Compromised Cosmic Shear: Approximations That Bias Cosmology

The distortion of the images of distant galaxies by the gravity of the large-scale structure of the Universe can be a powerful tool to help us understand our Universe. By measuring this distortion, known as cosmic shear, we can constrain cosmological parameters. However, in our analyses, we make certain approximations that may no longer be valid. Anurag Deshpande, a second-year PhD student tells us about two such effects; the reduced shear approximation and magnification bias.

Only about 5% of the Universe is made up of regular matter. The rest consists of dark matter and dark energy. However, these are both still poorly understood, and so need to be thoroughly probed. One way to do this is using the physical phenomenon known as gravitational lensing. One of the most profound discoveries of Einstein’s theory of General Relativity was the idea that gravity was a property of spacetime itself, and accordingly, light was also subject to it. When light rays pass in the vicinity of a massive object, they are bent by its gravity.

Illustration of gravitational lensing by the structure of the Universe. Image credit: CEASaclay

The light that travels to us from distant galaxies is deflected slightly by all the structure it encounters en route.  Accordingly, the images that we see of those galaxies are distorted; their ellipticities are sheared. By measuring this shear for billions of galaxies, we can compare and contrast different theories of dark energy and dark matter.

We are now on the precipice of a new generation of cosmic shear surveys: the European Space Agency’s Euclid telescope, NASA’s WFIRST mission, and the Vera C. Rubin Observatory. These new surveys will offer more than an order-of-magnitude leap in precision. This means that the theoretical formalism we use must also be improved to match this precision, otherwise we risk completely misinterpreting the data, and our Universe.

The Euclid space telescope, which will study Dark Energy and Dark Matter with unprecedented accuracy. Image credit: ESA

In our recent work, (, we have evaluated how badly we would misinterpret cosmological information if two key effects were neglected. One of these is the reduced shear approximation. In actuality, the distortion in a galaxy’s image depends on a quantity known as reduced shear, rather than shear directly. The reduced shear is a combination of both how much the image has been sheared and magnified. However, because the magnification of the image is typically very small, we just equate the shear to the reduced shear.

On the other hand, there is magnification bias. Any galaxy survey has a certain flux limit. Galaxies fainter than this limit cannot be seen by the survey. However, individual sources can be magnified enough to suddenly be above this limit, and the patch of sky around these sources can also be magnified, to dilute the number of galaxies that appear to be in them. These two effects change the number of galaxies that are then counted to be in your survey, and accordingly, can lead to you inferring incorrect cosmological information.

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Biases induced in cosmological parameters from neglecting reduced shear and magnification bias. Image Credit: Deshpande, et al., 2020

These two rather disparate effects – reduced shear and magnification bias – can be treated together because their corrections serendipitously have similar mathematical forms. We calculated the impact that neglecting these effects would have on the data obtained from the Euclid mission, and found that this would cause significant biases in the cosmological information that we would obtain. In fact, information about dark energy proved to be particularly sensitive to these effects, stressing the need for them to be fully taken into account for upcoming experiments. Considering the financial and labour costs invested in these experiments, it is imperative that we account for approximations such as these.

Featured Image Credit: ESA/NASA/Hubble Space Telescope.

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