Dr Obinna Umeh is a postdoctoral researcher at the University of the Western Cape in Cape Town, supported by the Square Kilometre Array project in South Africa

The accurate determination of cosmological distances is the most important probe in cosmology. Observations of type Ia supernovae imply dark energy exists because we know the relation between the distance of an object and its redshift – this changes with the relative amount of matter to dark energy, for example. But intervening matter between the supernovae and us cause fluctuations in this relationship. To a first approximation this is just normal gravitational lensing, an integrated contribution from the wobbly path the light takes to us.

Is this an accurate enough picture? Maybe at the moment, but not when the next generation of telescopes come online. For correct matching of theory to observations, our theory needs to be more accurate. In terms of light propagation in the inhomogeneous universe, this means we need to know how to calculate the distance – or magnification relative to a smooth hypothetical model – to all relevant accuracy.

In our two papers we have developed a new perturbative expansion which allows one to calculate distances as a function of redshift along any line of sight we are likely to encounter. We have shown that a plethora of new contributions appear, arising from coupling between fluctuations in bending of light by massive clusters and the relative fluctuation in the expansion of the light beam. Other effects lead to subtle changes in the Integrated Sachs Wolfe effect, the change of redshift with time varying gravitational potentials.

An important application of our result will be to calculate a mean bias to all observables which needs to be incorporated for accurate cosmological parameter estimation. Another is to improve N-body simulations to incorporate the new effects we have found – this will allow for much more accurate predictions of cosmic magnification maps.

Read the full articles in Classical and Quantum Gravity:

Nonlinear relativistic corrections to cosmological distances, redshift and gravitational lensing magnification: I. Key results
Obinna Umeh, Chris Clarkson and Roy Maartens
Class. Quantum Grav. 31 202001

Nonlinear relativistic corrections to cosmological distances, redshift and gravitational lensing magnification: II. Derivation
Obinna Umeh, Chris Clarkson and Roy Maartens
Class. Quantum Grav. 31 205001

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