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Time delay cosmography

  • Review Article
  • Published:
The Astronomy and Astrophysics Review Aims and scope

Abstract

Gravitational time delays, observed in strong lens systems where the variable background source is multiply imaged by a massive galaxy in the foreground, provide direct measurements of cosmological distance that are very complementary to other cosmographic probes. The success of the technique depends on the availability and size of a suitable sample of lensed quasars or supernovae, precise measurements of the time delays, accurate modeling of the gravitational potential of the main deflector, and our ability to characterize the distribution of mass along the line of sight to the source. We review the progress made during the last 15 years, during which the first competitive cosmological inferences with time delays were made, and look ahead to the potential of significantly larger lens samples in the near future.

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Notes

  1. Additional distance dependencies appear in the multi-plane formalism, but always as dimensionless ratios with weaker cosmological dependence. The inverse proportionality to the Hubble constant is the same as in the single plane case.

  2. The COSMOGRAIL curve-shifting analysis code is available from http://cosmograil.org.

  3. In the case of the shapelet basis set, regularization can effectively be achieved through choosing the number of basis functions to use as well as the scale of the underlying Gaussian. Most analyses using shapelets have taken this approach to date, with Tagore and Jackson (2016) being a notable exception. A promising alternative scheme would be to assign a less physically motivated prior for the shapelet coefficients.

  4. The original investigation by Refsdal (1964) involved the “assumption that the linear distance–redshift relation is valid”.

  5. Importantly, the authors agreed to publish the unblinded results, no matter what.

  6. For simplicity, we refer to equivalent uncertainty on an average time delay distance at the typical redshift of the deflector and source. In practice of course, there will be a distribution of redshifts and thus of individual distances. As the way in which the time delay distance depends on cosmological parameters varies slightly with redshift, the analysis of a real sample of lenses will have the added benefit of breaking some of the degeneracies between the cosmological parameters, and reducing the uncertainties more rapidly than if all the systems were at the same redshift.

  7. The time delay distance referred to here is the same as ensemble average quantity that Coe and Moustakas (2009) call \(\mathcal {\tau }_\mathrm{C}\).

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Acknowledgments

We are grateful to S. Suyu and E. Komatsu for insightful discussions about the cosmological distance information content of time delay lenses, and to S. Suyu for making the B1608 \(+\) 656 MCMC chains available for us to make Fig. 7. We thank A. Agnello, M. Bartelmann, S. Birrer, V. Bonvin, D. Coe, T. Collett, F. Courbin, I. Jee, C. Kochanek, E. Linder, D. Sluse, S.Suyu, and M. Tewes for very valuable feedback on a draft of this review. T.T. thanks the Packard Foundation for generous support through a Packard Research Fellowship, the NSF for funding through NSF Grant AST-1450141, “Collaborative Research: Accurate cosmology with strong gravitational lens time delays”. P.J.M. acknowledges support from the U.S. Department of Energy under Contract Number DE-AC02-76SF00515.

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  1. Department of Physics and Astronomy, University of California, Los Angeles, CA, 90095, USA

    Tommaso Treu

  2. Kavli Institute for Particle Astrophysics and Cosmology, P.O. Box 20450, MS29, Stanford, CA, 94309, USA

    Philip J. Marshall

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Treu, T., Marshall, P.J. Time delay cosmography. Astron Astrophys Rev 24, 11 (2016). https://doi.org/10.1007/s00159-016-0096-8

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