A Simple Gravitational Lens Model For Cosmic Voids

Abstract: We present a simple gravitational lens model to illustrate the ease of using the embedded lensing theory when studying cosmic voids. It confirms the previously used repulsive lensing models for deep voids. We start by estimating magnitude fluctuations and weak lensing shears of background sources lensed by large voids. We find that sources behind large ($\sim$$90\,\rm Mpc$) and deep voids (density contrast about $-0.9$) can be magnified or demagnified with magnitude fluctuations of up to $\sim$$0.05\,\rm mag$ and that the weak-lensing shear can be up to the $\sim$$10^{-2}$ level in the outer regions of large voids. Smaller or shallower voids produce proportionally smaller effects. We investigate the "wiggling" of the primary cosmic microwave background (CMB) temperature anisotropies caused by intervening cosmic voids. The void-wiggling of primary CMB temperature gradients is of the opposite sign to that caused by galaxy clusters. Only extremely large and deep voids can produce wiggling amplitudes similar to galaxy clusters, $\sim$$\rm 15\,\mu K$ by a large void of radius $\sim$$4^\circ$ and central density contrast $-0.9$ at redshift 0.5 assuming a CMB background gradient of $\sim$$\rm10\,\mu K\, arcmin^{-1}$. The dipole signal is spread over the entire void area, and not concentrated at the lens' center as it is for clusters. Finally we use our model to simulate CMB sky maps lensed by large cosmic voids. Our embedded theory can easily be applied to more complicated void models and used to study gravitational lensing of the CMB, to probe dark-matter profiles, to reduce the lensing-induced systematics in supernova Hubble diagrams, as well as study the integrated Sachs-Wolfe effect.