Detecting cosmic voids via maps of geometric-optics parameters
Résumé
Curved-spacetime geometric-optics maps derived from a deep photometric survey should contain information about the three-dimensional matter distribution and thus about cosmic voids in the survey, despite projection effects. We explore to what degree sky-plane geometric-optics maps can reveal the presence of intrinsic three-dimensional voids. We carry out a cosmological $N$-body simulation and place it further than a gigaparsec from the observer, at redshift 0.5. We infer three-dimensional void structures using the watershed algorithm. Independently, we calculate a surface overdensity map and maps of weak gravitational lensing and geometric-optics scalars. We propose and implement a heuristic algorithm for detecting (projected) radial void profiles from these maps. We find in our simulation that given the sky-plane centres of the three-dimensional watershed-detected voids, there is significant evidence of correlated void centres in the surface overdensity $\Sigma$, the averaged weak-lensing tangential shear $\overline{\gamma_\perp}$, the Sachs expansion $\theta$, and the Sachs shear modulus $\lvert\sigma\rvert$. Recovering the centres of the three-dimensional voids from the sky-plane information alone is significant given the weak-lensing shear $\overline{\gamma_\perp}$, the Sachs expansion $\theta$, or the Sachs shear $\lvert\sigma\rvert$, but not significant for the surface overdensity $\Sigma$. Void radii are uncorrelated between three-dimensional and two-dimensional voids; our algorithm is not designed to distinguish voids that are nearly concentric in projection. This investigation shows preliminary evidence encouraging observational studies of gravitational lensing through individual voids, either blind or with spectroscopic/photometric redshifts. The former case - blind searches - should generate falsifiable predictions of intrinsic three-dimensional void centres.
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