Abstract
We provide an analytical estimate of the effect of a spherical inhomogeneity
on light beams that travel through it. We model the interior of the
inhomogeneity in terms of the Lemaitre-Tolman-Bondi metric. We assume that the
beam source is located outside the inhomogeneity. We study the relative
deviations of travelling time, redshift, beam area and luminosity distance from
their values in a homogeneous cosmology. They depend on the ratio Hb=H r_0 of
the radius r_0 of the inhomogeneity to the horizon distance 1/H. For an
observer located at the center, the deviations are of order Hb^2. For an
observer outside the inhomogeneity, the deviations of crossing time and
redshift are of order Hb^3. The deviations of beam area and luminosity distance
are of order Hb^2. However, when averaged over all possible locations of the
observer outside the inhomogeneity, they also become of order Hb^3. We discuss
the implications for the possibility of attributing the observed cosmological
acceleration to the emergence of large-scale structure.
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