Lensing effects in inhomogeneous cosmological models

Concepts developed in the gravitational lensing techniques such as shear, convergence, tangential, and radial arcs maybe used to see how tenable inhomogeneous models proposed to explain the acceleration of the universe models are. We study the widely discussed Lemaitre-Tolman-Bondi (LTB) cosmological models. It turns out that for the observer sitting at origin of a global LTB solution the shear vanishes as in the Friedmann-Robertson-Walker models, while the value of convergence is different, which may lead to observable cosmological effects. We also consider Swiss-cheese models proposed recently based on LTB with an observer sitting in the Friedmann-Robertson-Walker part. It turns out that they have different behavior as far as the formation of radial and tangential arcs are concerned.

Figure 1

Source of convergence as a function of redshift. The solid curve stands for the FRW model and the dashed curve for flat LTB.

Figure 3

Mass of the lens inside radius $x$ in the sinusoidal Swiss-cheese model.

Figure 4

Behavior of ${\lambda }_r(x)$ with respect to $x$ in the Swiss-cheese model.

Figure 5

Behavior of ${\lambda }_t(x)$ with respect to $x$ in the Swiss-cheese model.

Figure 6

Behavior of $R(r,t)(Y(r,t))$ in the Marra et al. model, peculiar velocity $v(r,t)$, and the density profile $\rho (r,t)$ with respect to $r$ for the curved case at $t_i=-0.8$ and $t=0$ (present time). The straight lines in the $R(r,t)$ diagram are FRW solutions [4].

Figure 7

Behavior of ${\lambda }_r(x)$ with respect to $x$ in the Marra et al. model.

Figure 8

Behavior of ${\lambda }_t(x)$ with respect to $x$ in the Marra et al. model.