The Copernican Principle

The Copernican Principle posits that the Earth is not in any particularly special location in the universe. Prior to Copernicus, the Earth had been placed in the center of the universe and historically there was much resistance to moving it - early in his career even Galileo had a fanciful rationale for putting the earth at the center.
The Standard Model of Cosmology pretty much enshrines the Copernican Principle. It has had some success explaining phenomenon like the extragalactic redshifts, microwave background radiation and the abundances of light elements.
However there are some difficulties with this model, especially the observed acceleration of the redshifts (Dark Energy) and the abundance of lithium 7.
The preprint Do primordial Lithium abundances imply there's no Dark Energy? explains these observations by heretically suggesting that the Earth might be in a rather special place after all: near the center of a gigantic void. See also The Cosmic Microwave Background in an Inhomogeneous Universe - why void models of dark energy are only weakly constrained by the CMB by the same authors.