Qianjun Hang
The evolution of the universe since the Big Bang can be mainly probed at two key era: the early time at which light and matter just decouples, through the Cosmic Microwave Background (CMB), and relatively 'recent' times, through galaxy surveys. The evolution, following General Relativity, implies that there is information encoded in the near-by galaxy fields which corresponds to the early history of the universe. In this project, we aim to find such information by use cross-correlating the galaxy fields from the Legacy Survey with the CMB temperature map and weak lensing convergence map. These correlations directly correspond to the temporal and spatial perturbation of the photon trajectory through the history of the universe, thus testing the theory of gravity. The Legacy Survey, covering about a third of the sky area and containing tens of millions of galaxies, is excellent for the purpose of the study. A difficulty in the study is to find the distance of these galaxies form us, in other words, the 'redshifts'. In this study, we use our own method to find redshifts of the galaxies using the their colour information. The galaxy sample is then split into four tomographic slices to further reveal the change of correlation with time. By comparing our measurements and theory predictions from the standard cosmological model, we find that interestingly the lensing amplitude is slightly lower than expected, consistent with the recently announce results from the KiDS Survey. This may imply a slight tension with the current best fit cosmological parameters.
In order to exploit the connection between the early and late universe, we compute the angular cross-correlations between the galaxy density maps and the CMB lensing and temperature map. There are two effects to consider. The first effect is the weak gravitational lensing effect, referring to the small bending of light emitted from the CMB as it travels through clumps of matter. The lensing convergence map directly measures the projected total matter density from the CMB to today. The second effect is the Integrated Sachs-Wolfe (ISW) effect. This corresponding to the change in CMB photon’s frequency by traveling through gravitational potentials, and is only present quite ‘recently’, when dark energy dominates. Due to the dark energy acerbating the expansion of the universe, the potential gets flattened, and the photon gains extra energy when it pass through, leaving an imprint on the CMB temperature map.
Redshifts indicates the distance of a galaxy from us. One challenge in the study is to obtain the redshift distribution of the Legacy Survey galaxies from the limited photometric bands. We make use of several spectroscopic samples to calibrate and infer photometric redshifts of the Legacy Survey. Specifically, we use information of the 3D grid in g-r, r-z, and z-w1 colours to assign redshifts. We also model the error of this method by a modified Lorentzian curve with nuisance parameters. These parameters are marginalized over later in the study. Galaxies are then split into four tomographic redshift slices between redshift 0 and 0.8 to reveal evolution of the correlation signal. The redshift probability distribution and density maps of the four bins are shown in Fig.4 and 5.
Finally, we measure the angular cross-correlation for each redshift slice, and compute the theoretical prediction assuming a fiducial Planck 2018 Cosmology. The ratio between data and theory is captured by the amplitudes A_kappa and A_ISW. Our results show that while the ISW amplitude is full consistent with unity, the lensing amplitude is noticeably lower than the fiducial value at about 3 sigma level. This is interesting in light with the recently published KiDS-1000 galaxy lensing measurements (Asgari et al. 2020), which gives very similar results. This slight tension with the Planck cosmological parameters may suggest some unknown systematics in the study, or can be implications for modifications to the fiducial model.