How Does Gravitational Lensing Affect the Cosmological Distance Redshift Relation?
Abstract
A long standing question in cosmology is whether gravitational lensing biases the distance-redshift relation D(z) or the mean flux density of sources.
The problem was first considered by Jacob Zel'dovich in the early 1960s and reconsidered by many others since. Yet the situation remains confused. Steven Weinberg, for example, argued in 1976 that there is no effect on the grounds of flux conservation, yet that seems to conflict with other calculations and with the 'focusing theorem' obtained from Raychaudhuri's equation. Interest in this has been rekindled by recent results from second order relativistic perturbation theory which find biases qualitatively similar to those suggested by the focusing theorem. If correct, such bias would have profound implications for both supernova and CMB cosmology. John Peacock and the speaker have recently revisited this. In their paper, they make two main points: First, following Kibble and Lieu 2005, a relatively large bias in the source averaged distance D(z), for instance, was shown, but it is purely of a statistical nature and arises simply because D is a non-linear function of flux density, which itself is almost exactly unbiased. The speaker argues that some of the apparent contradictions and recently claimed significant effects result from confusion between different types of averaging (specifically between averaging over sources and averaging over directions on the sky). Second, the speaker carefully examines Weinberg's argument that there should be no effect. In this he makes the implicit assumption that the area of a surface of constant source redshift is unperturbed by lensing. The speaker shows that, while this is not strictly correct, the fractional perturbation to the area is on the order of the cumulative light deflection angle squared, or about a one part in a million effect. This effectively validates the conventional approach to CMB analysis and provides a firm basis for SN1a cosmology.
About the speaker
Prof. Nick Kaiser received his BSc in Physics from Leeds University in 1978, then completed his PhD in Astronomy at Cambridge University in 1982. He held postdoctoral fellowships at the University of California at Berkeley, University of California at Santa Barbara, and Cambridge before joining the faculty of the Canadian Institute for Theoretical Astrophysics (CITA) in Toronto in 1988. Prof Kaiser joined the University of Hawaii in 1997 and is currently the Professor of Theoretical Astrophysics.
Prof. Kaiser's research interests focus on a wide range of cosmological problems related to the formation of galaxies and large-scale structure in the Universe. These include anisotropy of the microwave background, "bulk-flows", analysis of galaxy clustering from redshift and angular surveys, and the evolution and clustering of clusters of galaxies. In recent years his research has been mainly focused on developing the theory and observational techniques for "Weak Gravitational Lensing" as a probe of the dark matter distribution.
Prof. Kaiser received a number of awards including the Helen Warner Prize of the American Astronomical Society (1989), an NSERC Steacie Fellowship (1991-92), the Herzberg Medal of the Canadian Association of Physicists (1993) and the Rutherford Medal of the Royal Society of Canada (1997). In 2008, he was elected as a Fellow of the Royal Society.
