A Simple Gravitational Lens Model For Cosmic Voids
  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.
