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The not-so-homogeneous universe

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The assumption of spatial homogeneity lies at the heart of the concordance cosmological model. But as I will discuss, truly solid empirical evidence for global (statistical) homogeneity is lacking, and tricky theoretical issues abound. I review a few recent advances in understanding the role inhomogeneity plays in cosmology, including some unexpected effects on light propagation, the death (and rebirth) of backreaction, and impending observational annoyances related to the lumpy local Universe. I'll also talk about some near-future observations that can give us a handle on these effects