncertainties in the lensing parameters, then the non-virialized lens fraction provides the most robust constraint on w, requiring ∼50 deg² of sky coverage in order to differentiate a ΛCDM model from a w = −0.6 model to 3σ.

Additional Information

© 2003 RAS. Accepted 2003 January 8. Received 2003 January 7; in original form 2002 October 8. We thank R. Caldwell for helpful suggestions and an anonymous referee for useful comments that have improved the presentation of this paper. NNW acknowledges the support of an NSF Graduate Fellowship. This work was supported by NSF AST−0096023, NASA NAG5-9821, and DoE DE-FG03-92-ER40701.

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