Weak Gravitational Lensing Tests the Cosmological Model

An international team of cosmologists and astrophysicists, led by Princeton University and the astronomical communities of Japan and Taiwan, and including researchers from Carnegie Mellon University, used precision measurements of the cosmological model of the universe to find that the universe is slightly less “clumpy” than it should be based on the cosmological standard model. Their findings, which could lead to a better understanding of dark matter, use data from the Hyper Suprime-Cam’s year 3 results and are contained in a series of five papers, which will be available on arXiv.

Dark energy and dark matter make up 95% of our universe. Since dark matter can’t be seen, it can’t be measured directly. Instead, researchers must derive information by measuring its effects on other visible objects like galaxies and stars.

One way this is done is by measuring a phenomenon called weak gravitational lensing. As the universe has expanded since the Big Bang, dark matter and galaxies have been drawn together by gravity, resulting in a clumpy distribution of matter throughout the universe. These clumps of matter exert a gravitational pull that bends light as it travels from distant galaxies towards Earth. As a result, when galaxies are observed by telescopes, the resulting images are slightly distorted. By measuring these distortions, researchers can learn more about the distribution of matter in the universe and the nature of dark matter and dark energy.

The new papers use data from the Hyper Suprime-Cam (HSC) sky survey, a wide-field imaging survey carried out by Japan’s 8.2-meter Subaru Telescope on the summit of Maunakea in Hawai’i. The data set includes the measurements for 25 million galaxies as they appeared billions of years ago. With measurements from so many galaxies, researchers were able to create a very precise analysis of weak gravitational lensing using a combination of sophisticated computer simulations and observations from the Hyper Suprime-Cam (HSC).

They found that the value for the clumpiness of the universe’s dark matter, a number referred to as S₈, to be 0.78. While this number aligns with what other recent gravitational lensing surveys have found, it does not align with the S₈ value of 0.83 derived from the radiation emitted in the earliest days of the universe called the cosmic microwave background.

The results suggest that the differences between these two numbers may not be coincidental. It could indicate that there is an unrecognized error in one of the two measurements or that the standard cosmological model, called the Lambda Cold Dark Matter Model, might be incomplete.

“The HSC weak lensing group has done a meticulous job of ensuring that our weak lensing results are robust, and there is about a 5% chance that the results disagree with the CMB only by chance,” said Rachel Mandelbaum, professor of physics and member of the McWilliams Center for Cosmology at Carnegie Mellon, and a member of the HSC collaboration. “It will be important to confirm this result with future datasets that can make the measurement even more precisely and to continue to refine our understanding of potential systematic biases. But this result is a tantalizing hint of potential physics beyond the Lambda-Cold Dark Matter cosmological paradigm.”

Three different analysis techniques were used on the HSC weak gravitational lensing data. The development and validation of the data catalog was led by Xiangchong Li while he was a doctoral student at the University of Tokyo. The analyses were blinded, so the researchers couldn’t compare results with each other or even view their results until they had finished all of their sanity checks on the analysis. After revealing the results, they were ecstatic to see that all methods yielded the same conclusions about S₈. 

Figure 1. The measurement results of S8 parameter from Subaru Hyper Suprime-Cam (HSC) Year 3 data. This graph shows the results from the four methods, which are different in the sense that the methods used the different parts of the HSC Year 3 data or combined the HSC Year 3 data with other data. For comparison, “Planck CMB” shows the measurement result of S₈ from the cosmic microwave background data from Planck satellite. “Other weak lensing results” show the result from the similar weak lensing measurements based on the U.S.-led Dark Energy Survey (DES) or the Europe-led Kilo-Degree Survey (KiDS) data. Figure courtesy of IPMU. 

Li, who is now a Carnegie Mellon postdoc working with Mandelbaum, led the real space analysis. This analysis established how the images of galaxies have been lensed by matter, including dark matter, by measuring the correlations of galaxy shapes from different time points.

Other papers used Fourier space analysis, which maps galaxy shapes and measures the power spectrum of the dark matter density field in Fourier space, and 3x2pt analysis, which constrains the cosmological constant by combining the galaxy shape data collected by HSC with the BOSS density distribution of foreground galaxies.

“Real space and Fourier space analyses are sensitive to the information of the matter distribution at different scales, and they have different responses to systematic errors. Doing two independent blinded analyses is an important test to validate the robustness of the cosmology constraint,” said Li. “3x2pt analysis includes observables from BOSS galaxy density distribution, which provides independent information to the measurement.”

Much of the analysis of the HSC data relied on methods developed by Tianqing Zhang, a physics graduate student at Carnegie Mellon. One method was a statistically principled method to propagate the uncertainty in redshift (or distance) measurements of the HSC galaxies. The second method establishes the impact of the point spread function, which describes the combined effect of atmospheric turbulence, telescope optics and detector on weak lensing observations.

“Our work is the ‘last line of defense’ to shield the cosmological results from the impact of the variables included in point spread function,” said Zhang. “Although the HSC enjoys one of the best atmospheric conditions on planet Earth and is equipped with a state-of-the-art optical and detector system, this problem is still a big challenge.”

Information about all five papers and the HSC public data release is available online: https://hsc-release.mtk.nao.ac.jp/doc/index.php/wly3/