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Complete solutions to the metric of spherically collapsing dust in an expanding spacetime with a cosmological constant
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We present semi-analytical solutions to the background equations describing the Lema\^itre-Tolman-Bondi (LTB) metric as well as the homogeneous Friedmann equations, in the presence of dust, curvature and a cosmological constant Lambda. For none of the presented solutions any numerical integration has to be performed. All presented solutions are given for expanding and collapsing phases, preserving continuity in time and radius. Hence, these solutions describe the complete space time of a collapsing spherical object in an expanding universe. In the appendix we present for completeness a solution of the Friedmann equations in the additional presence of radiation, only valid for the Robertson-Walker metric.
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CMB sky for an off-center observer in a local void I: framework for forecasts
An off-center observer in an LTB void would see off-diagonal CMB correlations; the paper develops a Fisher forecast framework and finds S/N > 10 for two illustrative void models with Planck.
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